# ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

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Página

**5**de**20**.Página **5** de **20**. • 1, 2, 3, 4, **5**, 6 ... 12 ... 20

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Dumbie escribió:@Frusciante escribió:https://twitter.com/noticiasnavarra/status/1352506270734053376?s=21

Se comenta solo

Esta claramente estabilizado que decian ayer

Llevamos estabilizados desde los 70 casos del 22 de Diciembre más o menos

**Frusciante**- Mensajes : 73390

Fecha de inscripción : 14/04/2012

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Poisonblade escribió:@Sugerio escribió:Me acaba de comentar una clienta que desde ayer es obligatoria una pcr para reentrar en Francia, incluso por carretera y para nacionales residentes.

Coñas las justas...

Pues aquí en la frontera nada de eso y sin ninguna noticia...

Que sepa para los que entran en avión.

Ya, por eso digo...

Por lo visto excluye a camioneros...

Francia pedirá una PCR negativa a todos los viajeros de la UE que quieran ingresar en el país

El presidente de Francia, Emmanuel Macron, ha informado este jueves por la noche, durante la Cumbre de los Veintisiete dedicada al coronavirus, de que Francia solicitará a partir del domingo por la noche una prueba negativa de PCR con una validez de menos de 72 horas a los viajeros europeos que quieran acceder al país. La medida excluirá los "viajes imprescindibles", según ha informado un comunicado del Elíseo expedido tras la cumbre, así como "a los trabajadores fronterizos y el transporte terrestre".

_________________

**Wenn ist das Nunstück git und Slotermeyer? Ja! Beiherhund das Oder die Flipperwaldt gersput!**

the_saturday_boy escribió:Subtítulos no encotré pero bueno, creo que es muda

**http://elparadigmadelsillonorejudo.wordpress.com/**

**Sugerio**- Moderador
- Mensajes : 35739

Fecha de inscripción : 24/03/2008

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Sugerio escribió:@Poisonblade escribió:@Sugerio escribió:Me acaba de comentar una clienta que desde ayer es obligatoria una pcr para reentrar en Francia, incluso por carretera y para nacionales residentes.

Coñas las justas...

Pues aquí en la frontera nada de eso y sin ninguna noticia...

Que sepa para los que entran en avión.

Ya, por eso digo...

Por lo visto excluye a camioneros...

Francia pedirá una PCR negativa a todos los viajeros de la UE que quieran ingresar en el país

El presidente de Francia, Emmanuel Macron, ha informado este jueves por la noche, durante la Cumbre de los Veintisiete dedicada al coronavirus, de que Francia solicitará a partir del domingo por la noche una prueba negativa de PCR con una validez de menos de 72 horas a los viajeros europeos que quieran acceder al país. La medida excluirá los "viajes imprescindibles", según ha informado un comunicado del Elíseo expedido tras la cumbre, así como "a los trabajadores fronterizos y el transporte terrestre".

Yo he leído esto.

https://www.eitb.eus/es/noticias/sociedad/detalle/7790249/francia-pide-pcr-negativa-entrar-al-pais-avion-25-enero/

**Poisonblade**- Mensajes : 49856

Fecha de inscripción : 06/03/2016

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

https://www.rac1.cat/programes/versio/20210121/491674337289/economia-crisi-coronavirus-espanya-gay-de-liebana-entrevista-deute-llibre-toni-clapes.html

Para los que no entendáis el catalino, nos quedan 4 añitos de nada para recuperarnos

Pero que sí, confinamiento ya, no mañana, ayer

Para los que no entendáis el catalino, nos quedan 4 añitos de nada para recuperarnos

Pero que sí, confinamiento ya, no mañana, ayer

**El facha catalán**- Mensajes : 8990

Fecha de inscripción : 22/01/2015

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Poisonblade escribió:@Sugerio escribió:@Poisonblade escribió:@Sugerio escribió:Me acaba de comentar una clienta que desde ayer es obligatoria una pcr para reentrar en Francia, incluso por carretera y para nacionales residentes.

Coñas las justas...

Pues aquí en la frontera nada de eso y sin ninguna noticia...

Que sepa para los que entran en avión.

Ya, por eso digo...

Por lo visto excluye a camioneros...

Francia pedirá una PCR negativa a todos los viajeros de la UE que quieran ingresar en el país

El presidente de Francia, Emmanuel Macron, ha informado este jueves por la noche, durante la Cumbre de los Veintisiete dedicada al coronavirus, de que Francia solicitará a partir del domingo por la noche una prueba negativa de PCR con una validez de menos de 72 horas a los viajeros europeos que quieran acceder al país. La medida excluirá los "viajes imprescindibles", según ha informado un comunicado del Elíseo expedido tras la cumbre, así como "a los trabajadores fronterizos y el transporte terrestre".

Yo he leído esto.

https://www.eitb.eus/es/noticias/sociedad/detalle/7790249/francia-pide-pcr-negativa-entrar-al-pais-avion-25-enero/

"Transporte terrestre" es la clave.

No se aclaran ni ellos...

_________________

**Wenn ist das Nunstück git und Slotermeyer? Ja! Beiherhund das Oder die Flipperwaldt gersput!**

the_saturday_boy escribió:Subtítulos no encotré pero bueno, creo que es muda

**http://elparadigmadelsillonorejudo.wordpress.com/**

**Sugerio**- Moderador
- Mensajes : 35739

Fecha de inscripción : 24/03/2008

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

https://twitter.com/MiguelFrigenti/status/1352372458544836611

**Dumbie**- Mensajes : 35735

Fecha de inscripción : 25/03/2008

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Dumbie escribió:https://twitter.com/MiguelFrigenti/status/1352372458544836611

joder

**ksmith**- Mensajes : 6313

Fecha de inscripción : 31/01/2018

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Dumbie escribió:https://twitter.com/MiguelFrigenti/status/1352372458544836611

Pues hoy hay fiestón y mañana también. Medidas Covid, dicen...

**Infernu**- Mensajes : 31692

Fecha de inscripción : 02/06/2015

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Dumbie escribió:https://twitter.com/MiguelFrigenti/status/1352372458544836611

Menudos borjamaris ostia puta

**Yen**- Mensajes : 5550

Fecha de inscripción : 13/05/2015

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

https://thehill.com/homenews/administration/535315-fauci-says-its-liberating-working-under-biden

**CountryJoe**- Mensajes : 11295

Fecha de inscripción : 02/08/2013

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

Ayer se abrió un debate sobre qué solución proponemos los que criticamos las medidas.

Mi opinión sobre las medidas que se deberían tomar o no tomar es compleja. Yo mismo la tengo que poner negro sobre blanco para aclararme un poco. Lo único que sé es que es un problema dilemático y aporético y que toda solución que pase por defender solo uno de los extremos economía-salud cae inmediatamente en el desastre.

Debajo está el problema más de fondo sobre qué consideramos una vida digna de ser vivida y si tiene mucho sentido una vida desnuda en la que solo se valora la mera supervivencia por encima de otros valores y derechos como la libertad negativa y positiva. Este problema parece algo que es fácilmente prorrogable y que la situación actual nos urge a posponerlo para otro momento menos crítico. Pero ese es el gran problema, porque si abrimos ese melón ahora cualquier otro momento futuro de crisis social va a justificar restricciones como los que estamos viviendo.

Sobre el tema de las medidas que tomaría eso es más jodido. Supongo que intentaría fundamentarlas en algún principio que considero rector. Ya que vivimos en sociedad y estamos ante un problema de salud pública de índole social en el que siempre se alude a la responsabilidad del ciudadano para anteponer lo colectivo a lo personal, pondremos que el principio más importante que tiene que informar cualquier medidas el de la justicia y el de solidaridad. Dicho en otras palabras, el de "o jugamos todos o rompemos el tapete" o "o pringamos todos o rompemos el contrato social". Ese parece haber sido el principio que ha justificado muchas de las medidas restrictivas (acertadas o no, aquí no me voy a meter porque ese es otro melón), sobre todo en un primer confinamiento total. Lo que sí tengo claro desde este principio es que de ninguna manera la vía para solucionar el problema puede ser DISCRECIONAL. No se puede cerrar un sector o sectores de manera discrecional justificando un bien superior de índole colectivo, al menos si no viene acompañado de un esfuerzo colectivo en forma de impuesto covid para compensar el agravio y las pérdidas del sector sacrificado. Si el Estado no puede pagar una ayuda igual o incluso mayor al daño ocasionado, las medidas son injustas y se cargan el contrato social. Justificando de esta forma que un colectivo tenga razones suficientes para considerar el Estado como algo simplemente impuesto desde arriba al que hay que combatir. Por eso mí única convicción en todo este asunto es que es absolutamente ilegítimo y perjudicial para el orden social medidas de cierres discrecionales.

El problema es que en esta segunda fase de la pandemia las decisiones políticas ya no se han basado en la justicia o la solidaridad. Se han basado en un supuesto balance de costes-beneficios dejando de lado los otros valores. Una parte de la sociedad ha visto cómo la dejaban atrás cuando ella en todo momento ha contribuido a ese supuesto principio de solidaridad y anteposición del bien común al individual. Lo único que puede salir de todo esto es una sociedad deslegitimada y mucho más fragmentada.

En resumen, no tengo muy claro lo que se debería hacer en un plano coyuntural e inmediato más allá de que no se tome ninguna medida discrecional sin que esta no sea apoyada por un esfuerzo en forma de impuesto del resto de ciudadanos, especialmente de las rentas medias-altas y altas. En el plano estructural de largo plazo todos o muchos nos podríamos poner de acuerdo en que el problema es que las instituciones están vaciadas, que no tienen poder real ni recursos y que la solución para que esto no vuelva a suceder pasa por fortalecerlas.

Y perdón por el ladrillo.

Mi opinión sobre las medidas que se deberían tomar o no tomar es compleja. Yo mismo la tengo que poner negro sobre blanco para aclararme un poco. Lo único que sé es que es un problema dilemático y aporético y que toda solución que pase por defender solo uno de los extremos economía-salud cae inmediatamente en el desastre.

Debajo está el problema más de fondo sobre qué consideramos una vida digna de ser vivida y si tiene mucho sentido una vida desnuda en la que solo se valora la mera supervivencia por encima de otros valores y derechos como la libertad negativa y positiva. Este problema parece algo que es fácilmente prorrogable y que la situación actual nos urge a posponerlo para otro momento menos crítico. Pero ese es el gran problema, porque si abrimos ese melón ahora cualquier otro momento futuro de crisis social va a justificar restricciones como los que estamos viviendo.

Sobre el tema de las medidas que tomaría eso es más jodido. Supongo que intentaría fundamentarlas en algún principio que considero rector. Ya que vivimos en sociedad y estamos ante un problema de salud pública de índole social en el que siempre se alude a la responsabilidad del ciudadano para anteponer lo colectivo a lo personal, pondremos que el principio más importante que tiene que informar cualquier medidas el de la justicia y el de solidaridad. Dicho en otras palabras, el de "o jugamos todos o rompemos el tapete" o "o pringamos todos o rompemos el contrato social". Ese parece haber sido el principio que ha justificado muchas de las medidas restrictivas (acertadas o no, aquí no me voy a meter porque ese es otro melón), sobre todo en un primer confinamiento total. Lo que sí tengo claro desde este principio es que de ninguna manera la vía para solucionar el problema puede ser DISCRECIONAL. No se puede cerrar un sector o sectores de manera discrecional justificando un bien superior de índole colectivo, al menos si no viene acompañado de un esfuerzo colectivo en forma de impuesto covid para compensar el agravio y las pérdidas del sector sacrificado. Si el Estado no puede pagar una ayuda igual o incluso mayor al daño ocasionado, las medidas son injustas y se cargan el contrato social. Justificando de esta forma que un colectivo tenga razones suficientes para considerar el Estado como algo simplemente impuesto desde arriba al que hay que combatir. Por eso mí única convicción en todo este asunto es que es absolutamente ilegítimo y perjudicial para el orden social medidas de cierres discrecionales.

El problema es que en esta segunda fase de la pandemia las decisiones políticas ya no se han basado en la justicia o la solidaridad. Se han basado en un supuesto balance de costes-beneficios dejando de lado los otros valores. Una parte de la sociedad ha visto cómo la dejaban atrás cuando ella en todo momento ha contribuido a ese supuesto principio de solidaridad y anteposición del bien común al individual. Lo único que puede salir de todo esto es una sociedad deslegitimada y mucho más fragmentada.

En resumen, no tengo muy claro lo que se debería hacer en un plano coyuntural e inmediato más allá de que no se tome ninguna medida discrecional sin que esta no sea apoyada por un esfuerzo en forma de impuesto del resto de ciudadanos, especialmente de las rentas medias-altas y altas. En el plano estructural de largo plazo todos o muchos nos podríamos poner de acuerdo en que el problema es que las instituciones están vaciadas, que no tienen poder real ni recursos y que la solución para que esto no vuelva a suceder pasa por fortalecerlas.

Y perdón por el ladrillo.

**morley**- Mensajes : 27754

Fecha de inscripción : 25/03/2008

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

Viendo la situación de los indicadores, y la fecha en la que estamos a mi me choca muchísimo que todo esto venga por el cambio de restricciones que hubo en navidad. Aquí el último alivio de medidas fue el 1 de enero y han pasado 22 días.

Yo no tengo ni idea pero intentando ver paralelismos con octubre cuando no había restricciones, las que tenemos ahora, y la pendiente que tienen las curvas a día de hoy, me hacen pensar o que las restricciones no sirven de demasiado o que directamente algo ha cambiado en el virus, o las cepas o lo que sea...

Yo no tengo ni idea pero intentando ver paralelismos con octubre cuando no había restricciones, las que tenemos ahora, y la pendiente que tienen las curvas a día de hoy, me hacen pensar o que las restricciones no sirven de demasiado o que directamente algo ha cambiado en el virus, o las cepas o lo que sea...

**Toro**- Mensajes : 20775

Fecha de inscripción : 14/05/2010

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

Seguimos con malos datos en Euskadi, y con tendencia negativa.

Toca sufrir (y cuidarse mucho)

Toca sufrir (y cuidarse mucho)

**Abuelo81**- Mensajes : 7735

Fecha de inscripción : 21/11/2017

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Frusciante escribió:@Dumbie escribió:@Frusciante escribió:https://twitter.com/noticiasnavarra/status/1352506270734053376?s=21

Se comenta solo

Esta claramente estabilizado que decian ayer

Llevamos estabilizados desde los 70 casos del 22 de Diciembre más o menos

es una obviedad que los casos han subido hoy bastante, esperemos que no se disparen hacía arriba, pero si que es cierto que estaban estabilizados en torno a los 200 casos; aunque viendo los datos de otras comunidades no parece que vaya a ser así desgraciadamente; lo que importa siempre es la presión hospitalaria; y la diferencia en UCIS respecto a ese 22 de Diciembre, es de 17 a 20 ingresados; prácticamente igual, lo que si ha crecido más es los ingresos, de 127 a 178; incluyendo en ellos la hospitalización domiciliaria, por lo que en planta siempre es algo menos. un 9,3% de ocupación hospitalaria y un 13% de UCIS; ojala no suba mucho, porque el efecto de la navidad ya debería haber pasado, pero da la impresión que esto va hacia arriba..

**Katxorro**- Mensajes : 34495

Fecha de inscripción : 19/11/2009

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Abuelo81 escribió:Seguimos con malos datos en Euskadi, y con tendencia negativa.

Toca sufrir (y cuidarse mucho)

Datos esperados lamentablemente... Ahora que no suba mañana y que se mantenga para los primeros día de semana que viene...

**Poisonblade**- Mensajes : 49856

Fecha de inscripción : 06/03/2016

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

Puto fetichismo del dato, ni en las grandes guerras habría partes diarios de bajas.

**morley**- Mensajes : 27754

Fecha de inscripción : 25/03/2008

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Toro escribió:Viendo la situación de los indicadores, y la fecha en la que estamos a mi me choca muchísimo que todo esto venga por el cambio de restricciones que hubo en navidad. Aquí el último alivio de medidas fue el 1 de enero y han pasado 22 días.

Yo no tengo ni idea pero intentando ver paralelismos con octubre cuando no había restricciones, las que tenemos ahora, y la pendiente que tienen las curvas a día de hoy, me hacen pensar o que las restricciones no sirven de demasiado o que directamente algo ha cambiado en el virus, o las cepas o lo que sea...

Es raro. Hay pueblos por aquí que estaban en 0 casos y en una semana se han puesto en rojo sin que haya ningún brote declarado en residencias ni nada.

**Ashra**- Mensajes : 16345

Fecha de inscripción : 27/06/2010

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

Y por aquí, 10 días sin casos y en cuatro días en rojo. Es sorprendente.@Ashra escribió:@Toro escribió:Viendo la situación de los indicadores, y la fecha en la que estamos a mi me choca muchísimo que todo esto venga por el cambio de restricciones que hubo en navidad. Aquí el último alivio de medidas fue el 1 de enero y han pasado 22 días.

Yo no tengo ni idea pero intentando ver paralelismos con octubre cuando no había restricciones, las que tenemos ahora, y la pendiente que tienen las curvas a día de hoy, me hacen pensar o que las restricciones no sirven de demasiado o que directamente algo ha cambiado en el virus, o las cepas o lo que sea...

Es raro. Hay pueblos por aquí que estaban en 0 casos y en una semana se han puesto en rojo sin que haya ningún brote declarado en residencias ni nada.

**Infernu**- Mensajes : 31692

Fecha de inscripción : 02/06/2015

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

[quote="morley"]Puto fetichismo del dato, ni en las grandes guerras habría partes diarios de bajas.[/quote]

Datos para asustar y concienciar a una sociedad egoísta que hasta que no les toca de cerca no son conscientes de lo peligroso que es y seguramente que a muchos les importa bien poco que su familia muera o se contagie.

Datos para asustar y concienciar a una sociedad egoísta que hasta que no les toca de cerca no son conscientes de lo peligroso que es y seguramente que a muchos les importa bien poco que su familia muera o se contagie.

**iontxu**- Mensajes : 3924

Fecha de inscripción : 24/03/2008

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Dumbie escribió:https://twitter.com/MiguelFrigenti/status/1352372458544836611

que haces insensato.

no se puede culpabilizar a la gente.

eso son todo ministros del gobierno, que son los culpables de todo.

**Eric Sachs**- Mensajes : 63353

Fecha de inscripción : 06/03/2012

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@El facha catalán escribió:https://www.rac1.cat/programes/versio/20210121/491674337289/economia-crisi-coronavirus-espanya-gay-de-liebana-entrevista-deute-llibre-toni-clapes.html

Para los que no entendáis el catalino, nos quedan 4 añitos de nada para recuperarnos

Pero que sí, confinamiento ya, no mañana, ayer

Por añadir algo, aclarar que Gay de Liébana es de los mejores economistas de España. De los que salen en TV, digo. De los mejores junto a Rallo.

**Blu3Fiv3**- Mensajes : 1239

Fecha de inscripción : 07/11/2019

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Eric Sachs escribió:@Dumbie escribió:https://twitter.com/MiguelFrigenti/status/1352372458544836611

que haces insensato.

no se puede culpabilizar a la gente.

eso son todo ministros del gobierno, que son los culpables de todo.

no, los políticos no son culpables. de hecho, son tan responsables que se están vacunando ellos primero.

**ksmith**- Mensajes : 6313

Fecha de inscripción : 31/01/2018

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@iontxu escribió:@morley escribió:Puto fetichismo del dato, ni en las grandes guerras habría partes diarios de bajas.

Datos para asustar y concienciar a una sociedad egoísta que hasta que no les toca de cerca no son conscientes de lo peligroso que es y seguramente que a muchos les importa bien poco que su familia muera o se contagie.

Oh, bucle, yo te invoco.

**Enric67**- Mensajes : 24903

Fecha de inscripción : 23/12/2012

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

Pues nada, en Jerez superamos los 1000 casos x 100000. Asi que si ya cerraba hosteleria a las 18:00 y comercios a las 20:00 en breve se cierra todo lo no esencial. Meses demasiado caseros se avecinan con todo lo bueno y malo que conlleva. Estoy jartito.

**Yomis**- Mensajes : 34448

Fecha de inscripción : 03/09/2008

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@ksmith escribió:@Eric Sachs escribió:@Dumbie escribió:https://twitter.com/MiguelFrigenti/status/1352372458544836611

que haces insensato.

no se puede culpabilizar a la gente.

eso son todo ministros del gobierno, que son los culpables de todo.

no, los políticos no son culpables. de hecho, son tan responsables que se están vacunando ellos primero.

pero no estaban los antivacunas hace nada diciendo " qi si li pinguin lis pilitiquis primiri!" ?

pues ya se la estan poniendo primero .

**Eric Sachs**- Mensajes : 63353

Fecha de inscripción : 06/03/2012

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Toro escribió:Viendo la situación de los indicadores, y la fecha en la que estamos a mi me choca muchísimo que todo esto venga por el cambio de restricciones que hubo en navidad. Aquí el último alivio de medidas fue el 1 de enero y han pasado 22 días.

Yo no tengo ni idea pero intentando ver paralelismos con octubre cuando no había restricciones, las que tenemos ahora, y la pendiente que tienen las curvas a día de hoy, me hacen pensar o que las restricciones no sirven de demasiado o que directamente algo ha cambiado en el virus, o las cepas o lo que sea...

Aquí en el pueblo desde fiestas, en septiembre, hasta prácticamente diciembre tuvimos un subidon del copón.

**disturbiau**- Mensajes : 31343

Fecha de inscripción : 11/04/2016

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Eric Sachs escribió:@ksmith escribió:@Eric Sachs escribió:@Dumbie escribió:https://twitter.com/MiguelFrigenti/status/1352372458544836611

que haces insensato.

no se puede culpabilizar a la gente.

eso son todo ministros del gobierno, que son los culpables de todo.

no, los políticos no son culpables. de hecho, son tan responsables que se están vacunando ellos primero.

pero no estaban los antivacunas hace nada diciendo " qi si li pinguin lis pilitiquis primiri!" ?

pues ya se la estan poniendo primero .

yo no sé qué estaban diciendo los antivacunas porque no lo soy, lo cual lo que digan esos imbéciles me la trae al pairo...

**ksmith**- Mensajes : 6313

Fecha de inscripción : 31/01/2018

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@iontxu escribió:@morley escribió:Puto fetichismo del dato, ni en las grandes guerras habría partes diarios de bajas.

Datos para asustar y concienciar a una sociedad egoísta que hasta que no les toca de cerca no son conscientes de lo peligroso que es y seguramente que a muchos les importa bien poco que su familia muera o se contagie.

**morley**- Mensajes : 27754

Fecha de inscripción : 25/03/2008

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

En Euskadi, como se rumoreaba, confinamiento perimetral de todos los municipios, y limitación de reuniones a 4.

Al final no cierran tiendas a las 19:00 porque lo quieren hacer unido al toque de queda a las 20:00, y de momento no pueden.

Al final no cierran tiendas a las 19:00 porque lo quieren hacer unido al toque de queda a las 20:00, y de momento no pueden.

**Reckoner**- Mensajes : 1549

Fecha de inscripción : 25/12/2014

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

Es oficial?@Reckoner escribió:En Euskadi, como se rumoreaba, confinamiento perimetral de todos los municipios, y limitación de reuniones a 4.

Al final no cierran tiendas a las 19:00 porque lo quieren hacer unido al toque de queda a las 20:00, y de momento no pueden.

**Infernu**- Mensajes : 31692

Fecha de inscripción : 02/06/2015

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

bisti yi di kilpibilizir i li histiliria!!!!!

https://www.nature.com/articles/s41586-020-2923-3

Mobility network models of COVID-19 explain inequities and inform reopening

https://www.nature.com/articles/s41586-020-2923-3

Mobility network models of COVID-19 explain inequities and inform reopening

- Spoiler:

Serina Chang, Emma Pierson, Pang Wei Koh, Jaline Gerardin, Beth Redbird, David Grusky & Jure Leskovec

Nature volume 589, pages82–87(2021)Cite this article

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Abstract

The coronavirus disease 2019 (COVID-19) pandemic markedly changed human mobility patterns, necessitating epidemiological models that can capture the effects of these changes in mobility on the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)1. Here we introduce a metapopulation susceptible–exposed–infectious–removed (SEIR) model that integrates fine-grained, dynamic mobility networks to simulate the spread of SARS-CoV-2 in ten of the largest US metropolitan areas. Our mobility networks are derived from mobile phone data and map the hourly movements of 98 million people from neighbourhoods (or census block groups) to points of interest such as restaurants and religious establishments, connecting 56,945 census block groups to 552,758 points of interest with 5.4 billion hourly edges. We show that by integrating these networks, a relatively simple SEIR model can accurately fit the real case trajectory, despite substantial changes in the behaviour of the population over time. Our model predicts that a small minority of ‘superspreader’ points of interest account for a large majority of the infections, and that restricting the maximum occupancy at each point of interest is more effective than uniformly reducing mobility. Our model also correctly predicts higher infection rates among disadvantaged racial and socioeconomic groups2,3,4,5,6,7,8 solely as the result of differences in mobility: we find that disadvantaged groups have not been able to reduce their mobility as sharply, and that the points of interest that they visit are more crowded and are therefore associated with higher risk. By capturing who is infected at which locations, our model supports detailed analyses that can inform more-effective and equitable policy responses to COVID-19.

Main

In response to the COVID-19 crisis, stay-at-home orders were enacted in many countries to reduce contact between individuals and slow the spread of the SARS-CoV-29. Since then, public officials have continued to deliberate over when to reopen, which places are safe to return to and how much activity to allow10. Answering these questions requires epidemiological models that can capture the effects of changes in mobility on virus spread. In particular, findings of COVID-19 superspreader events11,12,13,14 motivate models that can reflect the heterogeneous risks of visiting different locations, whereas well-reported disparities in infection rates among different racial and socioeconomic groups2,3,4,5,6,7,8 require models that can explain the disproportionate effect of the virus on disadvantaged groups.

To address these needs, we construct fine-grained dynamic mobility networks from mobile-phone geolocation data, and use these networks to model the spread of SARS-CoV-2 within 10 of the largest metropolitan statistical areas (hereafter referred to as metro areas) in the USA. These networks map the hourly movements of 98 million people from census block groups (CBGs), which are geographical units that typically contain 600–3,000 people, to specific points of interest (POIs). As shown in Supplementary Table 1, POIs are non-residential locations that people visit such as restaurants, grocery stores and religious establishments. On top of each network, we overlay a metapopulation SEIR model that tracks the infection trajectories of each CBG as well as the POIs at which these infections are likely to have occurred. This builds on prior research that models disease spread using aggregate15,16,17,18,19, historical20,21,22 or synthetic mobility data23,24,25; separately, other studies have analysed mobility data in the context of COVID-19, but without an underlying model of disease spread26,27,28,29,30.

Combining our epidemiological model with these mobility networks allows us to not only accurately fit observed case counts, but also to conduct detailed analyses that can inform more-effective and equitable policy responses to COVID-19. By capturing information about individual POIs (for example, the hourly number of visitors and median visit duration), our model can estimate the effects of specific reopening strategies, such as only reopening certain POI categories or restricting the maximum occupancy at each POI. By modelling movement from CBGs, our model can identify at-risk populations and correctly predict, solely from mobility patterns, that disadvantaged racial and socioeconomic groups face higher rates of infection. Our model thus enables the analysis of urgent health disparities; we use it to highlight two mobility-related mechanisms that drive these disparities and to evaluate the disparate effect of reopening on disadvantaged groups.

Mobility network model

We use data from SafeGraph, a company that aggregates anonymized location data from mobile applications, to study mobility patterns from 1 March to 2 May 2020. For each metro area, we represent the movement of individuals between CBGs and POIs as a bipartite network with time-varying edges, in which the weight of an edge between a CBG and POI represents the number of visitors from that CBG to that POI during a given hour (Fig. 1a). SafeGraph also provides the area in square feet of each POI, as well as its category in the North American industry classification system (for example, fitness centre or full-service restaurant) and median visit duration in minutes. We validated the SafeGraph mobility data by comparing the dataset to Google mobility data (Supplementary Fig. 1 and Supplementary Tables 2, 3) and used iterative proportional fitting31 to derive POI–CBG networks from the raw SafeGraph data. Overall, these networks comprise 5.4 billion hourly edges between 56,945 CBGs and 552,758 POIs (Extended Data Table 1).

Fig. 1: Model description and fit.

figure1

a, The mobility network captures hourly visits from each CBG to each POI. The vertical lines indicate that most visits are between nearby POIs and CBGs. Visits dropped markedly from March to April, as indicated by the lower density of grey lines. Mobility networks in the Chicago metro area are shown for 13:00 on two Mondays, 2 March 2020 (top) and 6 April 2020 (bottom). b, We overlaid a disease-spread model on the mobility network, with each CBG having its own set of SEIR compartments. New infections occur at both POIs and CBGs, with the mobility network governing how subpopulations from different CBGs interact as they visit POIs. c, Left, to test the out-of-sample prediction, we calibrated the model on data before 15 April 2020 (vertical black line). Even though its parameters remain fixed over time, the model accurately predicts the case trajectory in the Chicago metro area after 15 April using the mobility data (r.m.s.e. on daily cases = 406 for dates ranging from 15 April to 9 May). Right, model fit was further improved when we calibrated the model on the full range of data (r.m.s.e. on daily cases = 387 for the dates ranging from 15 April to 9 May). d, We fitted separate models to 10 of the largest US metro areas, modelling a total population of 98 million people; here, we show full model fits, as in c (right). In c and d, the blue line represents the model predictions and the grey crosses represent the number of daily reported cases; as the numbers of reported cases tend to have great variability, we also show the smoothed weekly average (orange line). Shaded regions denote the 2.5th and 97.5th percentiles across parameter sets and stochastic realizations. Across metro areas, we sample 97 parameter sets, with 30 stochastic realizations each (n = 2,910); see Supplementary Table 6 for the number of sets per metro area.

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We overlay a SEIR model on each mobility network15,20, in which each CBG maintains its own susceptible (S), exposed (E), infectious (I) and removed (R) states (Fig. 1b). New infections occur at both POIs and CBGs, with the mobility network governing how subpopulations from different CBGs interact as they visit POIs. We use the area, median visit duration and time-varying density of infectious individuals for each POI to determine the hourly infection rate of that POI. The model has only three free parameters that scale: (1) transmission rates at POIs, (2) transmission rates at CBGs and (3) the initial proportion of exposed individuals (Extended Data Table 2); all three parameters remain constant over time. We calibrate a separate model for each metro area using the confirmed case counts from The New York Times by minimizing the root mean square error (r.m.s.e.) to daily incident cases32. Our model accurately fits observed daily case counts in all 10 metro areas from 8 March to 9 May 2020 (Fig. 1c, d). In addition, when calibrated on only the case counts up to 14 April, the model predicts case counts reasonably well on the held-out time period of 15 April–9 May 2020 (Fig. 1c and Extended Data Fig. 1a). Our key technical finding is that the dynamic mobility network allows even our relatively simple SEIR model with just three static parameters to accurately fit observed cases, despite changing policies and behaviours during that period.

Mobility reduction and reopening plans

We can estimate the impact of mobility-related policies by constructing a hypothetical mobility network that reflects the expected effects of each policy, and running our SEIR model forward with this hypothetical network. Using this approach, we assess a wide range of mobility reduction and reopening strategies.

The magnitude of mobility reduction is at least as important as its timing

Mobility in the USA dropped sharply in March 2020: for example, overall POI visits in the Chicago metro area fell by 54.7% between the first week of March and the first week of April 2020. We constructed counterfactual mobility networks by scaling the magnitude of mobility reduction down and by shifting the timeline earlier and later, and applied our model to the counterfactual networks to simulate the resulting infection trajectories. Across metro areas, we found that the magnitude of mobility reduction was at least as important as its timing (Fig. 2a and Supplementary Tables 4, 5): for example, if the mobility reduction in the Chicago metro area had been only a quarter of the size, the predicted number of infections would have increased by 3.3× (95% confidence interval, 2.8–3.8×), compared with a 1.5× (95% confidence interval, 1.4–1.6×) increase had people begun reducing their mobility one full week later. Furthermore, if no mobility reduction had occurred at all, the predicted number of infections in the Chicago metro area would have increased by 6.2× (95% confidence interval, 5.2–7.1×). Our results are in accordance with previous findings that mobility reductions can markedly reduce infections18,19,33,34.

Fig. 2: Assessing mobility reduction and reopening.

figure2

The Chicago metro area is used as an example; results for all metro areas are included in Extended Data Figs. 3, 4, Supplementary Figs. 10, 15–24 and Supplementary Tables 4, 5, as indicated. a, Counterfactual simulations (left) of past reductions in mobility illustrate that the magnitude of the reduction (middle) was at least as important as its timing (right) (Supplementary Tables 4, 5). b, The model predicts that most infections at POIs occur at a small fraction of superspreader POIs (Supplementary Fig. 10). c, Left, the cumulative number of predicted infections after one month of reopening is plotted against the fraction of visits lost by partial instead of full reopening (Extended Data Fig. 3); the annotations within the plot show the fraction of maximum occupancy that is used as the cap and the horizontal red line indicates the cumulative number of predicted infections at the point of reopening (on 1 May 2020). Compared to full reopening, capping at 20% of the maximum occupancy in Chicago reduces the number of new infections by more than 80%, while only losing 42% of overall visits. Right, compared to uniformly reducing visits, the reduced maximum occupancy strategy always results in a smaller predicted increase in infections for the same number of visits (Extended Data Fig. 4). The horizontal grey line at 0% indicates when the two strategies result in an equal number of infections, and we observe that the curve falls well below this baseline. The y axis plots the relative difference between the predicted number of new infections under the reduced occupancy strategy compared to a uniform reduction. d, Reopening full-service restaurants has the largest predicted impact on infections, due to the large number of restaurants as well as their high visit densities and long dwell times (Supplementary Figs. 15–24). Colours are used to distinguish the different POI categories, but do not have any additional meaning. All results in this figure are aggregated across 4 parameter sets and 30 stochastic realizations (n = 120). Shaded regions in a–c denote the 2.5th to 97.5th percentiles; boxes in d denote the interquartile range and data points outside this range are shown as individual dots.

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A minority of POIs account for the majority of the predicted infections

We next investigated whether it matters how we reduce mobility—that is, to which POIs. We computed the number of infections that occurred at each POI in our simulations from 1 March to 2 May 2020, and found that the majority of the predicted infections occurred at a small fraction of superspreader POIs; for example, in the Chicago metro area, 10% of POIs accounted for 85% (95% confidence interval, 83–87%) of the predicted infections at the POIs (Fig. 2b and Supplementary Fig. 10). Certain categories of POIs also contributed far more to infections (for example, full-service restaurants and hotels), although our model predicted time-dependent variation in how much each category contributed (Extended Data Fig. 2). For example, restaurants and fitness centres contributed less to the predicted number of infections over time, probably because of lockdown orders to close these POIs, whereas grocery stores remained steady or even grew in their contribution, which is in agreement with their status as essential businesses.

Reopening with a reduced maximum occupancy

If a minority of POIs produce the majority of infections, then reopening strategies that specifically target high-risk POIs should be especially effective. To test one such strategy, we simulated reopening on 1 May, and modelled the effects of reducing the maximum occupancy in which the numbers of hourly visits to each POI returned to their ‘normal’ levels from the first week of March but were capped if they exceeded a fraction of the maximum occupancy of that POI35. Full reopening without reducing the maximum occupancy produced a spike in the predicted number of infections: in the Chicago metro area, our models projected that an additional 32% (95% confidence interval, 25–35%) of the population would be infected by the end of May (Fig. 2c). However, reducing the maximum occupancy substantially reduced the risk without sharply reducing overall mobility: capping at 20% of the maximum occupancy in the Chicago metro area reduced the predicted number of new infections by more than 80% but only lost 42% of overall visits, and we observed similar trends across other metro areas (Extended Data Fig. 3). This result highlights the nonlinearity of the predicted number of infections as a function of the number of visits: one can achieve a disproportionately large reduction in infections with a small reduction in visits. Furthermore, in comparison to a different reopening strategy, in which the number of visits to each POI was uniformly reduced from their levels in early March, reducing the maximum occupancy always resulted in fewer predicted infections for the same number of total visits (Fig. 2c and Extended Data Fig. 4). This is because reducing the maximum occupancies takes advantage of the time-varying visit density within each POI, disproportionately reducing visits to the POI during the high-density periods with the highest risk, but leaving visit counts unchanged during periods with lower risks. These results support previous findings that precise interventions, such as reducing the maximum occupancy, may be more effective than less targeted measures, while incurring substantially lower economic costs36.

Relative risk of reopening different categories of POIs

Because we found that certain POI categories contributed far more to predicted infections in March (Extended Data Fig. 2), we also expected that reopening some POI categories would be riskier than reopening others. To assess this, we simulated reopening each category in turn on 1 May 2020 (by returning its mobility patterns to early March levels, as above), while keeping all other POIs at their reduced mobility levels from the end of April. We found large variation in predicted reopening risks: on average across metro areas, full-service restaurants, gyms, hotels, cafes, religious organizations and limited-service restaurants produced the largest predicted increases in infections when reopened (Extended Data Fig. 5d). Reopening full-service restaurants was associated with a particularly high risk: in the Chicago metro area, we predicted an additional 595,805 (95% confidence interval, 433,735–685,959) infections by the end of May, more than triple that of the POI category with the next highest risk (Fig. 2d). These risks are summed over all POIs in the category, but the relative risks after normalizing by the number of POIs were broadly similar (Extended Data Fig. 5c). These categories were predicted to be have a higher risk because, in the mobility data, their POIs tended to have higher visit densities and/or visitors stayed there longer (Supplementary Figs. 15–24).

Demographic disparities in infections

We characterize the differential spread of SARS-CoV-2 along demographic lines by using US census data to annotate each CBG with its racial composition and median income, then tracking predicted infection rates in CBGs with different demographic compositions: for example, within each metro area, comparing CBGs in the top and bottom deciles for income. We use this approach to study the mobility mechanisms behind disparities and to quantify how different reopening strategies affect disadvantaged groups.

Predicting disparities from mobility data

Despite having access to only mobility data and no demographic information, our models correctly predicted higher risks of infection among disadvantaged racial and socioeconomic groups2,3,4,5,6,7,8. Across all metro areas, individuals from CBGs in the bottom decile for income had a substantially higher likelihood of being infected by the end of the simulation, even though all individuals began with equal likelihoods of infection (Fig. 3a). This predicted disparity was driven primarily by a few POI categories (for example, full-service restaurants); far greater proportions of individuals from lower-income CBGs than higher-income CBGs became infected in these POIs (Fig. 3c and Supplementary Fig. 2). We similarly found that CBGs with fewer white residents had higher predicted risks of infection, although results were more variable across metro areas (Fig. 3b). In the Supplementary Discussion, we confirm that the magnitude of the disparities that our model predicts is generally consistent with real-world disparities and further explore the large predicted disparities in Philadelphia, that stem from substantial differences in the POIs that are frequented by higher- versus lower-income CBGs. In the analysis below, we discuss two mechanisms that lead higher predicted infection rates among lower-income CBGs, and we show in Extended Data Fig. 6 and Extended Data Table 4 that similar results hold for racial disparities as well.

Fig. 3: Mobility patterns give rise to infection disparities.

figure3

a, In every metro area, our model predicts that people in lower-income CBGs are likelier to be infected. b, People in non-white CBGs area are also likelier to be infected, although results are more variable across metro areas. For c–f, the Chicago metro area is used as an example, but references to results for all metro areas are provided for each panel. c, The overall predicted disparity is driven by a few POI categories such as full-service restaurants (Supplementary Fig. 2). d, One reason for the predicted disparities is that higher-income CBGs were able to reduce their mobility levels below those of lower-income CBGs (Extended Data Fig. 6). e, Within each POI category, people from lower-income CBGs tend to visit POIs that have higher predicted transmission rates (Extended Data Table 3). The size of each dot represents the average number of visits per capita made to the category. The top 10 out of 20 categories with the most visits are labelled, covering 0.48–2.88 visits per capita (hardware stores–full-service restaurants). f, Reopening (at different levels of reduced maximum occupancy) leads to more predicted infections in lower-income CBGs than in the overall population (Extended Data Fig. 3). In c–f, purple denotes lower-income CBGs, yellow denotes higher-income CBGs and blue represents the overall population. Aside from d and e, which were directly extracted from mobility data, all results in this figure represent predictions aggregated over model realizations. Across metro areas, we sample 97 parameter sets, with 30 stochastic realizations each (n = 2,910); see Supplementary Table 6 for the number of sets per metro area. Shaded regions in c and f denote the 2.5th–97.5th percentiles; boxes in (a, b) denote the interquartile range; data points outside the range are shown as individual dots.

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Lower-income CBGs saw smaller reductions in mobility

A first mechanism producing disparities was that, across all metro areas, lower-income CBGs did not reduce their mobility as sharply in the first few weeks of March 2020, and these groups showed higher mobility than higher-income CBGs for most of March–May (Fig. 3d and Extended Data Fig. 6). For example, in April, individuals from lower-income CBGs in the Chicago metro area had 27% more POI visits per capita than those from higher-income CBGs. Category-level differences in visit patterns partially explained the infection disparities within each category: for example, individuals from lower-income CBGs made substantially more visits per capita to grocery stores than did those from higher-income CBGs (Supplementary Fig. 3) and consequently experienced more predicted infections for that category (Supplementary Fig. 2).

POIs visited by lower-income CBGs have higher transmission rates

Differences in visits per capita do not fully explain the infection disparities: for example, cafes and snack bars were visited more frequently by higher-income CBGs in every metro area (Supplementary Fig. 3), but our model predicted that a larger proportion of individuals from lower-income CBGs were infected at cafes and snack bars in the majority of metro areas (Supplementary Fig. 2). We found that even within a POI category, the predicted transmission rates at POIs frequented by individuals fom lower-income CBGs tended to be higher than the corresponding rates for those from higher-income CBGs (Fig. 3e and Extended Data Table 3), because POIs frequented by individuals from lower-income CBGs tended to be smaller and more crowded in the mobility data. As a case study, we examined grocery stores in further detail. In eight of the ten metro areas, visitors from lower-income CBGs encountered higher predicted transmission rates at grocery stores than visitors from higher-income CBGs (median transmission rate ratio of 2.19) (Extended Data Table 3). We investigated why one visit to the grocery store was predicted to be twice as dangerous for an individual from a lower-income CBG: the mobility data showed that the average grocery store visited by individuals from lower-income CBGs had 59% more hourly visitors per square foot, and their visitors stayed 17% longer on average (medians across metro areas). These findings highlight how fine-grained differences in mobility patterns—how often people go out and which POIs that they go to—can ultimately contribute to marked disparities in predicted infection outcomes.

Reopening plans must account for disparate effects

Because disadvantaged groups suffer a larger burden of infection, it is critical to not only consider the overall impact of reopening plans but also their disparate effects on disadvantaged groups specifically. For example, our model predicted that full reopening in the Chicago metro area would result in an additional 39% (95% confidence interval, 31–42%) of the population of CBGs in the bottom income decile being infected within a month, compared to 32% (95% confidence interval, 25–35%) of the overall population (Fig. 3f; results for all metro areas are shown in Extended Data Fig. 3). Similarly, Supplementary Fig. 4 illustrates that reopening individual POI categories tends to have a larger predicted effect on lower-income CBGs. More stringent reopening plans produce smaller absolute disparities in predicted infections—for example, we predict that reopening at 20% of the maximum occupancy in Chicago would result in additional infections for 6% (95% confidence interval, 4–8%) of the overall population and 10% (95% confidence interval, 7–13%) of the population in CBGs in the bottom income decile (Fig. 3f)—although the relative disparity remains.

Discussion

The mobility dataset that we use has limitations: it does not cover all populations, does not contain all POIs and cannot capture sub-CBG heterogeneity. Our model itself is also parsimonious, and does not include all real-world features that are relevant to disease transmission. We discuss these limitations in more detail in the Supplementary Discussion. However, the predictive accuracy of our model suggests that it broadly captures the relationship between mobility and transmission, and we thus expect our broad conclusions—for example, that people from lower-income CBGs have higher infection rates in part because they tend to visit denser POIs and because they have not reduced mobility by as much (probably because they cannot work from home as easily4)—to hold robustly. Our fine-grained network modelling approach naturally extends to other mobility datasets and models that capture more aspects of real-world transmission, and these represent interesting directions for future work.

Our results can guide policy-makers that seek to assess competing approaches to reopening. Despite growing concern about racial and socioeconomic disparities in infections and deaths, it has been difficult for policy-makers to act on those concerns; they are currently operating without much evidence on the disparate effects of reopening policies, prompting calls for research that both identifies the causes of observed disparities and suggests policy approaches to mitigate them5,8,37,38. Our fine-grained mobility modelling addresses both these needs. Our results suggest that infection disparities are not the unavoidable consequence of factors that are difficult to address in the short term, such as differences in preexisting conditions; on the contrary, short-term policy decisions can substantially affect infection outcomes by altering the overall amount of mobility allowed and the types of POIs reopened. Considering the disparate effects of reopening plans may lead policy-makers to adopt policies that can drive down infection densities in disadvantaged neighbourhoods by supporting, for example, more stringent caps on POI occupancies, emergency food distribution centres to reduce densities in high-risk stores, free and widely available testing in neighbourhoods predicted to be high risk (especially given known disparities in access to tests2), improved paid leave policy or income support that enables essential workers to curtail mobility when sick, and improved workplace infection prevention for essential workers, such as high-quality personal protective equipment, good ventilation and physical distancing when possible. As reopening policies continue to be debated, it is critical to build tools that can assess the effectiveness and equity of different approaches. We hope that our model, by capturing heterogeneity across POIs, demographic groups and cities, helps to address this need.

Methods

The Methods is structured as follows. We describe the datasets that we used in the ‘Datasets’ section and the mobility network that we derived from these datasets in the ‘Mobility network’ section. In the ‘Model dynamics’ section, we discuss the SEIR model that we overlaid on the mobility network; in the ‘Model calibration’ section, we describe how we calibrated this model and quantified uncertainty in its predictions. Finally, in the ‘Analysis details’ section, we provide details on the experimental procedures used for our analyses of mobility reduction, reopening plans and demographic disparities.

Datasets

SafeGraph

We use data provided by SafeGraph, a company that aggregates anonymized location data from numerous mobile applications. SafeGraph data captures the movement of people between CBGs, which are geographical units that typically contain a population of between 600 and 3,000 people, and POIs such as restaurants, grocery stores or religious establishments. Specifically, we use the following SafeGraph datasets.

First, we used the Places Patterns39 and Weekly Patterns (v1)40 datasets. These datasets contain, for each POI, hourly counts of the number of visitors, estimates of median visit duration in minutes (the ‘dwell time’) and aggregated weekly and monthly estimates of the home CBGs of visitors. We use visitor home CBG data from the Places Patterns dataset: for privacy reasons, SafeGraph excludes a home CBG from this dataset if fewer than five devices were recorded at the POI from that CBG over the course of the month. For each POI, SafeGraph also provides their North American industry classification system category, as well as estimates of its physical area in square feet. The area is computed using the footprint polygon SafeGraph that assigns to the POI41,42. We analyse Places Patterns data from 1 January 2019 to 29 February 2020 and Weekly Patterns data from 1 March 2020 to 2 May 2020.

Second, we used the Social Distancing Metrics dataset43, which contains daily estimates of the proportion of people staying home in each CBG. We analyse Social Distancing Metrics data from 1 March 2020 to 2 May 2020.

We focus on 10 of the largest metro areas in the United States (Extended Data Table 1). We chose these metro areas by taking a random subset of the SafeGraph Patterns data and selecting the 10 metro areas with the most POIs in the data. The application of the methods described in this paper to the other metro areas in the original SafeGraph data should be straightforward. For each metro area, we include all POIs that meet all of the following requirements: (1) the POI is located in the metro area ; (2) SafeGraph has visit data for this POI for every hour that we model, from 00:00 on 1 March 2020 to 23:00 on 2 May 2020; (3) SafeGraph has recorded the home CBGs of visitors to this POI for at least one month from January 2019 to February 2020; (4) the POI is not a ‘parent’ POI. Parent POIs comprise a small fraction of POIs in the dataset that overlap and include the visits from their ‘child’ POIs: for example, many malls in the dataset are parent POIs, which include the visits from stores that are their child POIs. To avoid double-counting visits, we remove all parent POIs from the dataset. After applying these POI filters, we include all CBGs that have at least one recorded visit to at least ten of the remaining POIs; this means that CBGs from outside the metro area may be included if they visit this metro area frequently enough. Summary statistics of the post-processed data are shown in Extended Data Table 1. Overall, we analyse 56,945 CBGs from the 10 metro areas, and more than 310 million visits from these CBGs to 552,758 POIs.

SafeGraph data have been used to study consumer preferences44 and political polarization45. More recently, it has been used as one of the primary sources of mobility data in the USA for tracking the effects of the COVID-19 pandemic26,28,46,47,48. In Supplementary Methods section 1, we show that aggregate trends in SafeGraph mobility data match the aggregate trends in Google mobility data in the USA49, before and after the imposition of stay-at-home measures. Previous analyses of SafeGraph data have shown that it is geographically representative—for example, it does not systematically overrepresent individuals from CBGs in different counties or with different racial compositions, income levels or educational levels50,51.

US census

Our data on the demographics of the CBGs comes from the American Community Survey (ACS) of the US Census Bureau52. We use the 5-year ACS data (2013–2017) to extract the median household income, the proportion of white residents and the proportion of Black residents of each CBG. For the total population of each CBG, we use the most-recent one-year estimates (2018); one-year estimates are noisier but we wanted to minimize systematic downward bias in our total population counts (due to population growth) by making them as recent as possible.

The New York Times dataset

We calibrated our models using the COVID-19 dataset published by the The New York Times32. Their dataset consists of cumulative counts of cases and deaths in the USA over time, at the state and county level. For each metro area that we modelled, we sum over the county-level counts to produce overall counts for the entire metro area. We convert the cumulative case and death counts to daily counts for the purposes of model calibration, as described in the ‘Model calibration’ section.

Data ethics

The dataset from The New York Times consists of aggregated COVID-19-confirmed case and death counts collected by journalists from public news conferences and public data releases. For the mobility data, consent was obtained by the third-party sources that collected the data. SafeGraph aggregates data from mobile applications that obtain opt-in consent from their users to collect anonymous location data. Google’s mobility data consists of aggregated, anonymized sets of data from users who have chosen to turn on the location history setting. Additionally, we obtained IRB exemption for SafeGraph data from the Northwestern University IRB office.

Mobility network

Definition

We consider a complete undirected bipartite graph G=(V,E) with time-varying edges. The vertices V are partitioned into two disjoint sets C={c1,…,cm}, representing m CBGs, and P={p1,…,pn}, representing n POIs. From US census data, each CBG ci is labelled with its population Nci, income distribution, and racial and age demographics. From SafeGraph data, each POI pj is similarly labelled with its category (for example, restaurant, grocery store or religious organization), its physical size in square feet apj, and the median dwell time dpj of visitors to pj. The weight w(t)ij on an edge (ci, pj) at time t represents our estimate of the number of individuals from CBG ci visiting POI pj at the tth hour of simulation. We record the number of edges (with non-zero weights) in each metro area and for all hours from 1 March 2020 to 2 May 2020 in Extended Data Table 1. Across all 10 metro areas, we study 5.4 billion edges between 56,945 CBGs and 552,758 POIs.

Overview of the network estimation

The central technical challenge in constructing this network is estimating the network weights W(t)={w(t)ij} from SafeGraph data, as this visit matrix is not directly available from the data. Our general methodology for network estimation is as follows.

First, from SafeGraph data, we derived a time-independent estimate W¯ of the visit matrix that captures the aggregate distribution of visits from CBGs to POIs from January 2019 to February 2020.

Second, because visit patterns differ substantially from hour to hour (for example, day versus night) and day to day (for example, before versus after lockdown), we used current SafeGraph data to capture these hourly variations and to estimate the CBG marginals U(t), that is, the number of people in each CBG who are out visiting POIs at hour t, as well as the POI marginals V(t), that is, the total number of visitors present at each POI pj at hour t.

Finally, we applied the iterative proportional fitting procedure (IPFP) to estimate an hourly visit matrix W(t) that is consistent with the hourly marginals U(t) and V(t) but otherwise ‘as similar as possible’ to the distribution of visits in the aggregate visit matrix W¯, in terms of Kullback–Leibler divergence.

IPFP is a classic statistical method31 for adjusting joint distributions to match prespecified marginal distributions, and it is also known in the literature as biproportional fitting, the RAS algorithm or raking53. In the social sciences, it has been widely used to infer the characteristics of local subpopulations (for example, within each CBG) from aggregate data54,55,56. IPFP estimates the joint distribution of visits from CBGs to POIs by alternating between scaling each row to match the hourly row (CBG) marginals U(t) and scaling each column to match the hourly column (POI) marginals V(t). Further details about the estimation procedure are provided in Supplementary Methods section 3.

Model dynamics

To model the spread of SARS-CoV-2, we overlay a metapopulation disease transmission model on the mobility network defined in the ‘Mobility Network’ section. The transmission model structure follows previous work15,20 on epidemiological models of SARS-CoV-2 but incorporates a fine-grained mobility network into the calculations of the transmission rate. We construct separate mobility networks and models for each metropolitan statistical area.

We use a SEIR model with susceptible (S), exposed (E), infectious (I) and removed (R) compartments. Susceptible individuals have never been infected, but can acquire the virus through contact with infectious individuals, which may happen at POIs or in their home CBG. They then enter the exposed state, during which they have been infected but are not infectious yet. Individuals transition from exposed to infectious at a rate inversely proportional to the mean latency period. Finally, they transition into the removed state at a rate inversely proportional to the mean infectious period. The removed state represents individuals who can no longer be infected or infect others, for example, because they have recovered, self-isolated or died.

Each CBG ci maintains its own SEIR instantiation, with S(t)ci, E(t)ci, I(t)ci and R(t)ci representing how many individuals in CBG ci are in each disease state at hour t, and Nci=S(t)ci+E(t)ci+I(t)ci+R(t)ci. At each hour t, we sample the transitions between states as follows:

N(t)S

**Eric Sachs**- Mensajes : 63353

Fecha de inscripción : 06/03/2012

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

Lo he leído en el Zorreo.

**Reckoner**- Mensajes : 1549

Fecha de inscripción : 25/12/2014

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

Jóder, 503 casos en Asturias.

**Rober75**- Mensajes : 3039

Fecha de inscripción : 12/08/2018

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@disturbiau escribió:

Yo no tengo ni idea pero intentando ver paralelismos con octubre cuando no había restricciones, las que tenemos ahora, y la pendiente que tienen las curvas a día de hoy, me hacen pensar o que las restricciones no sirven de demasiado o que directamente algo ha cambiado en el virus, o las cepas o lo que sea...

Aquí en el pueblo desde fiestas, en septiembre, hasta prácticamente diciembre tuvimos un subidon del copón.

Yo me refiero por las cifras que da conjuntas osakidetza sobre euskadi... donde se vio perfecta la evolución de segunda ola y la caida hasta diciembre.

Pero es que en enero no hemos estado demasiado diferentes de entonces, y ahora mismo ya no solo los valores, sino las pendientes ascendentes tienen la inclinación de cuando no había restricción... tenemos subida para un par de semanas a nivel de conjunto al parecer por las gráficas...

**Toro**- Mensajes : 20775

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## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Reckoner escribió:Lo he leído en el Zorreo.

Es oficial si, lo han transmitido en rueda de prensa.

No entiendo la excusa de que el cierre a las 19 va vinculado al toque de queda, no le veo el sentido, si lo quieres hacer lo puedes hacer, y no estoy diciendo que haya que hacerlo, hablo de que nos están mareando y diría que intencionadamente.

**Toro**- Mensajes : 20775

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## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@El facha catalán escribió:https://www.rac1.cat/programes/versio/20210121/491674337289/economia-crisi-coronavirus-espanya-gay-de-liebana-entrevista-deute-llibre-toni-clapes.html

Para los que no entendáis el catalino, nos quedan 4 añitos de nada para recuperarnos

Pero que sí, confinamiento ya, no mañana, ayer

Esta frase es muy devastadora

No és el mateix reanimar algú que està estabornit que ressuscitar un mort

**caniplaywithrainbows**- Mensajes : 4771

Fecha de inscripción : 22/11/2017

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Toro escribió:@Reckoner escribió:Lo he leído en el Zorreo.

Es oficial si, lo han transmitido en rueda de prensa.

No entiendo la excusa de que el cierre a las 19 va vinculado al toque de queda, no le veo el sentido, si lo quieres hacer lo puedes hacer, y no estoy diciendo que haya que hacerlo, hablo de que nos están mareando y diría que intencionadamente.

Es que el cierre a las 19h es una consecuencia del toque de queda a las 20h, por eso no lo han puesto.

**Poisonblade**- Mensajes : 49856

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## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Eric Sachs escribió:bisti yi di kilpibilizir i li histiliria!!!!!

https://www.nature.com/articles/s41586-020-2923-3

Mobility network models of COVID-19 explain inequities and inform reopening

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Serina Chang, Emma Pierson, Pang Wei Koh, Jaline Gerardin, Beth Redbird, David Grusky & Jure Leskovec

Nature volume 589, pages82–87(2021)Cite this article

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Abstract

The coronavirus disease 2019 (COVID-19) pandemic markedly changed human mobility patterns, necessitating epidemiological models that can capture the effects of these changes in mobility on the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)1. Here we introduce a metapopulation susceptible–exposed–infectious–removed (SEIR) model that integrates fine-grained, dynamic mobility networks to simulate the spread of SARS-CoV-2 in ten of the largest US metropolitan areas. Our mobility networks are derived from mobile phone data and map the hourly movements of 98 million people from neighbourhoods (or census block groups) to points of interest such as restaurants and religious establishments, connecting 56,945 census block groups to 552,758 points of interest with 5.4 billion hourly edges. We show that by integrating these networks, a relatively simple SEIR model can accurately fit the real case trajectory, despite substantial changes in the behaviour of the population over time. Our model predicts that a small minority of ‘superspreader’ points of interest account for a large majority of the infections, and that restricting the maximum occupancy at each point of interest is more effective than uniformly reducing mobility. Our model also correctly predicts higher infection rates among disadvantaged racial and socioeconomic groups2,3,4,5,6,7,8 solely as the result of differences in mobility: we find that disadvantaged groups have not been able to reduce their mobility as sharply, and that the points of interest that they visit are more crowded and are therefore associated with higher risk. By capturing who is infected at which locations, our model supports detailed analyses that can inform more-effective and equitable policy responses to COVID-19.

Main

In response to the COVID-19 crisis, stay-at-home orders were enacted in many countries to reduce contact between individuals and slow the spread of the SARS-CoV-29. Since then, public officials have continued to deliberate over when to reopen, which places are safe to return to and how much activity to allow10. Answering these questions requires epidemiological models that can capture the effects of changes in mobility on virus spread. In particular, findings of COVID-19 superspreader events11,12,13,14 motivate models that can reflect the heterogeneous risks of visiting different locations, whereas well-reported disparities in infection rates among different racial and socioeconomic groups2,3,4,5,6,7,8 require models that can explain the disproportionate effect of the virus on disadvantaged groups.

To address these needs, we construct fine-grained dynamic mobility networks from mobile-phone geolocation data, and use these networks to model the spread of SARS-CoV-2 within 10 of the largest metropolitan statistical areas (hereafter referred to as metro areas) in the USA. These networks map the hourly movements of 98 million people from census block groups (CBGs), which are geographical units that typically contain 600–3,000 people, to specific points of interest (POIs). As shown in Supplementary Table 1, POIs are non-residential locations that people visit such as restaurants, grocery stores and religious establishments. On top of each network, we overlay a metapopulation SEIR model that tracks the infection trajectories of each CBG as well as the POIs at which these infections are likely to have occurred. This builds on prior research that models disease spread using aggregate15,16,17,18,19, historical20,21,22 or synthetic mobility data23,24,25; separately, other studies have analysed mobility data in the context of COVID-19, but without an underlying model of disease spread26,27,28,29,30.

Combining our epidemiological model with these mobility networks allows us to not only accurately fit observed case counts, but also to conduct detailed analyses that can inform more-effective and equitable policy responses to COVID-19. By capturing information about individual POIs (for example, the hourly number of visitors and median visit duration), our model can estimate the effects of specific reopening strategies, such as only reopening certain POI categories or restricting the maximum occupancy at each POI. By modelling movement from CBGs, our model can identify at-risk populations and correctly predict, solely from mobility patterns, that disadvantaged racial and socioeconomic groups face higher rates of infection. Our model thus enables the analysis of urgent health disparities; we use it to highlight two mobility-related mechanisms that drive these disparities and to evaluate the disparate effect of reopening on disadvantaged groups.

Mobility network model

We use data from SafeGraph, a company that aggregates anonymized location data from mobile applications, to study mobility patterns from 1 March to 2 May 2020. For each metro area, we represent the movement of individuals between CBGs and POIs as a bipartite network with time-varying edges, in which the weight of an edge between a CBG and POI represents the number of visitors from that CBG to that POI during a given hour (Fig. 1a). SafeGraph also provides the area in square feet of each POI, as well as its category in the North American industry classification system (for example, fitness centre or full-service restaurant) and median visit duration in minutes. We validated the SafeGraph mobility data by comparing the dataset to Google mobility data (Supplementary Fig. 1 and Supplementary Tables 2, 3) and used iterative proportional fitting31 to derive POI–CBG networks from the raw SafeGraph data. Overall, these networks comprise 5.4 billion hourly edges between 56,945 CBGs and 552,758 POIs (Extended Data Table 1).

Fig. 1: Model description and fit.

figure1

a, The mobility network captures hourly visits from each CBG to each POI. The vertical lines indicate that most visits are between nearby POIs and CBGs. Visits dropped markedly from March to April, as indicated by the lower density of grey lines. Mobility networks in the Chicago metro area are shown for 13:00 on two Mondays, 2 March 2020 (top) and 6 April 2020 (bottom). b, We overlaid a disease-spread model on the mobility network, with each CBG having its own set of SEIR compartments. New infections occur at both POIs and CBGs, with the mobility network governing how subpopulations from different CBGs interact as they visit POIs. c, Left, to test the out-of-sample prediction, we calibrated the model on data before 15 April 2020 (vertical black line). Even though its parameters remain fixed over time, the model accurately predicts the case trajectory in the Chicago metro area after 15 April using the mobility data (r.m.s.e. on daily cases = 406 for dates ranging from 15 April to 9 May). Right, model fit was further improved when we calibrated the model on the full range of data (r.m.s.e. on daily cases = 387 for the dates ranging from 15 April to 9 May). d, We fitted separate models to 10 of the largest US metro areas, modelling a total population of 98 million people; here, we show full model fits, as in c (right). In c and d, the blue line represents the model predictions and the grey crosses represent the number of daily reported cases; as the numbers of reported cases tend to have great variability, we also show the smoothed weekly average (orange line). Shaded regions denote the 2.5th and 97.5th percentiles across parameter sets and stochastic realizations. Across metro areas, we sample 97 parameter sets, with 30 stochastic realizations each (n = 2,910); see Supplementary Table 6 for the number of sets per metro area.

Full size image

We overlay a SEIR model on each mobility network15,20, in which each CBG maintains its own susceptible (S), exposed (E), infectious (I) and removed (R) states (Fig. 1b). New infections occur at both POIs and CBGs, with the mobility network governing how subpopulations from different CBGs interact as they visit POIs. We use the area, median visit duration and time-varying density of infectious individuals for each POI to determine the hourly infection rate of that POI. The model has only three free parameters that scale: (1) transmission rates at POIs, (2) transmission rates at CBGs and (3) the initial proportion of exposed individuals (Extended Data Table 2); all three parameters remain constant over time. We calibrate a separate model for each metro area using the confirmed case counts from The New York Times by minimizing the root mean square error (r.m.s.e.) to daily incident cases32. Our model accurately fits observed daily case counts in all 10 metro areas from 8 March to 9 May 2020 (Fig. 1c, d). In addition, when calibrated on only the case counts up to 14 April, the model predicts case counts reasonably well on the held-out time period of 15 April–9 May 2020 (Fig. 1c and Extended Data Fig. 1a). Our key technical finding is that the dynamic mobility network allows even our relatively simple SEIR model with just three static parameters to accurately fit observed cases, despite changing policies and behaviours during that period.

Mobility reduction and reopening plans

We can estimate the impact of mobility-related policies by constructing a hypothetical mobility network that reflects the expected effects of each policy, and running our SEIR model forward with this hypothetical network. Using this approach, we assess a wide range of mobility reduction and reopening strategies.

The magnitude of mobility reduction is at least as important as its timing

Mobility in the USA dropped sharply in March 2020: for example, overall POI visits in the Chicago metro area fell by 54.7% between the first week of March and the first week of April 2020. We constructed counterfactual mobility networks by scaling the magnitude of mobility reduction down and by shifting the timeline earlier and later, and applied our model to the counterfactual networks to simulate the resulting infection trajectories. Across metro areas, we found that the magnitude of mobility reduction was at least as important as its timing (Fig. 2a and Supplementary Tables 4, 5): for example, if the mobility reduction in the Chicago metro area had been only a quarter of the size, the predicted number of infections would have increased by 3.3× (95% confidence interval, 2.8–3.8×), compared with a 1.5× (95% confidence interval, 1.4–1.6×) increase had people begun reducing their mobility one full week later. Furthermore, if no mobility reduction had occurred at all, the predicted number of infections in the Chicago metro area would have increased by 6.2× (95% confidence interval, 5.2–7.1×). Our results are in accordance with previous findings that mobility reductions can markedly reduce infections18,19,33,34.

Fig. 2: Assessing mobility reduction and reopening.

figure2

The Chicago metro area is used as an example; results for all metro areas are included in Extended Data Figs. 3, 4, Supplementary Figs. 10, 15–24 and Supplementary Tables 4, 5, as indicated. a, Counterfactual simulations (left) of past reductions in mobility illustrate that the magnitude of the reduction (middle) was at least as important as its timing (right) (Supplementary Tables 4, 5). b, The model predicts that most infections at POIs occur at a small fraction of superspreader POIs (Supplementary Fig. 10). c, Left, the cumulative number of predicted infections after one month of reopening is plotted against the fraction of visits lost by partial instead of full reopening (Extended Data Fig. 3); the annotations within the plot show the fraction of maximum occupancy that is used as the cap and the horizontal red line indicates the cumulative number of predicted infections at the point of reopening (on 1 May 2020). Compared to full reopening, capping at 20% of the maximum occupancy in Chicago reduces the number of new infections by more than 80%, while only losing 42% of overall visits. Right, compared to uniformly reducing visits, the reduced maximum occupancy strategy always results in a smaller predicted increase in infections for the same number of visits (Extended Data Fig. 4). The horizontal grey line at 0% indicates when the two strategies result in an equal number of infections, and we observe that the curve falls well below this baseline. The y axis plots the relative difference between the predicted number of new infections under the reduced occupancy strategy compared to a uniform reduction. d, Reopening full-service restaurants has the largest predicted impact on infections, due to the large number of restaurants as well as their high visit densities and long dwell times (Supplementary Figs. 15–24). Colours are used to distinguish the different POI categories, but do not have any additional meaning. All results in this figure are aggregated across 4 parameter sets and 30 stochastic realizations (n = 120). Shaded regions in a–c denote the 2.5th to 97.5th percentiles; boxes in d denote the interquartile range and data points outside this range are shown as individual dots.

Full size image

A minority of POIs account for the majority of the predicted infections

We next investigated whether it matters how we reduce mobility—that is, to which POIs. We computed the number of infections that occurred at each POI in our simulations from 1 March to 2 May 2020, and found that the majority of the predicted infections occurred at a small fraction of superspreader POIs; for example, in the Chicago metro area, 10% of POIs accounted for 85% (95% confidence interval, 83–87%) of the predicted infections at the POIs (Fig. 2b and Supplementary Fig. 10). Certain categories of POIs also contributed far more to infections (for example, full-service restaurants and hotels), although our model predicted time-dependent variation in how much each category contributed (Extended Data Fig. 2). For example, restaurants and fitness centres contributed less to the predicted number of infections over time, probably because of lockdown orders to close these POIs, whereas grocery stores remained steady or even grew in their contribution, which is in agreement with their status as essential businesses.

Reopening with a reduced maximum occupancy

If a minority of POIs produce the majority of infections, then reopening strategies that specifically target high-risk POIs should be especially effective. To test one such strategy, we simulated reopening on 1 May, and modelled the effects of reducing the maximum occupancy in which the numbers of hourly visits to each POI returned to their ‘normal’ levels from the first week of March but were capped if they exceeded a fraction of the maximum occupancy of that POI35. Full reopening without reducing the maximum occupancy produced a spike in the predicted number of infections: in the Chicago metro area, our models projected that an additional 32% (95% confidence interval, 25–35%) of the population would be infected by the end of May (Fig. 2c). However, reducing the maximum occupancy substantially reduced the risk without sharply reducing overall mobility: capping at 20% of the maximum occupancy in the Chicago metro area reduced the predicted number of new infections by more than 80% but only lost 42% of overall visits, and we observed similar trends across other metro areas (Extended Data Fig. 3). This result highlights the nonlinearity of the predicted number of infections as a function of the number of visits: one can achieve a disproportionately large reduction in infections with a small reduction in visits. Furthermore, in comparison to a different reopening strategy, in which the number of visits to each POI was uniformly reduced from their levels in early March, reducing the maximum occupancy always resulted in fewer predicted infections for the same number of total visits (Fig. 2c and Extended Data Fig. 4). This is because reducing the maximum occupancies takes advantage of the time-varying visit density within each POI, disproportionately reducing visits to the POI during the high-density periods with the highest risk, but leaving visit counts unchanged during periods with lower risks. These results support previous findings that precise interventions, such as reducing the maximum occupancy, may be more effective than less targeted measures, while incurring substantially lower economic costs36.

Relative risk of reopening different categories of POIs

Because we found that certain POI categories contributed far more to predicted infections in March (Extended Data Fig. 2), we also expected that reopening some POI categories would be riskier than reopening others. To assess this, we simulated reopening each category in turn on 1 May 2020 (by returning its mobility patterns to early March levels, as above), while keeping all other POIs at their reduced mobility levels from the end of April. We found large variation in predicted reopening risks: on average across metro areas, full-service restaurants, gyms, hotels, cafes, religious organizations and limited-service restaurants produced the largest predicted increases in infections when reopened (Extended Data Fig. 5d). Reopening full-service restaurants was associated with a particularly high risk: in the Chicago metro area, we predicted an additional 595,805 (95% confidence interval, 433,735–685,959) infections by the end of May, more than triple that of the POI category with the next highest risk (Fig. 2d). These risks are summed over all POIs in the category, but the relative risks after normalizing by the number of POIs were broadly similar (Extended Data Fig. 5c). These categories were predicted to be have a higher risk because, in the mobility data, their POIs tended to have higher visit densities and/or visitors stayed there longer (Supplementary Figs. 15–24).

Demographic disparities in infections

We characterize the differential spread of SARS-CoV-2 along demographic lines by using US census data to annotate each CBG with its racial composition and median income, then tracking predicted infection rates in CBGs with different demographic compositions: for example, within each metro area, comparing CBGs in the top and bottom deciles for income. We use this approach to study the mobility mechanisms behind disparities and to quantify how different reopening strategies affect disadvantaged groups.

Predicting disparities from mobility data

Despite having access to only mobility data and no demographic information, our models correctly predicted higher risks of infection among disadvantaged racial and socioeconomic groups2,3,4,5,6,7,8. Across all metro areas, individuals from CBGs in the bottom decile for income had a substantially higher likelihood of being infected by the end of the simulation, even though all individuals began with equal likelihoods of infection (Fig. 3a). This predicted disparity was driven primarily by a few POI categories (for example, full-service restaurants); far greater proportions of individuals from lower-income CBGs than higher-income CBGs became infected in these POIs (Fig. 3c and Supplementary Fig. 2). We similarly found that CBGs with fewer white residents had higher predicted risks of infection, although results were more variable across metro areas (Fig. 3b). In the Supplementary Discussion, we confirm that the magnitude of the disparities that our model predicts is generally consistent with real-world disparities and further explore the large predicted disparities in Philadelphia, that stem from substantial differences in the POIs that are frequented by higher- versus lower-income CBGs. In the analysis below, we discuss two mechanisms that lead higher predicted infection rates among lower-income CBGs, and we show in Extended Data Fig. 6 and Extended Data Table 4 that similar results hold for racial disparities as well.

Fig. 3: Mobility patterns give rise to infection disparities.

figure3

a, In every metro area, our model predicts that people in lower-income CBGs are likelier to be infected. b, People in non-white CBGs area are also likelier to be infected, although results are more variable across metro areas. For c–f, the Chicago metro area is used as an example, but references to results for all metro areas are provided for each panel. c, The overall predicted disparity is driven by a few POI categories such as full-service restaurants (Supplementary Fig. 2). d, One reason for the predicted disparities is that higher-income CBGs were able to reduce their mobility levels below those of lower-income CBGs (Extended Data Fig. 6). e, Within each POI category, people from lower-income CBGs tend to visit POIs that have higher predicted transmission rates (Extended Data Table 3). The size of each dot represents the average number of visits per capita made to the category. The top 10 out of 20 categories with the most visits are labelled, covering 0.48–2.88 visits per capita (hardware stores–full-service restaurants). f, Reopening (at different levels of reduced maximum occupancy) leads to more predicted infections in lower-income CBGs than in the overall population (Extended Data Fig. 3). In c–f, purple denotes lower-income CBGs, yellow denotes higher-income CBGs and blue represents the overall population. Aside from d and e, which were directly extracted from mobility data, all results in this figure represent predictions aggregated over model realizations. Across metro areas, we sample 97 parameter sets, with 30 stochastic realizations each (n = 2,910); see Supplementary Table 6 for the number of sets per metro area. Shaded regions in c and f denote the 2.5th–97.5th percentiles; boxes in (a, b) denote the interquartile range; data points outside the range are shown as individual dots.

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Lower-income CBGs saw smaller reductions in mobility

A first mechanism producing disparities was that, across all metro areas, lower-income CBGs did not reduce their mobility as sharply in the first few weeks of March 2020, and these groups showed higher mobility than higher-income CBGs for most of March–May (Fig. 3d and Extended Data Fig. 6). For example, in April, individuals from lower-income CBGs in the Chicago metro area had 27% more POI visits per capita than those from higher-income CBGs. Category-level differences in visit patterns partially explained the infection disparities within each category: for example, individuals from lower-income CBGs made substantially more visits per capita to grocery stores than did those from higher-income CBGs (Supplementary Fig. 3) and consequently experienced more predicted infections for that category (Supplementary Fig. 2).

POIs visited by lower-income CBGs have higher transmission rates

Differences in visits per capita do not fully explain the infection disparities: for example, cafes and snack bars were visited more frequently by higher-income CBGs in every metro area (Supplementary Fig. 3), but our model predicted that a larger proportion of individuals from lower-income CBGs were infected at cafes and snack bars in the majority of metro areas (Supplementary Fig. 2). We found that even within a POI category, the predicted transmission rates at POIs frequented by individuals fom lower-income CBGs tended to be higher than the corresponding rates for those from higher-income CBGs (Fig. 3e and Extended Data Table 3), because POIs frequented by individuals from lower-income CBGs tended to be smaller and more crowded in the mobility data. As a case study, we examined grocery stores in further detail. In eight of the ten metro areas, visitors from lower-income CBGs encountered higher predicted transmission rates at grocery stores than visitors from higher-income CBGs (median transmission rate ratio of 2.19) (Extended Data Table 3). We investigated why one visit to the grocery store was predicted to be twice as dangerous for an individual from a lower-income CBG: the mobility data showed that the average grocery store visited by individuals from lower-income CBGs had 59% more hourly visitors per square foot, and their visitors stayed 17% longer on average (medians across metro areas). These findings highlight how fine-grained differences in mobility patterns—how often people go out and which POIs that they go to—can ultimately contribute to marked disparities in predicted infection outcomes.

Reopening plans must account for disparate effects

Because disadvantaged groups suffer a larger burden of infection, it is critical to not only consider the overall impact of reopening plans but also their disparate effects on disadvantaged groups specifically. For example, our model predicted that full reopening in the Chicago metro area would result in an additional 39% (95% confidence interval, 31–42%) of the population of CBGs in the bottom income decile being infected within a month, compared to 32% (95% confidence interval, 25–35%) of the overall population (Fig. 3f; results for all metro areas are shown in Extended Data Fig. 3). Similarly, Supplementary Fig. 4 illustrates that reopening individual POI categories tends to have a larger predicted effect on lower-income CBGs. More stringent reopening plans produce smaller absolute disparities in predicted infections—for example, we predict that reopening at 20% of the maximum occupancy in Chicago would result in additional infections for 6% (95% confidence interval, 4–8%) of the overall population and 10% (95% confidence interval, 7–13%) of the population in CBGs in the bottom income decile (Fig. 3f)—although the relative disparity remains.

Discussion

The mobility dataset that we use has limitations: it does not cover all populations, does not contain all POIs and cannot capture sub-CBG heterogeneity. Our model itself is also parsimonious, and does not include all real-world features that are relevant to disease transmission. We discuss these limitations in more detail in the Supplementary Discussion. However, the predictive accuracy of our model suggests that it broadly captures the relationship between mobility and transmission, and we thus expect our broad conclusions—for example, that people from lower-income CBGs have higher infection rates in part because they tend to visit denser POIs and because they have not reduced mobility by as much (probably because they cannot work from home as easily4)—to hold robustly. Our fine-grained network modelling approach naturally extends to other mobility datasets and models that capture more aspects of real-world transmission, and these represent interesting directions for future work.

Our results can guide policy-makers that seek to assess competing approaches to reopening. Despite growing concern about racial and socioeconomic disparities in infections and deaths, it has been difficult for policy-makers to act on those concerns; they are currently operating without much evidence on the disparate effects of reopening policies, prompting calls for research that both identifies the causes of observed disparities and suggests policy approaches to mitigate them5,8,37,38. Our fine-grained mobility modelling addresses both these needs. Our results suggest that infection disparities are not the unavoidable consequence of factors that are difficult to address in the short term, such as differences in preexisting conditions; on the contrary, short-term policy decisions can substantially affect infection outcomes by altering the overall amount of mobility allowed and the types of POIs reopened. Considering the disparate effects of reopening plans may lead policy-makers to adopt policies that can drive down infection densities in disadvantaged neighbourhoods by supporting, for example, more stringent caps on POI occupancies, emergency food distribution centres to reduce densities in high-risk stores, free and widely available testing in neighbourhoods predicted to be high risk (especially given known disparities in access to tests2), improved paid leave policy or income support that enables essential workers to curtail mobility when sick, and improved workplace infection prevention for essential workers, such as high-quality personal protective equipment, good ventilation and physical distancing when possible. As reopening policies continue to be debated, it is critical to build tools that can assess the effectiveness and equity of different approaches. We hope that our model, by capturing heterogeneity across POIs, demographic groups and cities, helps to address this need.

Methods

The Methods is structured as follows. We describe the datasets that we used in the ‘Datasets’ section and the mobility network that we derived from these datasets in the ‘Mobility network’ section. In the ‘Model dynamics’ section, we discuss the SEIR model that we overlaid on the mobility network; in the ‘Model calibration’ section, we describe how we calibrated this model and quantified uncertainty in its predictions. Finally, in the ‘Analysis details’ section, we provide details on the experimental procedures used for our analyses of mobility reduction, reopening plans and demographic disparities.

Datasets

SafeGraph

We use data provided by SafeGraph, a company that aggregates anonymized location data from numerous mobile applications. SafeGraph data captures the movement of people between CBGs, which are geographical units that typically contain a population of between 600 and 3,000 people, and POIs such as restaurants, grocery stores or religious establishments. Specifically, we use the following SafeGraph datasets.

First, we used the Places Patterns39 and Weekly Patterns (v1)40 datasets. These datasets contain, for each POI, hourly counts of the number of visitors, estimates of median visit duration in minutes (the ‘dwell time’) and aggregated weekly and monthly estimates of the home CBGs of visitors. We use visitor home CBG data from the Places Patterns dataset: for privacy reasons, SafeGraph excludes a home CBG from this dataset if fewer than five devices were recorded at the POI from that CBG over the course of the month. For each POI, SafeGraph also provides their North American industry classification system category, as well as estimates of its physical area in square feet. The area is computed using the footprint polygon SafeGraph that assigns to the POI41,42. We analyse Places Patterns data from 1 January 2019 to 29 February 2020 and Weekly Patterns data from 1 March 2020 to 2 May 2020.

Second, we used the Social Distancing Metrics dataset43, which contains daily estimates of the proportion of people staying home in each CBG. We analyse Social Distancing Metrics data from 1 March 2020 to 2 May 2020.

We focus on 10 of the largest metro areas in the United States (Extended Data Table 1). We chose these metro areas by taking a random subset of the SafeGraph Patterns data and selecting the 10 metro areas with the most POIs in the data. The application of the methods described in this paper to the other metro areas in the original SafeGraph data should be straightforward. For each metro area, we include all POIs that meet all of the following requirements: (1) the POI is located in the metro area ; (2) SafeGraph has visit data for this POI for every hour that we model, from 00:00 on 1 March 2020 to 23:00 on 2 May 2020; (3) SafeGraph has recorded the home CBGs of visitors to this POI for at least one month from January 2019 to February 2020; (4) the POI is not a ‘parent’ POI. Parent POIs comprise a small fraction of POIs in the dataset that overlap and include the visits from their ‘child’ POIs: for example, many malls in the dataset are parent POIs, which include the visits from stores that are their child POIs. To avoid double-counting visits, we remove all parent POIs from the dataset. After applying these POI filters, we include all CBGs that have at least one recorded visit to at least ten of the remaining POIs; this means that CBGs from outside the metro area may be included if they visit this metro area frequently enough. Summary statistics of the post-processed data are shown in Extended Data Table 1. Overall, we analyse 56,945 CBGs from the 10 metro areas, and more than 310 million visits from these CBGs to 552,758 POIs.

SafeGraph data have been used to study consumer preferences44 and political polarization45. More recently, it has been used as one of the primary sources of mobility data in the USA for tracking the effects of the COVID-19 pandemic26,28,46,47,48. In Supplementary Methods section 1, we show that aggregate trends in SafeGraph mobility data match the aggregate trends in Google mobility data in the USA49, before and after the imposition of stay-at-home measures. Previous analyses of SafeGraph data have shown that it is geographically representative—for example, it does not systematically overrepresent individuals from CBGs in different counties or with different racial compositions, income levels or educational levels50,51.

US census

Our data on the demographics of the CBGs comes from the American Community Survey (ACS) of the US Census Bureau52. We use the 5-year ACS data (2013–2017) to extract the median household income, the proportion of white residents and the proportion of Black residents of each CBG. For the total population of each CBG, we use the most-recent one-year estimates (2018); one-year estimates are noisier but we wanted to minimize systematic downward bias in our total population counts (due to population growth) by making them as recent as possible.

The New York Times dataset

We calibrated our models using the COVID-19 dataset published by the The New York Times32. Their dataset consists of cumulative counts of cases and deaths in the USA over time, at the state and county level. For each metro area that we modelled, we sum over the county-level counts to produce overall counts for the entire metro area. We convert the cumulative case and death counts to daily counts for the purposes of model calibration, as described in the ‘Model calibration’ section.

Data ethics

The dataset from The New York Times consists of aggregated COVID-19-confirmed case and death counts collected by journalists from public news conferences and public data releases. For the mobility data, consent was obtained by the third-party sources that collected the data. SafeGraph aggregates data from mobile applications that obtain opt-in consent from their users to collect anonymous location data. Google’s mobility data consists of aggregated, anonymized sets of data from users who have chosen to turn on the location history setting. Additionally, we obtained IRB exemption for SafeGraph data from the Northwestern University IRB office.

Mobility network

Definition

We consider a complete undirected bipartite graph G=(V,E) with time-varying edges. The vertices V are partitioned into two disjoint sets C={c1,…,cm}, representing m CBGs, and P={p1,…,pn}, representing n POIs. From US census data, each CBG ci is labelled with its population Nci, income distribution, and racial and age demographics. From SafeGraph data, each POI pj is similarly labelled with its category (for example, restaurant, grocery store or religious organization), its physical size in square feet apj, and the median dwell time dpj of visitors to pj. The weight w(t)ij on an edge (ci, pj) at time t represents our estimate of the number of individuals from CBG ci visiting POI pj at the tth hour of simulation. We record the number of edges (with non-zero weights) in each metro area and for all hours from 1 March 2020 to 2 May 2020 in Extended Data Table 1. Across all 10 metro areas, we study 5.4 billion edges between 56,945 CBGs and 552,758 POIs.

Overview of the network estimation

The central technical challenge in constructing this network is estimating the network weights W(t)={w(t)ij} from SafeGraph data, as this visit matrix is not directly available from the data. Our general methodology for network estimation is as follows.

First, from SafeGraph data, we derived a time-independent estimate W¯ of the visit matrix that captures the aggregate distribution of visits from CBGs to POIs from January 2019 to February 2020.

Second, because visit patterns differ substantially from hour to hour (for example, day versus night) and day to day (for example, before versus after lockdown), we used current SafeGraph data to capture these hourly variations and to estimate the CBG marginals U(t), that is, the number of people in each CBG who are out visiting POIs at hour t, as well as the POI marginals V(t), that is, the total number of visitors present at each POI pj at hour t.

Finally, we applied the iterative proportional fitting procedure (IPFP) to estimate an hourly visit matrix W(t) that is consistent with the hourly marginals U(t) and V(t) but otherwise ‘as similar as possible’ to the distribution of visits in the aggregate visit matrix W¯, in terms of Kullback–Leibler divergence.

IPFP is a classic statistical method31 for adjusting joint distributions to match prespecified marginal distributions, and it is also known in the literature as biproportional fitting, the RAS algorithm or raking53. In the social sciences, it has been widely used to infer the characteristics of local subpopulations (for example, within each CBG) from aggregate data54,55,56. IPFP estimates the joint distribution of visits from CBGs to POIs by alternating between scaling each row to match the hourly row (CBG) marginals U(t) and scaling each column to match the hourly column (POI) marginals V(t). Further details about the estimation procedure are provided in Supplementary Methods section 3.

Model dynamics

To model the spread of SARS-CoV-2, we overlay a metapopulation disease transmission model on the mobility network defined in the ‘Mobility Network’ section. The transmission model structure follows previous work15,20 on epidemiological models of SARS-CoV-2 but incorporates a fine-grained mobility network into the calculations of the transmission rate. We construct separate mobility networks and models for each metropolitan statistical area.

We use a SEIR model with susceptible (S), exposed (E), infectious (I) and removed (R) compartments. Susceptible individuals have never been infected, but can acquire the virus through contact with infectious individuals, which may happen at POIs or in their home CBG. They then enter the exposed state, during which they have been infected but are not infectious yet. Individuals transition from exposed to infectious at a rate inversely proportional to the mean latency period. Finally, they transition into the removed state at a rate inversely proportional to the mean infectious period. The removed state represents individuals who can no longer be infected or infect others, for example, because they have recovered, self-isolated or died.

Each CBG ci maintains its own SEIR instantiation, with S(t)ci, E(t)ci, I(t)ci and R(t)ci representing how many individuals in CBG ci are in each disease state at hour t, and Nci=S(t)ci+E(t)ci+I(t)ci+R(t)ci. At each hour t, we sample the transitions between states as follows:

N(t)S

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## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

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https://www.nature.com/articles/s41586-020-2923-3

Mobility network models of COVID-19 explain inequities and inform reopening

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Serina Chang, Emma Pierson, Pang Wei Koh, Jaline Gerardin, Beth Redbird, David Grusky & Jure Leskovec

Nature volume 589, pages82–87(2021)Cite this article

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Abstract

The coronavirus disease 2019 (COVID-19) pandemic markedly changed human mobility patterns, necessitating epidemiological models that can capture the effects of these changes in mobility on the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)1. Here we introduce a metapopulation susceptible–exposed–infectious–removed (SEIR) model that integrates fine-grained, dynamic mobility networks to simulate the spread of SARS-CoV-2 in ten of the largest US metropolitan areas. Our mobility networks are derived from mobile phone data and map the hourly movements of 98 million people from neighbourhoods (or census block groups) to points of interest such as restaurants and religious establishments, connecting 56,945 census block groups to 552,758 points of interest with 5.4 billion hourly edges. We show that by integrating these networks, a relatively simple SEIR model can accurately fit the real case trajectory, despite substantial changes in the behaviour of the population over time. Our model predicts that a small minority of ‘superspreader’ points of interest account for a large majority of the infections, and that restricting the maximum occupancy at each point of interest is more effective than uniformly reducing mobility. Our model also correctly predicts higher infection rates among disadvantaged racial and socioeconomic groups2,3,4,5,6,7,8 solely as the result of differences in mobility: we find that disadvantaged groups have not been able to reduce their mobility as sharply, and that the points of interest that they visit are more crowded and are therefore associated with higher risk. By capturing who is infected at which locations, our model supports detailed analyses that can inform more-effective and equitable policy responses to COVID-19.

Main

In response to the COVID-19 crisis, stay-at-home orders were enacted in many countries to reduce contact between individuals and slow the spread of the SARS-CoV-29. Since then, public officials have continued to deliberate over when to reopen, which places are safe to return to and how much activity to allow10. Answering these questions requires epidemiological models that can capture the effects of changes in mobility on virus spread. In particular, findings of COVID-19 superspreader events11,12,13,14 motivate models that can reflect the heterogeneous risks of visiting different locations, whereas well-reported disparities in infection rates among different racial and socioeconomic groups2,3,4,5,6,7,8 require models that can explain the disproportionate effect of the virus on disadvantaged groups.

To address these needs, we construct fine-grained dynamic mobility networks from mobile-phone geolocation data, and use these networks to model the spread of SARS-CoV-2 within 10 of the largest metropolitan statistical areas (hereafter referred to as metro areas) in the USA. These networks map the hourly movements of 98 million people from census block groups (CBGs), which are geographical units that typically contain 600–3,000 people, to specific points of interest (POIs). As shown in Supplementary Table 1, POIs are non-residential locations that people visit such as restaurants, grocery stores and religious establishments. On top of each network, we overlay a metapopulation SEIR model that tracks the infection trajectories of each CBG as well as the POIs at which these infections are likely to have occurred. This builds on prior research that models disease spread using aggregate15,16,17,18,19, historical20,21,22 or synthetic mobility data23,24,25; separately, other studies have analysed mobility data in the context of COVID-19, but without an underlying model of disease spread26,27,28,29,30.

Combining our epidemiological model with these mobility networks allows us to not only accurately fit observed case counts, but also to conduct detailed analyses that can inform more-effective and equitable policy responses to COVID-19. By capturing information about individual POIs (for example, the hourly number of visitors and median visit duration), our model can estimate the effects of specific reopening strategies, such as only reopening certain POI categories or restricting the maximum occupancy at each POI. By modelling movement from CBGs, our model can identify at-risk populations and correctly predict, solely from mobility patterns, that disadvantaged racial and socioeconomic groups face higher rates of infection. Our model thus enables the analysis of urgent health disparities; we use it to highlight two mobility-related mechanisms that drive these disparities and to evaluate the disparate effect of reopening on disadvantaged groups.

Mobility network model

We use data from SafeGraph, a company that aggregates anonymized location data from mobile applications, to study mobility patterns from 1 March to 2 May 2020. For each metro area, we represent the movement of individuals between CBGs and POIs as a bipartite network with time-varying edges, in which the weight of an edge between a CBG and POI represents the number of visitors from that CBG to that POI during a given hour (Fig. 1a). SafeGraph also provides the area in square feet of each POI, as well as its category in the North American industry classification system (for example, fitness centre or full-service restaurant) and median visit duration in minutes. We validated the SafeGraph mobility data by comparing the dataset to Google mobility data (Supplementary Fig. 1 and Supplementary Tables 2, 3) and used iterative proportional fitting31 to derive POI–CBG networks from the raw SafeGraph data. Overall, these networks comprise 5.4 billion hourly edges between 56,945 CBGs and 552,758 POIs (Extended Data Table 1).

Fig. 1: Model description and fit.

figure1

a, The mobility network captures hourly visits from each CBG to each POI. The vertical lines indicate that most visits are between nearby POIs and CBGs. Visits dropped markedly from March to April, as indicated by the lower density of grey lines. Mobility networks in the Chicago metro area are shown for 13:00 on two Mondays, 2 March 2020 (top) and 6 April 2020 (bottom). b, We overlaid a disease-spread model on the mobility network, with each CBG having its own set of SEIR compartments. New infections occur at both POIs and CBGs, with the mobility network governing how subpopulations from different CBGs interact as they visit POIs. c, Left, to test the out-of-sample prediction, we calibrated the model on data before 15 April 2020 (vertical black line). Even though its parameters remain fixed over time, the model accurately predicts the case trajectory in the Chicago metro area after 15 April using the mobility data (r.m.s.e. on daily cases = 406 for dates ranging from 15 April to 9 May). Right, model fit was further improved when we calibrated the model on the full range of data (r.m.s.e. on daily cases = 387 for the dates ranging from 15 April to 9 May). d, We fitted separate models to 10 of the largest US metro areas, modelling a total population of 98 million people; here, we show full model fits, as in c (right). In c and d, the blue line represents the model predictions and the grey crosses represent the number of daily reported cases; as the numbers of reported cases tend to have great variability, we also show the smoothed weekly average (orange line). Shaded regions denote the 2.5th and 97.5th percentiles across parameter sets and stochastic realizations. Across metro areas, we sample 97 parameter sets, with 30 stochastic realizations each (n = 2,910); see Supplementary Table 6 for the number of sets per metro area.

Full size image

We overlay a SEIR model on each mobility network15,20, in which each CBG maintains its own susceptible (S), exposed (E), infectious (I) and removed (R) states (Fig. 1b). New infections occur at both POIs and CBGs, with the mobility network governing how subpopulations from different CBGs interact as they visit POIs. We use the area, median visit duration and time-varying density of infectious individuals for each POI to determine the hourly infection rate of that POI. The model has only three free parameters that scale: (1) transmission rates at POIs, (2) transmission rates at CBGs and (3) the initial proportion of exposed individuals (Extended Data Table 2); all three parameters remain constant over time. We calibrate a separate model for each metro area using the confirmed case counts from The New York Times by minimizing the root mean square error (r.m.s.e.) to daily incident cases32. Our model accurately fits observed daily case counts in all 10 metro areas from 8 March to 9 May 2020 (Fig. 1c, d). In addition, when calibrated on only the case counts up to 14 April, the model predicts case counts reasonably well on the held-out time period of 15 April–9 May 2020 (Fig. 1c and Extended Data Fig. 1a). Our key technical finding is that the dynamic mobility network allows even our relatively simple SEIR model with just three static parameters to accurately fit observed cases, despite changing policies and behaviours during that period.

Mobility reduction and reopening plans

We can estimate the impact of mobility-related policies by constructing a hypothetical mobility network that reflects the expected effects of each policy, and running our SEIR model forward with this hypothetical network. Using this approach, we assess a wide range of mobility reduction and reopening strategies.

The magnitude of mobility reduction is at least as important as its timing

Mobility in the USA dropped sharply in March 2020: for example, overall POI visits in the Chicago metro area fell by 54.7% between the first week of March and the first week of April 2020. We constructed counterfactual mobility networks by scaling the magnitude of mobility reduction down and by shifting the timeline earlier and later, and applied our model to the counterfactual networks to simulate the resulting infection trajectories. Across metro areas, we found that the magnitude of mobility reduction was at least as important as its timing (Fig. 2a and Supplementary Tables 4, 5): for example, if the mobility reduction in the Chicago metro area had been only a quarter of the size, the predicted number of infections would have increased by 3.3× (95% confidence interval, 2.8–3.8×), compared with a 1.5× (95% confidence interval, 1.4–1.6×) increase had people begun reducing their mobility one full week later. Furthermore, if no mobility reduction had occurred at all, the predicted number of infections in the Chicago metro area would have increased by 6.2× (95% confidence interval, 5.2–7.1×). Our results are in accordance with previous findings that mobility reductions can markedly reduce infections18,19,33,34.

Fig. 2: Assessing mobility reduction and reopening.

figure2

The Chicago metro area is used as an example; results for all metro areas are included in Extended Data Figs. 3, 4, Supplementary Figs. 10, 15–24 and Supplementary Tables 4, 5, as indicated. a, Counterfactual simulations (left) of past reductions in mobility illustrate that the magnitude of the reduction (middle) was at least as important as its timing (right) (Supplementary Tables 4, 5). b, The model predicts that most infections at POIs occur at a small fraction of superspreader POIs (Supplementary Fig. 10). c, Left, the cumulative number of predicted infections after one month of reopening is plotted against the fraction of visits lost by partial instead of full reopening (Extended Data Fig. 3); the annotations within the plot show the fraction of maximum occupancy that is used as the cap and the horizontal red line indicates the cumulative number of predicted infections at the point of reopening (on 1 May 2020). Compared to full reopening, capping at 20% of the maximum occupancy in Chicago reduces the number of new infections by more than 80%, while only losing 42% of overall visits. Right, compared to uniformly reducing visits, the reduced maximum occupancy strategy always results in a smaller predicted increase in infections for the same number of visits (Extended Data Fig. 4). The horizontal grey line at 0% indicates when the two strategies result in an equal number of infections, and we observe that the curve falls well below this baseline. The y axis plots the relative difference between the predicted number of new infections under the reduced occupancy strategy compared to a uniform reduction. d, Reopening full-service restaurants has the largest predicted impact on infections, due to the large number of restaurants as well as their high visit densities and long dwell times (Supplementary Figs. 15–24). Colours are used to distinguish the different POI categories, but do not have any additional meaning. All results in this figure are aggregated across 4 parameter sets and 30 stochastic realizations (n = 120). Shaded regions in a–c denote the 2.5th to 97.5th percentiles; boxes in d denote the interquartile range and data points outside this range are shown as individual dots.

Full size image

A minority of POIs account for the majority of the predicted infections

We next investigated whether it matters how we reduce mobility—that is, to which POIs. We computed the number of infections that occurred at each POI in our simulations from 1 March to 2 May 2020, and found that the majority of the predicted infections occurred at a small fraction of superspreader POIs; for example, in the Chicago metro area, 10% of POIs accounted for 85% (95% confidence interval, 83–87%) of the predicted infections at the POIs (Fig. 2b and Supplementary Fig. 10). Certain categories of POIs also contributed far more to infections (for example, full-service restaurants and hotels), although our model predicted time-dependent variation in how much each category contributed (Extended Data Fig. 2). For example, restaurants and fitness centres contributed less to the predicted number of infections over time, probably because of lockdown orders to close these POIs, whereas grocery stores remained steady or even grew in their contribution, which is in agreement with their status as essential businesses.

Reopening with a reduced maximum occupancy

If a minority of POIs produce the majority of infections, then reopening strategies that specifically target high-risk POIs should be especially effective. To test one such strategy, we simulated reopening on 1 May, and modelled the effects of reducing the maximum occupancy in which the numbers of hourly visits to each POI returned to their ‘normal’ levels from the first week of March but were capped if they exceeded a fraction of the maximum occupancy of that POI35. Full reopening without reducing the maximum occupancy produced a spike in the predicted number of infections: in the Chicago metro area, our models projected that an additional 32% (95% confidence interval, 25–35%) of the population would be infected by the end of May (Fig. 2c). However, reducing the maximum occupancy substantially reduced the risk without sharply reducing overall mobility: capping at 20% of the maximum occupancy in the Chicago metro area reduced the predicted number of new infections by more than 80% but only lost 42% of overall visits, and we observed similar trends across other metro areas (Extended Data Fig. 3). This result highlights the nonlinearity of the predicted number of infections as a function of the number of visits: one can achieve a disproportionately large reduction in infections with a small reduction in visits. Furthermore, in comparison to a different reopening strategy, in which the number of visits to each POI was uniformly reduced from their levels in early March, reducing the maximum occupancy always resulted in fewer predicted infections for the same number of total visits (Fig. 2c and Extended Data Fig. 4). This is because reducing the maximum occupancies takes advantage of the time-varying visit density within each POI, disproportionately reducing visits to the POI during the high-density periods with the highest risk, but leaving visit counts unchanged during periods with lower risks. These results support previous findings that precise interventions, such as reducing the maximum occupancy, may be more effective than less targeted measures, while incurring substantially lower economic costs36.

Relative risk of reopening different categories of POIs

Because we found that certain POI categories contributed far more to predicted infections in March (Extended Data Fig. 2), we also expected that reopening some POI categories would be riskier than reopening others. To assess this, we simulated reopening each category in turn on 1 May 2020 (by returning its mobility patterns to early March levels, as above), while keeping all other POIs at their reduced mobility levels from the end of April. We found large variation in predicted reopening risks: on average across metro areas, full-service restaurants, gyms, hotels, cafes, religious organizations and limited-service restaurants produced the largest predicted increases in infections when reopened (Extended Data Fig. 5d). Reopening full-service restaurants was associated with a particularly high risk: in the Chicago metro area, we predicted an additional 595,805 (95% confidence interval, 433,735–685,959) infections by the end of May, more than triple that of the POI category with the next highest risk (Fig. 2d). These risks are summed over all POIs in the category, but the relative risks after normalizing by the number of POIs were broadly similar (Extended Data Fig. 5c). These categories were predicted to be have a higher risk because, in the mobility data, their POIs tended to have higher visit densities and/or visitors stayed there longer (Supplementary Figs. 15–24).

Demographic disparities in infections

We characterize the differential spread of SARS-CoV-2 along demographic lines by using US census data to annotate each CBG with its racial composition and median income, then tracking predicted infection rates in CBGs with different demographic compositions: for example, within each metro area, comparing CBGs in the top and bottom deciles for income. We use this approach to study the mobility mechanisms behind disparities and to quantify how different reopening strategies affect disadvantaged groups.

Predicting disparities from mobility data

Despite having access to only mobility data and no demographic information, our models correctly predicted higher risks of infection among disadvantaged racial and socioeconomic groups2,3,4,5,6,7,8. Across all metro areas, individuals from CBGs in the bottom decile for income had a substantially higher likelihood of being infected by the end of the simulation, even though all individuals began with equal likelihoods of infection (Fig. 3a). This predicted disparity was driven primarily by a few POI categories (for example, full-service restaurants); far greater proportions of individuals from lower-income CBGs than higher-income CBGs became infected in these POIs (Fig. 3c and Supplementary Fig. 2). We similarly found that CBGs with fewer white residents had higher predicted risks of infection, although results were more variable across metro areas (Fig. 3b). In the Supplementary Discussion, we confirm that the magnitude of the disparities that our model predicts is generally consistent with real-world disparities and further explore the large predicted disparities in Philadelphia, that stem from substantial differences in the POIs that are frequented by higher- versus lower-income CBGs. In the analysis below, we discuss two mechanisms that lead higher predicted infection rates among lower-income CBGs, and we show in Extended Data Fig. 6 and Extended Data Table 4 that similar results hold for racial disparities as well.

Fig. 3: Mobility patterns give rise to infection disparities.

figure3

a, In every metro area, our model predicts that people in lower-income CBGs are likelier to be infected. b, People in non-white CBGs area are also likelier to be infected, although results are more variable across metro areas. For c–f, the Chicago metro area is used as an example, but references to results for all metro areas are provided for each panel. c, The overall predicted disparity is driven by a few POI categories such as full-service restaurants (Supplementary Fig. 2). d, One reason for the predicted disparities is that higher-income CBGs were able to reduce their mobility levels below those of lower-income CBGs (Extended Data Fig. 6). e, Within each POI category, people from lower-income CBGs tend to visit POIs that have higher predicted transmission rates (Extended Data Table 3). The size of each dot represents the average number of visits per capita made to the category. The top 10 out of 20 categories with the most visits are labelled, covering 0.48–2.88 visits per capita (hardware stores–full-service restaurants). f, Reopening (at different levels of reduced maximum occupancy) leads to more predicted infections in lower-income CBGs than in the overall population (Extended Data Fig. 3). In c–f, purple denotes lower-income CBGs, yellow denotes higher-income CBGs and blue represents the overall population. Aside from d and e, which were directly extracted from mobility data, all results in this figure represent predictions aggregated over model realizations. Across metro areas, we sample 97 parameter sets, with 30 stochastic realizations each (n = 2,910); see Supplementary Table 6 for the number of sets per metro area. Shaded regions in c and f denote the 2.5th–97.5th percentiles; boxes in (a, b) denote the interquartile range; data points outside the range are shown as individual dots.

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Lower-income CBGs saw smaller reductions in mobility

A first mechanism producing disparities was that, across all metro areas, lower-income CBGs did not reduce their mobility as sharply in the first few weeks of March 2020, and these groups showed higher mobility than higher-income CBGs for most of March–May (Fig. 3d and Extended Data Fig. 6). For example, in April, individuals from lower-income CBGs in the Chicago metro area had 27% more POI visits per capita than those from higher-income CBGs. Category-level differences in visit patterns partially explained the infection disparities within each category: for example, individuals from lower-income CBGs made substantially more visits per capita to grocery stores than did those from higher-income CBGs (Supplementary Fig. 3) and consequently experienced more predicted infections for that category (Supplementary Fig. 2).

POIs visited by lower-income CBGs have higher transmission rates

Differences in visits per capita do not fully explain the infection disparities: for example, cafes and snack bars were visited more frequently by higher-income CBGs in every metro area (Supplementary Fig. 3), but our model predicted that a larger proportion of individuals from lower-income CBGs were infected at cafes and snack bars in the majority of metro areas (Supplementary Fig. 2). We found that even within a POI category, the predicted transmission rates at POIs frequented by individuals fom lower-income CBGs tended to be higher than the corresponding rates for those from higher-income CBGs (Fig. 3e and Extended Data Table 3), because POIs frequented by individuals from lower-income CBGs tended to be smaller and more crowded in the mobility data. As a case study, we examined grocery stores in further detail. In eight of the ten metro areas, visitors from lower-income CBGs encountered higher predicted transmission rates at grocery stores than visitors from higher-income CBGs (median transmission rate ratio of 2.19) (Extended Data Table 3). We investigated why one visit to the grocery store was predicted to be twice as dangerous for an individual from a lower-income CBG: the mobility data showed that the average grocery store visited by individuals from lower-income CBGs had 59% more hourly visitors per square foot, and their visitors stayed 17% longer on average (medians across metro areas). These findings highlight how fine-grained differences in mobility patterns—how often people go out and which POIs that they go to—can ultimately contribute to marked disparities in predicted infection outcomes.

Reopening plans must account for disparate effects

Because disadvantaged groups suffer a larger burden of infection, it is critical to not only consider the overall impact of reopening plans but also their disparate effects on disadvantaged groups specifically. For example, our model predicted that full reopening in the Chicago metro area would result in an additional 39% (95% confidence interval, 31–42%) of the population of CBGs in the bottom income decile being infected within a month, compared to 32% (95% confidence interval, 25–35%) of the overall population (Fig. 3f; results for all metro areas are shown in Extended Data Fig. 3). Similarly, Supplementary Fig. 4 illustrates that reopening individual POI categories tends to have a larger predicted effect on lower-income CBGs. More stringent reopening plans produce smaller absolute disparities in predicted infections—for example, we predict that reopening at 20% of the maximum occupancy in Chicago would result in additional infections for 6% (95% confidence interval, 4–8%) of the overall population and 10% (95% confidence interval, 7–13%) of the population in CBGs in the bottom income decile (Fig. 3f)—although the relative disparity remains.

Discussion

The mobility dataset that we use has limitations: it does not cover all populations, does not contain all POIs and cannot capture sub-CBG heterogeneity. Our model itself is also parsimonious, and does not include all real-world features that are relevant to disease transmission. We discuss these limitations in more detail in the Supplementary Discussion. However, the predictive accuracy of our model suggests that it broadly captures the relationship between mobility and transmission, and we thus expect our broad conclusions—for example, that people from lower-income CBGs have higher infection rates in part because they tend to visit denser POIs and because they have not reduced mobility by as much (probably because they cannot work from home as easily4)—to hold robustly. Our fine-grained network modelling approach naturally extends to other mobility datasets and models that capture more aspects of real-world transmission, and these represent interesting directions for future work.

Our results can guide policy-makers that seek to assess competing approaches to reopening. Despite growing concern about racial and socioeconomic disparities in infections and deaths, it has been difficult for policy-makers to act on those concerns; they are currently operating without much evidence on the disparate effects of reopening policies, prompting calls for research that both identifies the causes of observed disparities and suggests policy approaches to mitigate them5,8,37,38. Our fine-grained mobility modelling addresses both these needs. Our results suggest that infection disparities are not the unavoidable consequence of factors that are difficult to address in the short term, such as differences in preexisting conditions; on the contrary, short-term policy decisions can substantially affect infection outcomes by altering the overall amount of mobility allowed and the types of POIs reopened. Considering the disparate effects of reopening plans may lead policy-makers to adopt policies that can drive down infection densities in disadvantaged neighbourhoods by supporting, for example, more stringent caps on POI occupancies, emergency food distribution centres to reduce densities in high-risk stores, free and widely available testing in neighbourhoods predicted to be high risk (especially given known disparities in access to tests2), improved paid leave policy or income support that enables essential workers to curtail mobility when sick, and improved workplace infection prevention for essential workers, such as high-quality personal protective equipment, good ventilation and physical distancing when possible. As reopening policies continue to be debated, it is critical to build tools that can assess the effectiveness and equity of different approaches. We hope that our model, by capturing heterogeneity across POIs, demographic groups and cities, helps to address this need.

Methods

The Methods is structured as follows. We describe the datasets that we used in the ‘Datasets’ section and the mobility network that we derived from these datasets in the ‘Mobility network’ section. In the ‘Model dynamics’ section, we discuss the SEIR model that we overlaid on the mobility network; in the ‘Model calibration’ section, we describe how we calibrated this model and quantified uncertainty in its predictions. Finally, in the ‘Analysis details’ section, we provide details on the experimental procedures used for our analyses of mobility reduction, reopening plans and demographic disparities.

Datasets

SafeGraph

We use data provided by SafeGraph, a company that aggregates anonymized location data from numerous mobile applications. SafeGraph data captures the movement of people between CBGs, which are geographical units that typically contain a population of between 600 and 3,000 people, and POIs such as restaurants, grocery stores or religious establishments. Specifically, we use the following SafeGraph datasets.

First, we used the Places Patterns39 and Weekly Patterns (v1)40 datasets. These datasets contain, for each POI, hourly counts of the number of visitors, estimates of median visit duration in minutes (the ‘dwell time’) and aggregated weekly and monthly estimates of the home CBGs of visitors. We use visitor home CBG data from the Places Patterns dataset: for privacy reasons, SafeGraph excludes a home CBG from this dataset if fewer than five devices were recorded at the POI from that CBG over the course of the month. For each POI, SafeGraph also provides their North American industry classification system category, as well as estimates of its physical area in square feet. The area is computed using the footprint polygon SafeGraph that assigns to the POI41,42. We analyse Places Patterns data from 1 January 2019 to 29 February 2020 and Weekly Patterns data from 1 March 2020 to 2 May 2020.

Second, we used the Social Distancing Metrics dataset43, which contains daily estimates of the proportion of people staying home in each CBG. We analyse Social Distancing Metrics data from 1 March 2020 to 2 May 2020.

We focus on 10 of the largest metro areas in the United States (Extended Data Table 1). We chose these metro areas by taking a random subset of the SafeGraph Patterns data and selecting the 10 metro areas with the most POIs in the data. The application of the methods described in this paper to the other metro areas in the original SafeGraph data should be straightforward. For each metro area, we include all POIs that meet all of the following requirements: (1) the POI is located in the metro area ; (2) SafeGraph has visit data for this POI for every hour that we model, from 00:00 on 1 March 2020 to 23:00 on 2 May 2020; (3) SafeGraph has recorded the home CBGs of visitors to this POI for at least one month from January 2019 to February 2020; (4) the POI is not a ‘parent’ POI. Parent POIs comprise a small fraction of POIs in the dataset that overlap and include the visits from their ‘child’ POIs: for example, many malls in the dataset are parent POIs, which include the visits from stores that are their child POIs. To avoid double-counting visits, we remove all parent POIs from the dataset. After applying these POI filters, we include all CBGs that have at least one recorded visit to at least ten of the remaining POIs; this means that CBGs from outside the metro area may be included if they visit this metro area frequently enough. Summary statistics of the post-processed data are shown in Extended Data Table 1. Overall, we analyse 56,945 CBGs from the 10 metro areas, and more than 310 million visits from these CBGs to 552,758 POIs.

SafeGraph data have been used to study consumer preferences44 and political polarization45. More recently, it has been used as one of the primary sources of mobility data in the USA for tracking the effects of the COVID-19 pandemic26,28,46,47,48. In Supplementary Methods section 1, we show that aggregate trends in SafeGraph mobility data match the aggregate trends in Google mobility data in the USA49, before and after the imposition of stay-at-home measures. Previous analyses of SafeGraph data have shown that it is geographically representative—for example, it does not systematically overrepresent individuals from CBGs in different counties or with different racial compositions, income levels or educational levels50,51.

US census

Our data on the demographics of the CBGs comes from the American Community Survey (ACS) of the US Census Bureau52. We use the 5-year ACS data (2013–2017) to extract the median household income, the proportion of white residents and the proportion of Black residents of each CBG. For the total population of each CBG, we use the most-recent one-year estimates (2018); one-year estimates are noisier but we wanted to minimize systematic downward bias in our total population counts (due to population growth) by making them as recent as possible.

The New York Times dataset

We calibrated our models using the COVID-19 dataset published by the The New York Times32. Their dataset consists of cumulative counts of cases and deaths in the USA over time, at the state and county level. For each metro area that we modelled, we sum over the county-level counts to produce overall counts for the entire metro area. We convert the cumulative case and death counts to daily counts for the purposes of model calibration, as described in the ‘Model calibration’ section.

Data ethics

The dataset from The New York Times consists of aggregated COVID-19-confirmed case and death counts collected by journalists from public news conferences and public data releases. For the mobility data, consent was obtained by the third-party sources that collected the data. SafeGraph aggregates data from mobile applications that obtain opt-in consent from their users to collect anonymous location data. Google’s mobility data consists of aggregated, anonymized sets of data from users who have chosen to turn on the location history setting. Additionally, we obtained IRB exemption for SafeGraph data from the Northwestern University IRB office.

Mobility network

Definition

We consider a complete undirected bipartite graph G=(V,E) with time-varying edges. The vertices V are partitioned into two disjoint sets C={c1,…,cm}, representing m CBGs, and P={p1,…,pn}, representing n POIs. From US census data, each CBG ci is labelled with its population Nci, income distribution, and racial and age demographics. From SafeGraph data, each POI pj is similarly labelled with its category (for example, restaurant, grocery store or religious organization), its physical size in square feet apj, and the median dwell time dpj of visitors to pj. The weight w(t)ij on an edge (ci, pj) at time t represents our estimate of the number of individuals from CBG ci visiting POI pj at the tth hour of simulation. We record the number of edges (with non-zero weights) in each metro area and for all hours from 1 March 2020 to 2 May 2020 in Extended Data Table 1. Across all 10 metro areas, we study 5.4 billion edges between 56,945 CBGs and 552,758 POIs.

Overview of the network estimation

The central technical challenge in constructing this network is estimating the network weights W(t)={w(t)ij} from SafeGraph data, as this visit matrix is not directly available from the data. Our general methodology for network estimation is as follows.

First, from SafeGraph data, we derived a time-independent estimate W¯ of the visit matrix that captures the aggregate distribution of visits from CBGs to POIs from January 2019 to February 2020.

Second, because visit patterns differ substantially from hour to hour (for example, day versus night) and day to day (for example, before versus after lockdown), we used current SafeGraph data to capture these hourly variations and to estimate the CBG marginals U(t), that is, the number of people in each CBG who are out visiting POIs at hour t, as well as the POI marginals V(t), that is, the total number of visitors present at each POI pj at hour t.

Finally, we applied the iterative proportional fitting procedure (IPFP) to estimate an hourly visit matrix W(t) that is consistent with the hourly marginals U(t) and V(t) but otherwise ‘as similar as possible’ to the distribution of visits in the aggregate visit matrix W¯, in terms of Kullback–Leibler divergence.

IPFP is a classic statistical method31 for adjusting joint distributions to match prespecified marginal distributions, and it is also known in the literature as biproportional fitting, the RAS algorithm or raking53. In the social sciences, it has been widely used to infer the characteristics of local subpopulations (for example, within each CBG) from aggregate data54,55,56. IPFP estimates the joint distribution of visits from CBGs to POIs by alternating between scaling each row to match the hourly row (CBG) marginals U(t) and scaling each column to match the hourly column (POI) marginals V(t). Further details about the estimation procedure are provided in Supplementary Methods section 3.

Model dynamics

To model the spread of SARS-CoV-2, we overlay a metapopulation disease transmission model on the mobility network defined in the ‘Mobility Network’ section. The transmission model structure follows previous work15,20 on epidemiological models of SARS-CoV-2 but incorporates a fine-grained mobility network into the calculations of the transmission rate. We construct separate mobility networks and models for each metropolitan statistical area.

We use a SEIR model with susceptible (S), exposed (E), infectious (I) and removed (R) compartments. Susceptible individuals have never been infected, but can acquire the virus through contact with infectious individuals, which may happen at POIs or in their home CBG. They then enter the exposed state, during which they have been infected but are not infectious yet. Individuals transition from exposed to infectious at a rate inversely proportional to the mean latency period. Finally, they transition into the removed state at a rate inversely proportional to the mean infectious period. The removed state represents individuals who can no longer be infected or infect others, for example, because they have recovered, self-isolated or died.

Each CBG ci maintains its own SEIR instantiation, with S(t)ci, E(t)ci, I(t)ci and R(t)ci representing how many individuals in CBG ci are in each disease state at hour t, and Nci=S(t)ci+E(t)ci+I(t)ci+R(t)ci. At each hour t, we sample the transitions between states as follows:

N(t)S

¿Esto es el kernel de Windows?

esto es un estudio serio de en establecimientos abiertos al publico donde se dan mas contagios.

sorpresa es mas arriesgado tomr una cerveza que comprar un coche

**Eric Sachs**- Mensajes : 63353

Fecha de inscripción : 06/03/2012

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Itlotg escribió:@Eric Sachs escribió:bisti yi di kilpibilizir i li histiliria!!!!!

https://www.nature.com/articles/s41586-020-2923-3

Mobility network models of COVID-19 explain inequities and inform reopening

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Serina Chang, Emma Pierson, Pang Wei Koh, Jaline Gerardin, Beth Redbird, David Grusky & Jure Leskovec

Nature volume 589, pages82–87(2021)Cite this article

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Abstract

The coronavirus disease 2019 (COVID-19) pandemic markedly changed human mobility patterns, necessitating epidemiological models that can capture the effects of these changes in mobility on the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)1. Here we introduce a metapopulation susceptible–exposed–infectious–removed (SEIR) model that integrates fine-grained, dynamic mobility networks to simulate the spread of SARS-CoV-2 in ten of the largest US metropolitan areas. Our mobility networks are derived from mobile phone data and map the hourly movements of 98 million people from neighbourhoods (or census block groups) to points of interest such as restaurants and religious establishments, connecting 56,945 census block groups to 552,758 points of interest with 5.4 billion hourly edges. We show that by integrating these networks, a relatively simple SEIR model can accurately fit the real case trajectory, despite substantial changes in the behaviour of the population over time. Our model predicts that a small minority of ‘superspreader’ points of interest account for a large majority of the infections, and that restricting the maximum occupancy at each point of interest is more effective than uniformly reducing mobility. Our model also correctly predicts higher infection rates among disadvantaged racial and socioeconomic groups2,3,4,5,6,7,8 solely as the result of differences in mobility: we find that disadvantaged groups have not been able to reduce their mobility as sharply, and that the points of interest that they visit are more crowded and are therefore associated with higher risk. By capturing who is infected at which locations, our model supports detailed analyses that can inform more-effective and equitable policy responses to COVID-19.

Main

In response to the COVID-19 crisis, stay-at-home orders were enacted in many countries to reduce contact between individuals and slow the spread of the SARS-CoV-29. Since then, public officials have continued to deliberate over when to reopen, which places are safe to return to and how much activity to allow10. Answering these questions requires epidemiological models that can capture the effects of changes in mobility on virus spread. In particular, findings of COVID-19 superspreader events11,12,13,14 motivate models that can reflect the heterogeneous risks of visiting different locations, whereas well-reported disparities in infection rates among different racial and socioeconomic groups2,3,4,5,6,7,8 require models that can explain the disproportionate effect of the virus on disadvantaged groups.

To address these needs, we construct fine-grained dynamic mobility networks from mobile-phone geolocation data, and use these networks to model the spread of SARS-CoV-2 within 10 of the largest metropolitan statistical areas (hereafter referred to as metro areas) in the USA. These networks map the hourly movements of 98 million people from census block groups (CBGs), which are geographical units that typically contain 600–3,000 people, to specific points of interest (POIs). As shown in Supplementary Table 1, POIs are non-residential locations that people visit such as restaurants, grocery stores and religious establishments. On top of each network, we overlay a metapopulation SEIR model that tracks the infection trajectories of each CBG as well as the POIs at which these infections are likely to have occurred. This builds on prior research that models disease spread using aggregate15,16,17,18,19, historical20,21,22 or synthetic mobility data23,24,25; separately, other studies have analysed mobility data in the context of COVID-19, but without an underlying model of disease spread26,27,28,29,30.

Combining our epidemiological model with these mobility networks allows us to not only accurately fit observed case counts, but also to conduct detailed analyses that can inform more-effective and equitable policy responses to COVID-19. By capturing information about individual POIs (for example, the hourly number of visitors and median visit duration), our model can estimate the effects of specific reopening strategies, such as only reopening certain POI categories or restricting the maximum occupancy at each POI. By modelling movement from CBGs, our model can identify at-risk populations and correctly predict, solely from mobility patterns, that disadvantaged racial and socioeconomic groups face higher rates of infection. Our model thus enables the analysis of urgent health disparities; we use it to highlight two mobility-related mechanisms that drive these disparities and to evaluate the disparate effect of reopening on disadvantaged groups.

Mobility network model

We use data from SafeGraph, a company that aggregates anonymized location data from mobile applications, to study mobility patterns from 1 March to 2 May 2020. For each metro area, we represent the movement of individuals between CBGs and POIs as a bipartite network with time-varying edges, in which the weight of an edge between a CBG and POI represents the number of visitors from that CBG to that POI during a given hour (Fig. 1a). SafeGraph also provides the area in square feet of each POI, as well as its category in the North American industry classification system (for example, fitness centre or full-service restaurant) and median visit duration in minutes. We validated the SafeGraph mobility data by comparing the dataset to Google mobility data (Supplementary Fig. 1 and Supplementary Tables 2, 3) and used iterative proportional fitting31 to derive POI–CBG networks from the raw SafeGraph data. Overall, these networks comprise 5.4 billion hourly edges between 56,945 CBGs and 552,758 POIs (Extended Data Table 1).

Fig. 1: Model description and fit.

figure1

a, The mobility network captures hourly visits from each CBG to each POI. The vertical lines indicate that most visits are between nearby POIs and CBGs. Visits dropped markedly from March to April, as indicated by the lower density of grey lines. Mobility networks in the Chicago metro area are shown for 13:00 on two Mondays, 2 March 2020 (top) and 6 April 2020 (bottom). b, We overlaid a disease-spread model on the mobility network, with each CBG having its own set of SEIR compartments. New infections occur at both POIs and CBGs, with the mobility network governing how subpopulations from different CBGs interact as they visit POIs. c, Left, to test the out-of-sample prediction, we calibrated the model on data before 15 April 2020 (vertical black line). Even though its parameters remain fixed over time, the model accurately predicts the case trajectory in the Chicago metro area after 15 April using the mobility data (r.m.s.e. on daily cases = 406 for dates ranging from 15 April to 9 May). Right, model fit was further improved when we calibrated the model on the full range of data (r.m.s.e. on daily cases = 387 for the dates ranging from 15 April to 9 May). d, We fitted separate models to 10 of the largest US metro areas, modelling a total population of 98 million people; here, we show full model fits, as in c (right). In c and d, the blue line represents the model predictions and the grey crosses represent the number of daily reported cases; as the numbers of reported cases tend to have great variability, we also show the smoothed weekly average (orange line). Shaded regions denote the 2.5th and 97.5th percentiles across parameter sets and stochastic realizations. Across metro areas, we sample 97 parameter sets, with 30 stochastic realizations each (n = 2,910); see Supplementary Table 6 for the number of sets per metro area.

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We overlay a SEIR model on each mobility network15,20, in which each CBG maintains its own susceptible (S), exposed (E), infectious (I) and removed (R) states (Fig. 1b). New infections occur at both POIs and CBGs, with the mobility network governing how subpopulations from different CBGs interact as they visit POIs. We use the area, median visit duration and time-varying density of infectious individuals for each POI to determine the hourly infection rate of that POI. The model has only three free parameters that scale: (1) transmission rates at POIs, (2) transmission rates at CBGs and (3) the initial proportion of exposed individuals (Extended Data Table 2); all three parameters remain constant over time. We calibrate a separate model for each metro area using the confirmed case counts from The New York Times by minimizing the root mean square error (r.m.s.e.) to daily incident cases32. Our model accurately fits observed daily case counts in all 10 metro areas from 8 March to 9 May 2020 (Fig. 1c, d). In addition, when calibrated on only the case counts up to 14 April, the model predicts case counts reasonably well on the held-out time period of 15 April–9 May 2020 (Fig. 1c and Extended Data Fig. 1a). Our key technical finding is that the dynamic mobility network allows even our relatively simple SEIR model with just three static parameters to accurately fit observed cases, despite changing policies and behaviours during that period.

Mobility reduction and reopening plans

We can estimate the impact of mobility-related policies by constructing a hypothetical mobility network that reflects the expected effects of each policy, and running our SEIR model forward with this hypothetical network. Using this approach, we assess a wide range of mobility reduction and reopening strategies.

The magnitude of mobility reduction is at least as important as its timing

Mobility in the USA dropped sharply in March 2020: for example, overall POI visits in the Chicago metro area fell by 54.7% between the first week of March and the first week of April 2020. We constructed counterfactual mobility networks by scaling the magnitude of mobility reduction down and by shifting the timeline earlier and later, and applied our model to the counterfactual networks to simulate the resulting infection trajectories. Across metro areas, we found that the magnitude of mobility reduction was at least as important as its timing (Fig. 2a and Supplementary Tables 4, 5): for example, if the mobility reduction in the Chicago metro area had been only a quarter of the size, the predicted number of infections would have increased by 3.3× (95% confidence interval, 2.8–3.8×), compared with a 1.5× (95% confidence interval, 1.4–1.6×) increase had people begun reducing their mobility one full week later. Furthermore, if no mobility reduction had occurred at all, the predicted number of infections in the Chicago metro area would have increased by 6.2× (95% confidence interval, 5.2–7.1×). Our results are in accordance with previous findings that mobility reductions can markedly reduce infections18,19,33,34.

Fig. 2: Assessing mobility reduction and reopening.

figure2

The Chicago metro area is used as an example; results for all metro areas are included in Extended Data Figs. 3, 4, Supplementary Figs. 10, 15–24 and Supplementary Tables 4, 5, as indicated. a, Counterfactual simulations (left) of past reductions in mobility illustrate that the magnitude of the reduction (middle) was at least as important as its timing (right) (Supplementary Tables 4, 5). b, The model predicts that most infections at POIs occur at a small fraction of superspreader POIs (Supplementary Fig. 10). c, Left, the cumulative number of predicted infections after one month of reopening is plotted against the fraction of visits lost by partial instead of full reopening (Extended Data Fig. 3); the annotations within the plot show the fraction of maximum occupancy that is used as the cap and the horizontal red line indicates the cumulative number of predicted infections at the point of reopening (on 1 May 2020). Compared to full reopening, capping at 20% of the maximum occupancy in Chicago reduces the number of new infections by more than 80%, while only losing 42% of overall visits. Right, compared to uniformly reducing visits, the reduced maximum occupancy strategy always results in a smaller predicted increase in infections for the same number of visits (Extended Data Fig. 4). The horizontal grey line at 0% indicates when the two strategies result in an equal number of infections, and we observe that the curve falls well below this baseline. The y axis plots the relative difference between the predicted number of new infections under the reduced occupancy strategy compared to a uniform reduction. d, Reopening full-service restaurants has the largest predicted impact on infections, due to the large number of restaurants as well as their high visit densities and long dwell times (Supplementary Figs. 15–24). Colours are used to distinguish the different POI categories, but do not have any additional meaning. All results in this figure are aggregated across 4 parameter sets and 30 stochastic realizations (n = 120). Shaded regions in a–c denote the 2.5th to 97.5th percentiles; boxes in d denote the interquartile range and data points outside this range are shown as individual dots.

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A minority of POIs account for the majority of the predicted infections

We next investigated whether it matters how we reduce mobility—that is, to which POIs. We computed the number of infections that occurred at each POI in our simulations from 1 March to 2 May 2020, and found that the majority of the predicted infections occurred at a small fraction of superspreader POIs; for example, in the Chicago metro area, 10% of POIs accounted for 85% (95% confidence interval, 83–87%) of the predicted infections at the POIs (Fig. 2b and Supplementary Fig. 10). Certain categories of POIs also contributed far more to infections (for example, full-service restaurants and hotels), although our model predicted time-dependent variation in how much each category contributed (Extended Data Fig. 2). For example, restaurants and fitness centres contributed less to the predicted number of infections over time, probably because of lockdown orders to close these POIs, whereas grocery stores remained steady or even grew in their contribution, which is in agreement with their status as essential businesses.

Reopening with a reduced maximum occupancy

If a minority of POIs produce the majority of infections, then reopening strategies that specifically target high-risk POIs should be especially effective. To test one such strategy, we simulated reopening on 1 May, and modelled the effects of reducing the maximum occupancy in which the numbers of hourly visits to each POI returned to their ‘normal’ levels from the first week of March but were capped if they exceeded a fraction of the maximum occupancy of that POI35. Full reopening without reducing the maximum occupancy produced a spike in the predicted number of infections: in the Chicago metro area, our models projected that an additional 32% (95% confidence interval, 25–35%) of the population would be infected by the end of May (Fig. 2c). However, reducing the maximum occupancy substantially reduced the risk without sharply reducing overall mobility: capping at 20% of the maximum occupancy in the Chicago metro area reduced the predicted number of new infections by more than 80% but only lost 42% of overall visits, and we observed similar trends across other metro areas (Extended Data Fig. 3). This result highlights the nonlinearity of the predicted number of infections as a function of the number of visits: one can achieve a disproportionately large reduction in infections with a small reduction in visits. Furthermore, in comparison to a different reopening strategy, in which the number of visits to each POI was uniformly reduced from their levels in early March, reducing the maximum occupancy always resulted in fewer predicted infections for the same number of total visits (Fig. 2c and Extended Data Fig. 4). This is because reducing the maximum occupancies takes advantage of the time-varying visit density within each POI, disproportionately reducing visits to the POI during the high-density periods with the highest risk, but leaving visit counts unchanged during periods with lower risks. These results support previous findings that precise interventions, such as reducing the maximum occupancy, may be more effective than less targeted measures, while incurring substantially lower economic costs36.

Relative risk of reopening different categories of POIs

Because we found that certain POI categories contributed far more to predicted infections in March (Extended Data Fig. 2), we also expected that reopening some POI categories would be riskier than reopening others. To assess this, we simulated reopening each category in turn on 1 May 2020 (by returning its mobility patterns to early March levels, as above), while keeping all other POIs at their reduced mobility levels from the end of April. We found large variation in predicted reopening risks: on average across metro areas, full-service restaurants, gyms, hotels, cafes, religious organizations and limited-service restaurants produced the largest predicted increases in infections when reopened (Extended Data Fig. 5d). Reopening full-service restaurants was associated with a particularly high risk: in the Chicago metro area, we predicted an additional 595,805 (95% confidence interval, 433,735–685,959) infections by the end of May, more than triple that of the POI category with the next highest risk (Fig. 2d). These risks are summed over all POIs in the category, but the relative risks after normalizing by the number of POIs were broadly similar (Extended Data Fig. 5c). These categories were predicted to be have a higher risk because, in the mobility data, their POIs tended to have higher visit densities and/or visitors stayed there longer (Supplementary Figs. 15–24).

Demographic disparities in infections

We characterize the differential spread of SARS-CoV-2 along demographic lines by using US census data to annotate each CBG with its racial composition and median income, then tracking predicted infection rates in CBGs with different demographic compositions: for example, within each metro area, comparing CBGs in the top and bottom deciles for income. We use this approach to study the mobility mechanisms behind disparities and to quantify how different reopening strategies affect disadvantaged groups.

Predicting disparities from mobility data

Despite having access to only mobility data and no demographic information, our models correctly predicted higher risks of infection among disadvantaged racial and socioeconomic groups2,3,4,5,6,7,8. Across all metro areas, individuals from CBGs in the bottom decile for income had a substantially higher likelihood of being infected by the end of the simulation, even though all individuals began with equal likelihoods of infection (Fig. 3a). This predicted disparity was driven primarily by a few POI categories (for example, full-service restaurants); far greater proportions of individuals from lower-income CBGs than higher-income CBGs became infected in these POIs (Fig. 3c and Supplementary Fig. 2). We similarly found that CBGs with fewer white residents had higher predicted risks of infection, although results were more variable across metro areas (Fig. 3b). In the Supplementary Discussion, we confirm that the magnitude of the disparities that our model predicts is generally consistent with real-world disparities and further explore the large predicted disparities in Philadelphia, that stem from substantial differences in the POIs that are frequented by higher- versus lower-income CBGs. In the analysis below, we discuss two mechanisms that lead higher predicted infection rates among lower-income CBGs, and we show in Extended Data Fig. 6 and Extended Data Table 4 that similar results hold for racial disparities as well.

Fig. 3: Mobility patterns give rise to infection disparities.

figure3

a, In every metro area, our model predicts that people in lower-income CBGs are likelier to be infected. b, People in non-white CBGs area are also likelier to be infected, although results are more variable across metro areas. For c–f, the Chicago metro area is used as an example, but references to results for all metro areas are provided for each panel. c, The overall predicted disparity is driven by a few POI categories such as full-service restaurants (Supplementary Fig. 2). d, One reason for the predicted disparities is that higher-income CBGs were able to reduce their mobility levels below those of lower-income CBGs (Extended Data Fig. 6). e, Within each POI category, people from lower-income CBGs tend to visit POIs that have higher predicted transmission rates (Extended Data Table 3). The size of each dot represents the average number of visits per capita made to the category. The top 10 out of 20 categories with the most visits are labelled, covering 0.48–2.88 visits per capita (hardware stores–full-service restaurants). f, Reopening (at different levels of reduced maximum occupancy) leads to more predicted infections in lower-income CBGs than in the overall population (Extended Data Fig. 3). In c–f, purple denotes lower-income CBGs, yellow denotes higher-income CBGs and blue represents the overall population. Aside from d and e, which were directly extracted from mobility data, all results in this figure represent predictions aggregated over model realizations. Across metro areas, we sample 97 parameter sets, with 30 stochastic realizations each (n = 2,910); see Supplementary Table 6 for the number of sets per metro area. Shaded regions in c and f denote the 2.5th–97.5th percentiles; boxes in (a, b) denote the interquartile range; data points outside the range are shown as individual dots.

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Lower-income CBGs saw smaller reductions in mobility

A first mechanism producing disparities was that, across all metro areas, lower-income CBGs did not reduce their mobility as sharply in the first few weeks of March 2020, and these groups showed higher mobility than higher-income CBGs for most of March–May (Fig. 3d and Extended Data Fig. 6). For example, in April, individuals from lower-income CBGs in the Chicago metro area had 27% more POI visits per capita than those from higher-income CBGs. Category-level differences in visit patterns partially explained the infection disparities within each category: for example, individuals from lower-income CBGs made substantially more visits per capita to grocery stores than did those from higher-income CBGs (Supplementary Fig. 3) and consequently experienced more predicted infections for that category (Supplementary Fig. 2).

POIs visited by lower-income CBGs have higher transmission rates

Differences in visits per capita do not fully explain the infection disparities: for example, cafes and snack bars were visited more frequently by higher-income CBGs in every metro area (Supplementary Fig. 3), but our model predicted that a larger proportion of individuals from lower-income CBGs were infected at cafes and snack bars in the majority of metro areas (Supplementary Fig. 2). We found that even within a POI category, the predicted transmission rates at POIs frequented by individuals fom lower-income CBGs tended to be higher than the corresponding rates for those from higher-income CBGs (Fig. 3e and Extended Data Table 3), because POIs frequented by individuals from lower-income CBGs tended to be smaller and more crowded in the mobility data. As a case study, we examined grocery stores in further detail. In eight of the ten metro areas, visitors from lower-income CBGs encountered higher predicted transmission rates at grocery stores than visitors from higher-income CBGs (median transmission rate ratio of 2.19) (Extended Data Table 3). We investigated why one visit to the grocery store was predicted to be twice as dangerous for an individual from a lower-income CBG: the mobility data showed that the average grocery store visited by individuals from lower-income CBGs had 59% more hourly visitors per square foot, and their visitors stayed 17% longer on average (medians across metro areas). These findings highlight how fine-grained differences in mobility patterns—how often people go out and which POIs that they go to—can ultimately contribute to marked disparities in predicted infection outcomes.

Reopening plans must account for disparate effects

Because disadvantaged groups suffer a larger burden of infection, it is critical to not only consider the overall impact of reopening plans but also their disparate effects on disadvantaged groups specifically. For example, our model predicted that full reopening in the Chicago metro area would result in an additional 39% (95% confidence interval, 31–42%) of the population of CBGs in the bottom income decile being infected within a month, compared to 32% (95% confidence interval, 25–35%) of the overall population (Fig. 3f; results for all metro areas are shown in Extended Data Fig. 3). Similarly, Supplementary Fig. 4 illustrates that reopening individual POI categories tends to have a larger predicted effect on lower-income CBGs. More stringent reopening plans produce smaller absolute disparities in predicted infections—for example, we predict that reopening at 20% of the maximum occupancy in Chicago would result in additional infections for 6% (95% confidence interval, 4–8%) of the overall population and 10% (95% confidence interval, 7–13%) of the population in CBGs in the bottom income decile (Fig. 3f)—although the relative disparity remains.

Discussion

The mobility dataset that we use has limitations: it does not cover all populations, does not contain all POIs and cannot capture sub-CBG heterogeneity. Our model itself is also parsimonious, and does not include all real-world features that are relevant to disease transmission. We discuss these limitations in more detail in the Supplementary Discussion. However, the predictive accuracy of our model suggests that it broadly captures the relationship between mobility and transmission, and we thus expect our broad conclusions—for example, that people from lower-income CBGs have higher infection rates in part because they tend to visit denser POIs and because they have not reduced mobility by as much (probably because they cannot work from home as easily4)—to hold robustly. Our fine-grained network modelling approach naturally extends to other mobility datasets and models that capture more aspects of real-world transmission, and these represent interesting directions for future work.

Our results can guide policy-makers that seek to assess competing approaches to reopening. Despite growing concern about racial and socioeconomic disparities in infections and deaths, it has been difficult for policy-makers to act on those concerns; they are currently operating without much evidence on the disparate effects of reopening policies, prompting calls for research that both identifies the causes of observed disparities and suggests policy approaches to mitigate them5,8,37,38. Our fine-grained mobility modelling addresses both these needs. Our results suggest that infection disparities are not the unavoidable consequence of factors that are difficult to address in the short term, such as differences in preexisting conditions; on the contrary, short-term policy decisions can substantially affect infection outcomes by altering the overall amount of mobility allowed and the types of POIs reopened. Considering the disparate effects of reopening plans may lead policy-makers to adopt policies that can drive down infection densities in disadvantaged neighbourhoods by supporting, for example, more stringent caps on POI occupancies, emergency food distribution centres to reduce densities in high-risk stores, free and widely available testing in neighbourhoods predicted to be high risk (especially given known disparities in access to tests2), improved paid leave policy or income support that enables essential workers to curtail mobility when sick, and improved workplace infection prevention for essential workers, such as high-quality personal protective equipment, good ventilation and physical distancing when possible. As reopening policies continue to be debated, it is critical to build tools that can assess the effectiveness and equity of different approaches. We hope that our model, by capturing heterogeneity across POIs, demographic groups and cities, helps to address this need.

Methods

The Methods is structured as follows. We describe the datasets that we used in the ‘Datasets’ section and the mobility network that we derived from these datasets in the ‘Mobility network’ section. In the ‘Model dynamics’ section, we discuss the SEIR model that we overlaid on the mobility network; in the ‘Model calibration’ section, we describe how we calibrated this model and quantified uncertainty in its predictions. Finally, in the ‘Analysis details’ section, we provide details on the experimental procedures used for our analyses of mobility reduction, reopening plans and demographic disparities.

Datasets

SafeGraph

We use data provided by SafeGraph, a company that aggregates anonymized location data from numerous mobile applications. SafeGraph data captures the movement of people between CBGs, which are geographical units that typically contain a population of between 600 and 3,000 people, and POIs such as restaurants, grocery stores or religious establishments. Specifically, we use the following SafeGraph datasets.

First, we used the Places Patterns39 and Weekly Patterns (v1)40 datasets. These datasets contain, for each POI, hourly counts of the number of visitors, estimates of median visit duration in minutes (the ‘dwell time’) and aggregated weekly and monthly estimates of the home CBGs of visitors. We use visitor home CBG data from the Places Patterns dataset: for privacy reasons, SafeGraph excludes a home CBG from this dataset if fewer than five devices were recorded at the POI from that CBG over the course of the month. For each POI, SafeGraph also provides their North American industry classification system category, as well as estimates of its physical area in square feet. The area is computed using the footprint polygon SafeGraph that assigns to the POI41,42. We analyse Places Patterns data from 1 January 2019 to 29 February 2020 and Weekly Patterns data from 1 March 2020 to 2 May 2020.

Second, we used the Social Distancing Metrics dataset43, which contains daily estimates of the proportion of people staying home in each CBG. We analyse Social Distancing Metrics data from 1 March 2020 to 2 May 2020.

We focus on 10 of the largest metro areas in the United States (Extended Data Table 1). We chose these metro areas by taking a random subset of the SafeGraph Patterns data and selecting the 10 metro areas with the most POIs in the data. The application of the methods described in this paper to the other metro areas in the original SafeGraph data should be straightforward. For each metro area, we include all POIs that meet all of the following requirements: (1) the POI is located in the metro area ; (2) SafeGraph has visit data for this POI for every hour that we model, from 00:00 on 1 March 2020 to 23:00 on 2 May 2020; (3) SafeGraph has recorded the home CBGs of visitors to this POI for at least one month from January 2019 to February 2020; (4) the POI is not a ‘parent’ POI. Parent POIs comprise a small fraction of POIs in the dataset that overlap and include the visits from their ‘child’ POIs: for example, many malls in the dataset are parent POIs, which include the visits from stores that are their child POIs. To avoid double-counting visits, we remove all parent POIs from the dataset. After applying these POI filters, we include all CBGs that have at least one recorded visit to at least ten of the remaining POIs; this means that CBGs from outside the metro area may be included if they visit this metro area frequently enough. Summary statistics of the post-processed data are shown in Extended Data Table 1. Overall, we analyse 56,945 CBGs from the 10 metro areas, and more than 310 million visits from these CBGs to 552,758 POIs.

SafeGraph data have been used to study consumer preferences44 and political polarization45. More recently, it has been used as one of the primary sources of mobility data in the USA for tracking the effects of the COVID-19 pandemic26,28,46,47,48. In Supplementary Methods section 1, we show that aggregate trends in SafeGraph mobility data match the aggregate trends in Google mobility data in the USA49, before and after the imposition of stay-at-home measures. Previous analyses of SafeGraph data have shown that it is geographically representative—for example, it does not systematically overrepresent individuals from CBGs in different counties or with different racial compositions, income levels or educational levels50,51.

US census

Our data on the demographics of the CBGs comes from the American Community Survey (ACS) of the US Census Bureau52. We use the 5-year ACS data (2013–2017) to extract the median household income, the proportion of white residents and the proportion of Black residents of each CBG. For the total population of each CBG, we use the most-recent one-year estimates (2018); one-year estimates are noisier but we wanted to minimize systematic downward bias in our total population counts (due to population growth) by making them as recent as possible.

The New York Times dataset

We calibrated our models using the COVID-19 dataset published by the The New York Times32. Their dataset consists of cumulative counts of cases and deaths in the USA over time, at the state and county level. For each metro area that we modelled, we sum over the county-level counts to produce overall counts for the entire metro area. We convert the cumulative case and death counts to daily counts for the purposes of model calibration, as described in the ‘Model calibration’ section.

Data ethics

The dataset from The New York Times consists of aggregated COVID-19-confirmed case and death counts collected by journalists from public news conferences and public data releases. For the mobility data, consent was obtained by the third-party sources that collected the data. SafeGraph aggregates data from mobile applications that obtain opt-in consent from their users to collect anonymous location data. Google’s mobility data consists of aggregated, anonymized sets of data from users who have chosen to turn on the location history setting. Additionally, we obtained IRB exemption for SafeGraph data from the Northwestern University IRB office.

Mobility network

Definition

We consider a complete undirected bipartite graph G=(V,E) with time-varying edges. The vertices V are partitioned into two disjoint sets C={c1,…,cm}, representing m CBGs, and P={p1,…,pn}, representing n POIs. From US census data, each CBG ci is labelled with its population Nci, income distribution, and racial and age demographics. From SafeGraph data, each POI pj is similarly labelled with its category (for example, restaurant, grocery store or religious organization), its physical size in square feet apj, and the median dwell time dpj of visitors to pj. The weight w(t)ij on an edge (ci, pj) at time t represents our estimate of the number of individuals from CBG ci visiting POI pj at the tth hour of simulation. We record the number of edges (with non-zero weights) in each metro area and for all hours from 1 March 2020 to 2 May 2020 in Extended Data Table 1. Across all 10 metro areas, we study 5.4 billion edges between 56,945 CBGs and 552,758 POIs.

Overview of the network estimation

The central technical challenge in constructing this network is estimating the network weights W(t)={w(t)ij} from SafeGraph data, as this visit matrix is not directly available from the data. Our general methodology for network estimation is as follows.

First, from SafeGraph data, we derived a time-independent estimate W¯ of the visit matrix that captures the aggregate distribution of visits from CBGs to POIs from January 2019 to February 2020.

Second, because visit patterns differ substantially from hour to hour (for example, day versus night) and day to day (for example, before versus after lockdown), we used current SafeGraph data to capture these hourly variations and to estimate the CBG marginals U(t), that is, the number of people in each CBG who are out visiting POIs at hour t, as well as the POI marginals V(t), that is, the total number of visitors present at each POI pj at hour t.

Finally, we applied the iterative proportional fitting procedure (IPFP) to estimate an hourly visit matrix W(t) that is consistent with the hourly marginals U(t) and V(t) but otherwise ‘as similar as possible’ to the distribution of visits in the aggregate visit matrix W¯, in terms of Kullback–Leibler divergence.

IPFP is a classic statistical method31 for adjusting joint distributions to match prespecified marginal distributions, and it is also known in the literature as biproportional fitting, the RAS algorithm or raking53. In the social sciences, it has been widely used to infer the characteristics of local subpopulations (for example, within each CBG) from aggregate data54,55,56. IPFP estimates the joint distribution of visits from CBGs to POIs by alternating between scaling each row to match the hourly row (CBG) marginals U(t) and scaling each column to match the hourly column (POI) marginals V(t). Further details about the estimation procedure are provided in Supplementary Methods section 3.

Model dynamics

To model the spread of SARS-CoV-2, we overlay a metapopulation disease transmission model on the mobility network defined in the ‘Mobility Network’ section. The transmission model structure follows previous work15,20 on epidemiological models of SARS-CoV-2 but incorporates a fine-grained mobility network into the calculations of the transmission rate. We construct separate mobility networks and models for each metropolitan statistical area.

We use a SEIR model with susceptible (S), exposed (E), infectious (I) and removed (R) compartments. Susceptible individuals have never been infected, but can acquire the virus through contact with infectious individuals, which may happen at POIs or in their home CBG. They then enter the exposed state, during which they have been infected but are not infectious yet. Individuals transition from exposed to infectious at a rate inversely proportional to the mean latency period. Finally, they transition into the removed state at a rate inversely proportional to the mean infectious period. The removed state represents individuals who can no longer be infected or infect others, for example, because they have recovered, self-isolated or died.

Each CBG ci maintains its own SEIR instantiation, with S(t)ci, E(t)ci, I(t)ci and R(t)ci representing how many individuals in CBG ci are in each disease state at hour t, and Nci=S(t)ci+E(t)ci+I(t)ci+R(t)ci. At each hour t, we sample the transitions between states as follows:

N(t)S

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## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

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https://www.nature.com/articles/s41586-020-2923-3

Mobility network models of COVID-19 explain inequities and inform reopening

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Serina Chang, Emma Pierson, Pang Wei Koh, Jaline Gerardin, Beth Redbird, David Grusky & Jure Leskovec

Nature volume 589, pages82–87(2021)Cite this article

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Abstract

The coronavirus disease 2019 (COVID-19) pandemic markedly changed human mobility patterns, necessitating epidemiological models that can capture the effects of these changes in mobility on the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)1. Here we introduce a metapopulation susceptible–exposed–infectious–removed (SEIR) model that integrates fine-grained, dynamic mobility networks to simulate the spread of SARS-CoV-2 in ten of the largest US metropolitan areas. Our mobility networks are derived from mobile phone data and map the hourly movements of 98 million people from neighbourhoods (or census block groups) to points of interest such as restaurants and religious establishments, connecting 56,945 census block groups to 552,758 points of interest with 5.4 billion hourly edges. We show that by integrating these networks, a relatively simple SEIR model can accurately fit the real case trajectory, despite substantial changes in the behaviour of the population over time. Our model predicts that a small minority of ‘superspreader’ points of interest account for a large majority of the infections, and that restricting the maximum occupancy at each point of interest is more effective than uniformly reducing mobility. Our model also correctly predicts higher infection rates among disadvantaged racial and socioeconomic groups2,3,4,5,6,7,8 solely as the result of differences in mobility: we find that disadvantaged groups have not been able to reduce their mobility as sharply, and that the points of interest that they visit are more crowded and are therefore associated with higher risk. By capturing who is infected at which locations, our model supports detailed analyses that can inform more-effective and equitable policy responses to COVID-19.

Main

In response to the COVID-19 crisis, stay-at-home orders were enacted in many countries to reduce contact between individuals and slow the spread of the SARS-CoV-29. Since then, public officials have continued to deliberate over when to reopen, which places are safe to return to and how much activity to allow10. Answering these questions requires epidemiological models that can capture the effects of changes in mobility on virus spread. In particular, findings of COVID-19 superspreader events11,12,13,14 motivate models that can reflect the heterogeneous risks of visiting different locations, whereas well-reported disparities in infection rates among different racial and socioeconomic groups2,3,4,5,6,7,8 require models that can explain the disproportionate effect of the virus on disadvantaged groups.

To address these needs, we construct fine-grained dynamic mobility networks from mobile-phone geolocation data, and use these networks to model the spread of SARS-CoV-2 within 10 of the largest metropolitan statistical areas (hereafter referred to as metro areas) in the USA. These networks map the hourly movements of 98 million people from census block groups (CBGs), which are geographical units that typically contain 600–3,000 people, to specific points of interest (POIs). As shown in Supplementary Table 1, POIs are non-residential locations that people visit such as restaurants, grocery stores and religious establishments. On top of each network, we overlay a metapopulation SEIR model that tracks the infection trajectories of each CBG as well as the POIs at which these infections are likely to have occurred. This builds on prior research that models disease spread using aggregate15,16,17,18,19, historical20,21,22 or synthetic mobility data23,24,25; separately, other studies have analysed mobility data in the context of COVID-19, but without an underlying model of disease spread26,27,28,29,30.

Combining our epidemiological model with these mobility networks allows us to not only accurately fit observed case counts, but also to conduct detailed analyses that can inform more-effective and equitable policy responses to COVID-19. By capturing information about individual POIs (for example, the hourly number of visitors and median visit duration), our model can estimate the effects of specific reopening strategies, such as only reopening certain POI categories or restricting the maximum occupancy at each POI. By modelling movement from CBGs, our model can identify at-risk populations and correctly predict, solely from mobility patterns, that disadvantaged racial and socioeconomic groups face higher rates of infection. Our model thus enables the analysis of urgent health disparities; we use it to highlight two mobility-related mechanisms that drive these disparities and to evaluate the disparate effect of reopening on disadvantaged groups.

Mobility network model

We use data from SafeGraph, a company that aggregates anonymized location data from mobile applications, to study mobility patterns from 1 March to 2 May 2020. For each metro area, we represent the movement of individuals between CBGs and POIs as a bipartite network with time-varying edges, in which the weight of an edge between a CBG and POI represents the number of visitors from that CBG to that POI during a given hour (Fig. 1a). SafeGraph also provides the area in square feet of each POI, as well as its category in the North American industry classification system (for example, fitness centre or full-service restaurant) and median visit duration in minutes. We validated the SafeGraph mobility data by comparing the dataset to Google mobility data (Supplementary Fig. 1 and Supplementary Tables 2, 3) and used iterative proportional fitting31 to derive POI–CBG networks from the raw SafeGraph data. Overall, these networks comprise 5.4 billion hourly edges between 56,945 CBGs and 552,758 POIs (Extended Data Table 1).

Fig. 1: Model description and fit.

figure1

a, The mobility network captures hourly visits from each CBG to each POI. The vertical lines indicate that most visits are between nearby POIs and CBGs. Visits dropped markedly from March to April, as indicated by the lower density of grey lines. Mobility networks in the Chicago metro area are shown for 13:00 on two Mondays, 2 March 2020 (top) and 6 April 2020 (bottom). b, We overlaid a disease-spread model on the mobility network, with each CBG having its own set of SEIR compartments. New infections occur at both POIs and CBGs, with the mobility network governing how subpopulations from different CBGs interact as they visit POIs. c, Left, to test the out-of-sample prediction, we calibrated the model on data before 15 April 2020 (vertical black line). Even though its parameters remain fixed over time, the model accurately predicts the case trajectory in the Chicago metro area after 15 April using the mobility data (r.m.s.e. on daily cases = 406 for dates ranging from 15 April to 9 May). Right, model fit was further improved when we calibrated the model on the full range of data (r.m.s.e. on daily cases = 387 for the dates ranging from 15 April to 9 May). d, We fitted separate models to 10 of the largest US metro areas, modelling a total population of 98 million people; here, we show full model fits, as in c (right). In c and d, the blue line represents the model predictions and the grey crosses represent the number of daily reported cases; as the numbers of reported cases tend to have great variability, we also show the smoothed weekly average (orange line). Shaded regions denote the 2.5th and 97.5th percentiles across parameter sets and stochastic realizations. Across metro areas, we sample 97 parameter sets, with 30 stochastic realizations each (n = 2,910); see Supplementary Table 6 for the number of sets per metro area.

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We overlay a SEIR model on each mobility network15,20, in which each CBG maintains its own susceptible (S), exposed (E), infectious (I) and removed (R) states (Fig. 1b). New infections occur at both POIs and CBGs, with the mobility network governing how subpopulations from different CBGs interact as they visit POIs. We use the area, median visit duration and time-varying density of infectious individuals for each POI to determine the hourly infection rate of that POI. The model has only three free parameters that scale: (1) transmission rates at POIs, (2) transmission rates at CBGs and (3) the initial proportion of exposed individuals (Extended Data Table 2); all three parameters remain constant over time. We calibrate a separate model for each metro area using the confirmed case counts from The New York Times by minimizing the root mean square error (r.m.s.e.) to daily incident cases32. Our model accurately fits observed daily case counts in all 10 metro areas from 8 March to 9 May 2020 (Fig. 1c, d). In addition, when calibrated on only the case counts up to 14 April, the model predicts case counts reasonably well on the held-out time period of 15 April–9 May 2020 (Fig. 1c and Extended Data Fig. 1a). Our key technical finding is that the dynamic mobility network allows even our relatively simple SEIR model with just three static parameters to accurately fit observed cases, despite changing policies and behaviours during that period.

Mobility reduction and reopening plans

We can estimate the impact of mobility-related policies by constructing a hypothetical mobility network that reflects the expected effects of each policy, and running our SEIR model forward with this hypothetical network. Using this approach, we assess a wide range of mobility reduction and reopening strategies.

The magnitude of mobility reduction is at least as important as its timing

Mobility in the USA dropped sharply in March 2020: for example, overall POI visits in the Chicago metro area fell by 54.7% between the first week of March and the first week of April 2020. We constructed counterfactual mobility networks by scaling the magnitude of mobility reduction down and by shifting the timeline earlier and later, and applied our model to the counterfactual networks to simulate the resulting infection trajectories. Across metro areas, we found that the magnitude of mobility reduction was at least as important as its timing (Fig. 2a and Supplementary Tables 4, 5): for example, if the mobility reduction in the Chicago metro area had been only a quarter of the size, the predicted number of infections would have increased by 3.3× (95% confidence interval, 2.8–3.8×), compared with a 1.5× (95% confidence interval, 1.4–1.6×) increase had people begun reducing their mobility one full week later. Furthermore, if no mobility reduction had occurred at all, the predicted number of infections in the Chicago metro area would have increased by 6.2× (95% confidence interval, 5.2–7.1×). Our results are in accordance with previous findings that mobility reductions can markedly reduce infections18,19,33,34.

Fig. 2: Assessing mobility reduction and reopening.

figure2

The Chicago metro area is used as an example; results for all metro areas are included in Extended Data Figs. 3, 4, Supplementary Figs. 10, 15–24 and Supplementary Tables 4, 5, as indicated. a, Counterfactual simulations (left) of past reductions in mobility illustrate that the magnitude of the reduction (middle) was at least as important as its timing (right) (Supplementary Tables 4, 5). b, The model predicts that most infections at POIs occur at a small fraction of superspreader POIs (Supplementary Fig. 10). c, Left, the cumulative number of predicted infections after one month of reopening is plotted against the fraction of visits lost by partial instead of full reopening (Extended Data Fig. 3); the annotations within the plot show the fraction of maximum occupancy that is used as the cap and the horizontal red line indicates the cumulative number of predicted infections at the point of reopening (on 1 May 2020). Compared to full reopening, capping at 20% of the maximum occupancy in Chicago reduces the number of new infections by more than 80%, while only losing 42% of overall visits. Right, compared to uniformly reducing visits, the reduced maximum occupancy strategy always results in a smaller predicted increase in infections for the same number of visits (Extended Data Fig. 4). The horizontal grey line at 0% indicates when the two strategies result in an equal number of infections, and we observe that the curve falls well below this baseline. The y axis plots the relative difference between the predicted number of new infections under the reduced occupancy strategy compared to a uniform reduction. d, Reopening full-service restaurants has the largest predicted impact on infections, due to the large number of restaurants as well as their high visit densities and long dwell times (Supplementary Figs. 15–24). Colours are used to distinguish the different POI categories, but do not have any additional meaning. All results in this figure are aggregated across 4 parameter sets and 30 stochastic realizations (n = 120). Shaded regions in a–c denote the 2.5th to 97.5th percentiles; boxes in d denote the interquartile range and data points outside this range are shown as individual dots.

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A minority of POIs account for the majority of the predicted infections

We next investigated whether it matters how we reduce mobility—that is, to which POIs. We computed the number of infections that occurred at each POI in our simulations from 1 March to 2 May 2020, and found that the majority of the predicted infections occurred at a small fraction of superspreader POIs; for example, in the Chicago metro area, 10% of POIs accounted for 85% (95% confidence interval, 83–87%) of the predicted infections at the POIs (Fig. 2b and Supplementary Fig. 10). Certain categories of POIs also contributed far more to infections (for example, full-service restaurants and hotels), although our model predicted time-dependent variation in how much each category contributed (Extended Data Fig. 2). For example, restaurants and fitness centres contributed less to the predicted number of infections over time, probably because of lockdown orders to close these POIs, whereas grocery stores remained steady or even grew in their contribution, which is in agreement with their status as essential businesses.

Reopening with a reduced maximum occupancy

If a minority of POIs produce the majority of infections, then reopening strategies that specifically target high-risk POIs should be especially effective. To test one such strategy, we simulated reopening on 1 May, and modelled the effects of reducing the maximum occupancy in which the numbers of hourly visits to each POI returned to their ‘normal’ levels from the first week of March but were capped if they exceeded a fraction of the maximum occupancy of that POI35. Full reopening without reducing the maximum occupancy produced a spike in the predicted number of infections: in the Chicago metro area, our models projected that an additional 32% (95% confidence interval, 25–35%) of the population would be infected by the end of May (Fig. 2c). However, reducing the maximum occupancy substantially reduced the risk without sharply reducing overall mobility: capping at 20% of the maximum occupancy in the Chicago metro area reduced the predicted number of new infections by more than 80% but only lost 42% of overall visits, and we observed similar trends across other metro areas (Extended Data Fig. 3). This result highlights the nonlinearity of the predicted number of infections as a function of the number of visits: one can achieve a disproportionately large reduction in infections with a small reduction in visits. Furthermore, in comparison to a different reopening strategy, in which the number of visits to each POI was uniformly reduced from their levels in early March, reducing the maximum occupancy always resulted in fewer predicted infections for the same number of total visits (Fig. 2c and Extended Data Fig. 4). This is because reducing the maximum occupancies takes advantage of the time-varying visit density within each POI, disproportionately reducing visits to the POI during the high-density periods with the highest risk, but leaving visit counts unchanged during periods with lower risks. These results support previous findings that precise interventions, such as reducing the maximum occupancy, may be more effective than less targeted measures, while incurring substantially lower economic costs36.

Relative risk of reopening different categories of POIs

Because we found that certain POI categories contributed far more to predicted infections in March (Extended Data Fig. 2), we also expected that reopening some POI categories would be riskier than reopening others. To assess this, we simulated reopening each category in turn on 1 May 2020 (by returning its mobility patterns to early March levels, as above), while keeping all other POIs at their reduced mobility levels from the end of April. We found large variation in predicted reopening risks: on average across metro areas, full-service restaurants, gyms, hotels, cafes, religious organizations and limited-service restaurants produced the largest predicted increases in infections when reopened (Extended Data Fig. 5d). Reopening full-service restaurants was associated with a particularly high risk: in the Chicago metro area, we predicted an additional 595,805 (95% confidence interval, 433,735–685,959) infections by the end of May, more than triple that of the POI category with the next highest risk (Fig. 2d). These risks are summed over all POIs in the category, but the relative risks after normalizing by the number of POIs were broadly similar (Extended Data Fig. 5c). These categories were predicted to be have a higher risk because, in the mobility data, their POIs tended to have higher visit densities and/or visitors stayed there longer (Supplementary Figs. 15–24).

Demographic disparities in infections

We characterize the differential spread of SARS-CoV-2 along demographic lines by using US census data to annotate each CBG with its racial composition and median income, then tracking predicted infection rates in CBGs with different demographic compositions: for example, within each metro area, comparing CBGs in the top and bottom deciles for income. We use this approach to study the mobility mechanisms behind disparities and to quantify how different reopening strategies affect disadvantaged groups.

Predicting disparities from mobility data

Despite having access to only mobility data and no demographic information, our models correctly predicted higher risks of infection among disadvantaged racial and socioeconomic groups2,3,4,5,6,7,8. Across all metro areas, individuals from CBGs in the bottom decile for income had a substantially higher likelihood of being infected by the end of the simulation, even though all individuals began with equal likelihoods of infection (Fig. 3a). This predicted disparity was driven primarily by a few POI categories (for example, full-service restaurants); far greater proportions of individuals from lower-income CBGs than higher-income CBGs became infected in these POIs (Fig. 3c and Supplementary Fig. 2). We similarly found that CBGs with fewer white residents had higher predicted risks of infection, although results were more variable across metro areas (Fig. 3b). In the Supplementary Discussion, we confirm that the magnitude of the disparities that our model predicts is generally consistent with real-world disparities and further explore the large predicted disparities in Philadelphia, that stem from substantial differences in the POIs that are frequented by higher- versus lower-income CBGs. In the analysis below, we discuss two mechanisms that lead higher predicted infection rates among lower-income CBGs, and we show in Extended Data Fig. 6 and Extended Data Table 4 that similar results hold for racial disparities as well.

Fig. 3: Mobility patterns give rise to infection disparities.

figure3

a, In every metro area, our model predicts that people in lower-income CBGs are likelier to be infected. b, People in non-white CBGs area are also likelier to be infected, although results are more variable across metro areas. For c–f, the Chicago metro area is used as an example, but references to results for all metro areas are provided for each panel. c, The overall predicted disparity is driven by a few POI categories such as full-service restaurants (Supplementary Fig. 2). d, One reason for the predicted disparities is that higher-income CBGs were able to reduce their mobility levels below those of lower-income CBGs (Extended Data Fig. 6). e, Within each POI category, people from lower-income CBGs tend to visit POIs that have higher predicted transmission rates (Extended Data Table 3). The size of each dot represents the average number of visits per capita made to the category. The top 10 out of 20 categories with the most visits are labelled, covering 0.48–2.88 visits per capita (hardware stores–full-service restaurants). f, Reopening (at different levels of reduced maximum occupancy) leads to more predicted infections in lower-income CBGs than in the overall population (Extended Data Fig. 3). In c–f, purple denotes lower-income CBGs, yellow denotes higher-income CBGs and blue represents the overall population. Aside from d and e, which were directly extracted from mobility data, all results in this figure represent predictions aggregated over model realizations. Across metro areas, we sample 97 parameter sets, with 30 stochastic realizations each (n = 2,910); see Supplementary Table 6 for the number of sets per metro area. Shaded regions in c and f denote the 2.5th–97.5th percentiles; boxes in (a, b) denote the interquartile range; data points outside the range are shown as individual dots.

Full size image

Lower-income CBGs saw smaller reductions in mobility

A first mechanism producing disparities was that, across all metro areas, lower-income CBGs did not reduce their mobility as sharply in the first few weeks of March 2020, and these groups showed higher mobility than higher-income CBGs for most of March–May (Fig. 3d and Extended Data Fig. 6). For example, in April, individuals from lower-income CBGs in the Chicago metro area had 27% more POI visits per capita than those from higher-income CBGs. Category-level differences in visit patterns partially explained the infection disparities within each category: for example, individuals from lower-income CBGs made substantially more visits per capita to grocery stores than did those from higher-income CBGs (Supplementary Fig. 3) and consequently experienced more predicted infections for that category (Supplementary Fig. 2).

POIs visited by lower-income CBGs have higher transmission rates

Differences in visits per capita do not fully explain the infection disparities: for example, cafes and snack bars were visited more frequently by higher-income CBGs in every metro area (Supplementary Fig. 3), but our model predicted that a larger proportion of individuals from lower-income CBGs were infected at cafes and snack bars in the majority of metro areas (Supplementary Fig. 2). We found that even within a POI category, the predicted transmission rates at POIs frequented by individuals fom lower-income CBGs tended to be higher than the corresponding rates for those from higher-income CBGs (Fig. 3e and Extended Data Table 3), because POIs frequented by individuals from lower-income CBGs tended to be smaller and more crowded in the mobility data. As a case study, we examined grocery stores in further detail. In eight of the ten metro areas, visitors from lower-income CBGs encountered higher predicted transmission rates at grocery stores than visitors from higher-income CBGs (median transmission rate ratio of 2.19) (Extended Data Table 3). We investigated why one visit to the grocery store was predicted to be twice as dangerous for an individual from a lower-income CBG: the mobility data showed that the average grocery store visited by individuals from lower-income CBGs had 59% more hourly visitors per square foot, and their visitors stayed 17% longer on average (medians across metro areas). These findings highlight how fine-grained differences in mobility patterns—how often people go out and which POIs that they go to—can ultimately contribute to marked disparities in predicted infection outcomes.

Reopening plans must account for disparate effects

Because disadvantaged groups suffer a larger burden of infection, it is critical to not only consider the overall impact of reopening plans but also their disparate effects on disadvantaged groups specifically. For example, our model predicted that full reopening in the Chicago metro area would result in an additional 39% (95% confidence interval, 31–42%) of the population of CBGs in the bottom income decile being infected within a month, compared to 32% (95% confidence interval, 25–35%) of the overall population (Fig. 3f; results for all metro areas are shown in Extended Data Fig. 3). Similarly, Supplementary Fig. 4 illustrates that reopening individual POI categories tends to have a larger predicted effect on lower-income CBGs. More stringent reopening plans produce smaller absolute disparities in predicted infections—for example, we predict that reopening at 20% of the maximum occupancy in Chicago would result in additional infections for 6% (95% confidence interval, 4–8%) of the overall population and 10% (95% confidence interval, 7–13%) of the population in CBGs in the bottom income decile (Fig. 3f)—although the relative disparity remains.

Discussion

The mobility dataset that we use has limitations: it does not cover all populations, does not contain all POIs and cannot capture sub-CBG heterogeneity. Our model itself is also parsimonious, and does not include all real-world features that are relevant to disease transmission. We discuss these limitations in more detail in the Supplementary Discussion. However, the predictive accuracy of our model suggests that it broadly captures the relationship between mobility and transmission, and we thus expect our broad conclusions—for example, that people from lower-income CBGs have higher infection rates in part because they tend to visit denser POIs and because they have not reduced mobility by as much (probably because they cannot work from home as easily4)—to hold robustly. Our fine-grained network modelling approach naturally extends to other mobility datasets and models that capture more aspects of real-world transmission, and these represent interesting directions for future work.

Our results can guide policy-makers that seek to assess competing approaches to reopening. Despite growing concern about racial and socioeconomic disparities in infections and deaths, it has been difficult for policy-makers to act on those concerns; they are currently operating without much evidence on the disparate effects of reopening policies, prompting calls for research that both identifies the causes of observed disparities and suggests policy approaches to mitigate them5,8,37,38. Our fine-grained mobility modelling addresses both these needs. Our results suggest that infection disparities are not the unavoidable consequence of factors that are difficult to address in the short term, such as differences in preexisting conditions; on the contrary, short-term policy decisions can substantially affect infection outcomes by altering the overall amount of mobility allowed and the types of POIs reopened. Considering the disparate effects of reopening plans may lead policy-makers to adopt policies that can drive down infection densities in disadvantaged neighbourhoods by supporting, for example, more stringent caps on POI occupancies, emergency food distribution centres to reduce densities in high-risk stores, free and widely available testing in neighbourhoods predicted to be high risk (especially given known disparities in access to tests2), improved paid leave policy or income support that enables essential workers to curtail mobility when sick, and improved workplace infection prevention for essential workers, such as high-quality personal protective equipment, good ventilation and physical distancing when possible. As reopening policies continue to be debated, it is critical to build tools that can assess the effectiveness and equity of different approaches. We hope that our model, by capturing heterogeneity across POIs, demographic groups and cities, helps to address this need.

Methods

The Methods is structured as follows. We describe the datasets that we used in the ‘Datasets’ section and the mobility network that we derived from these datasets in the ‘Mobility network’ section. In the ‘Model dynamics’ section, we discuss the SEIR model that we overlaid on the mobility network; in the ‘Model calibration’ section, we describe how we calibrated this model and quantified uncertainty in its predictions. Finally, in the ‘Analysis details’ section, we provide details on the experimental procedures used for our analyses of mobility reduction, reopening plans and demographic disparities.

Datasets

SafeGraph

We use data provided by SafeGraph, a company that aggregates anonymized location data from numerous mobile applications. SafeGraph data captures the movement of people between CBGs, which are geographical units that typically contain a population of between 600 and 3,000 people, and POIs such as restaurants, grocery stores or religious establishments. Specifically, we use the following SafeGraph datasets.

First, we used the Places Patterns39 and Weekly Patterns (v1)40 datasets. These datasets contain, for each POI, hourly counts of the number of visitors, estimates of median visit duration in minutes (the ‘dwell time’) and aggregated weekly and monthly estimates of the home CBGs of visitors. We use visitor home CBG data from the Places Patterns dataset: for privacy reasons, SafeGraph excludes a home CBG from this dataset if fewer than five devices were recorded at the POI from that CBG over the course of the month. For each POI, SafeGraph also provides their North American industry classification system category, as well as estimates of its physical area in square feet. The area is computed using the footprint polygon SafeGraph that assigns to the POI41,42. We analyse Places Patterns data from 1 January 2019 to 29 February 2020 and Weekly Patterns data from 1 March 2020 to 2 May 2020.

Second, we used the Social Distancing Metrics dataset43, which contains daily estimates of the proportion of people staying home in each CBG. We analyse Social Distancing Metrics data from 1 March 2020 to 2 May 2020.

We focus on 10 of the largest metro areas in the United States (Extended Data Table 1). We chose these metro areas by taking a random subset of the SafeGraph Patterns data and selecting the 10 metro areas with the most POIs in the data. The application of the methods described in this paper to the other metro areas in the original SafeGraph data should be straightforward. For each metro area, we include all POIs that meet all of the following requirements: (1) the POI is located in the metro area ; (2) SafeGraph has visit data for this POI for every hour that we model, from 00:00 on 1 March 2020 to 23:00 on 2 May 2020; (3) SafeGraph has recorded the home CBGs of visitors to this POI for at least one month from January 2019 to February 2020; (4) the POI is not a ‘parent’ POI. Parent POIs comprise a small fraction of POIs in the dataset that overlap and include the visits from their ‘child’ POIs: for example, many malls in the dataset are parent POIs, which include the visits from stores that are their child POIs. To avoid double-counting visits, we remove all parent POIs from the dataset. After applying these POI filters, we include all CBGs that have at least one recorded visit to at least ten of the remaining POIs; this means that CBGs from outside the metro area may be included if they visit this metro area frequently enough. Summary statistics of the post-processed data are shown in Extended Data Table 1. Overall, we analyse 56,945 CBGs from the 10 metro areas, and more than 310 million visits from these CBGs to 552,758 POIs.

SafeGraph data have been used to study consumer preferences44 and political polarization45. More recently, it has been used as one of the primary sources of mobility data in the USA for tracking the effects of the COVID-19 pandemic26,28,46,47,48. In Supplementary Methods section 1, we show that aggregate trends in SafeGraph mobility data match the aggregate trends in Google mobility data in the USA49, before and after the imposition of stay-at-home measures. Previous analyses of SafeGraph data have shown that it is geographically representative—for example, it does not systematically overrepresent individuals from CBGs in different counties or with different racial compositions, income levels or educational levels50,51.

US census

Our data on the demographics of the CBGs comes from the American Community Survey (ACS) of the US Census Bureau52. We use the 5-year ACS data (2013–2017) to extract the median household income, the proportion of white residents and the proportion of Black residents of each CBG. For the total population of each CBG, we use the most-recent one-year estimates (2018); one-year estimates are noisier but we wanted to minimize systematic downward bias in our total population counts (due to population growth) by making them as recent as possible.

The New York Times dataset

We calibrated our models using the COVID-19 dataset published by the The New York Times32. Their dataset consists of cumulative counts of cases and deaths in the USA over time, at the state and county level. For each metro area that we modelled, we sum over the county-level counts to produce overall counts for the entire metro area. We convert the cumulative case and death counts to daily counts for the purposes of model calibration, as described in the ‘Model calibration’ section.

Data ethics

The dataset from The New York Times consists of aggregated COVID-19-confirmed case and death counts collected by journalists from public news conferences and public data releases. For the mobility data, consent was obtained by the third-party sources that collected the data. SafeGraph aggregates data from mobile applications that obtain opt-in consent from their users to collect anonymous location data. Google’s mobility data consists of aggregated, anonymized sets of data from users who have chosen to turn on the location history setting. Additionally, we obtained IRB exemption for SafeGraph data from the Northwestern University IRB office.

Mobility network

Definition

We consider a complete undirected bipartite graph G=(V,E) with time-varying edges. The vertices V are partitioned into two disjoint sets C={c1,…,cm}, representing m CBGs, and P={p1,…,pn}, representing n POIs. From US census data, each CBG ci is labelled with its population Nci, income distribution, and racial and age demographics. From SafeGraph data, each POI pj is similarly labelled with its category (for example, restaurant, grocery store or religious organization), its physical size in square feet apj, and the median dwell time dpj of visitors to pj. The weight w(t)ij on an edge (ci, pj) at time t represents our estimate of the number of individuals from CBG ci visiting POI pj at the tth hour of simulation. We record the number of edges (with non-zero weights) in each metro area and for all hours from 1 March 2020 to 2 May 2020 in Extended Data Table 1. Across all 10 metro areas, we study 5.4 billion edges between 56,945 CBGs and 552,758 POIs.

Overview of the network estimation

The central technical challenge in constructing this network is estimating the network weights W(t)={w(t)ij} from SafeGraph data, as this visit matrix is not directly available from the data. Our general methodology for network estimation is as follows.

First, from SafeGraph data, we derived a time-independent estimate W¯ of the visit matrix that captures the aggregate distribution of visits from CBGs to POIs from January 2019 to February 2020.

Second, because visit patterns differ substantially from hour to hour (for example, day versus night) and day to day (for example, before versus after lockdown), we used current SafeGraph data to capture these hourly variations and to estimate the CBG marginals U(t), that is, the number of people in each CBG who are out visiting POIs at hour t, as well as the POI marginals V(t), that is, the total number of visitors present at each POI pj at hour t.

Finally, we applied the iterative proportional fitting procedure (IPFP) to estimate an hourly visit matrix W(t) that is consistent with the hourly marginals U(t) and V(t) but otherwise ‘as similar as possible’ to the distribution of visits in the aggregate visit matrix W¯, in terms of Kullback–Leibler divergence.

IPFP is a classic statistical method31 for adjusting joint distributions to match prespecified marginal distributions, and it is also known in the literature as biproportional fitting, the RAS algorithm or raking53. In the social sciences, it has been widely used to infer the characteristics of local subpopulations (for example, within each CBG) from aggregate data54,55,56. IPFP estimates the joint distribution of visits from CBGs to POIs by alternating between scaling each row to match the hourly row (CBG) marginals U(t) and scaling each column to match the hourly column (POI) marginals V(t). Further details about the estimation procedure are provided in Supplementary Methods section 3.

Model dynamics

To model the spread of SARS-CoV-2, we overlay a metapopulation disease transmission model on the mobility network defined in the ‘Mobility Network’ section. The transmission model structure follows previous work15,20 on epidemiological models of SARS-CoV-2 but incorporates a fine-grained mobility network into the calculations of the transmission rate. We construct separate mobility networks and models for each metropolitan statistical area.

We use a SEIR model with susceptible (S), exposed (E), infectious (I) and removed (R) compartments. Susceptible individuals have never been infected, but can acquire the virus through contact with infectious individuals, which may happen at POIs or in their home CBG. They then enter the exposed state, during which they have been infected but are not infectious yet. Individuals transition from exposed to infectious at a rate inversely proportional to the mean latency period. Finally, they transition into the removed state at a rate inversely proportional to the mean infectious period. The removed state represents individuals who can no longer be infected or infect others, for example, because they have recovered, self-isolated or died.

Each CBG ci maintains its own SEIR instantiation, with S(t)ci, E(t)ci, I(t)ci and R(t)ci representing how many individuals in CBG ci are in each disease state at hour t, and Nci=S(t)ci+E(t)ci+I(t)ci+R(t)ci. At each hour t, we sample the transitions between states as follows:

N(t)S

¿Esto es el kernel de Windows?

No lo citeis mas que si no la pagina se hace horrible

Y eso que Eric no le ha dado dos veces al botón.

**Poisonblade**- Mensajes : 49856

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## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@morley escribió:Ayer se abrió un debate sobre qué solución proponemos los que criticamos las medidas.

Mi opinión sobre las medidas que se deberían tomar o no tomar es compleja. Yo mismo la tengo que poner negro sobre blanco para aclararme un poco. Lo único que sé es que es un problema dilemático y aporético y que toda solución que pase por defender solo uno de los extremos economía-salud cae inmediatamente en el desastre.

Debajo está el problema más de fondo sobre qué consideramos una vida digna de ser vivida y si tiene mucho sentido una vida desnuda en la que solo se valora la mera supervivencia por encima de otros valores y derechos como la libertad negativa y positiva. Este problema parece algo que es fácilmente prorrogable y que la situación actual nos urge a posponerlo para otro momento menos crítico. Pero ese es el gran problema, porque si abrimos ese melón ahora cualquier otro momento futuro de crisis social va a justificar restricciones como los que estamos viviendo.

Sobre el tema de las medidas que tomaría eso es más jodido. Supongo que intentaría fundamentarlas en algún principio que considero rector. Ya que vivimos en sociedad y estamos ante un problema de salud pública de índole social en el que siempre se alude a la responsabilidad del ciudadano para anteponer lo colectivo a lo personal, pondremos que el principio más importante que tiene que informar cualquier medidas el de la justicia y el de solidaridad. Dicho en otras palabras, el de "o jugamos todos o rompemos el tapete" o "o pringamos todos o rompemos el contrato social". Ese parece haber sido el principio que ha justificado muchas de las medidas restrictivas (acertadas o no, aquí no me voy a meter porque ese es otro melón), sobre todo en un primer confinamiento total. Lo que sí tengo claro desde este principio es que de ninguna manera la vía para solucionar el problema puede ser DISCRECIONAL. No se puede cerrar un sector o sectores de manera discrecional justificando un bien superior de índole colectivo, al menos si no viene acompañado de un esfuerzo colectivo en forma de impuesto covid para compensar el agravio y las pérdidas del sector sacrificado. Si el Estado no puede pagar una ayuda igual o incluso mayor al daño ocasionado, las medidas son injustas y se cargan el contrato social. Justificando de esta forma que un colectivo tenga razones suficientes para considerar el Estado como algo simplemente impuesto desde arriba al que hay que combatir. Por eso mí única convicción en todo este asunto es que es absolutamente ilegítimo y perjudicial para el orden social medidas de cierres discrecionales.

El problema es que en esta segunda fase de la pandemia las decisiones políticas ya no se han basado en la justicia o la solidaridad. Se han basado en un supuesto balance de costes-beneficios dejando de lado los otros valores. Una parte de la sociedad ha visto cómo la dejaban atrás cuando ella en todo momento ha contribuido a ese supuesto principio de solidaridad y anteposición del bien común al individual. Lo único que puede salir de todo esto es una sociedad deslegitimada y mucho más fragmentada.

En resumen, no tengo muy claro lo que se debería hacer en un plano coyuntural e inmediato más allá de que no se tome ninguna medida discrecional sin que esta no sea apoyada por un esfuerzo en forma de impuesto del resto de ciudadanos, especialmente de las rentas medias-altas y altas. En el plano estructural de largo plazo todos o muchos nos podríamos poner de acuerdo en que el problema es que las instituciones están vaciadas, que no tienen poder real ni recursos y que la solución para que esto no vuelva a suceder pasa por fortalecerlas.

Y perdón por el ladrillo.

Me parece muy interesante el modo en que lo enfocas y lo comparto. Creo que primero de todo hay que plantear a que estamos jugando, porque el juego es muy distinto depende de donde se mire. Traer a colación el contrato social lo veo muy oportuno, de fondo creo que se está debilitando, aproximándose al papel mojado según el caso, y encima con instituciones debilitadas o deslegitimadas para defenderlo, como también apuntas.

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## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

*Respecto al mayor número de sintomáticos detectados, asegura que los contactos localizados siguen superando el 40% y que hay una situación en la que el incremento de los contagios hace que haya más enfermos. El aumento de sintomáticos, dice, significa que los ciudadanos ya saben que deben llamar a Osakidetza.*

El incremento de sintomáticos va relacionado con el aumento de la positividad. Ya que los que no se detectan suelen ser asintomáticos. Pero vamos, que pueden vender lo que quieran.

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## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Poisonblade escribió:@Dumbie escribió:

https://www.nature.com/articles/s41586-020-2923-3

Mobility network models of COVID-19 explain inequities and inform reopening

- Spoiler:

Serina Chang, Emma Pierson, Pang Wei Koh, Jaline Gerardin, Beth Redbird, David Grusky & Jure Leskovec

Nature volume 589, pages82–87(2021)Cite this article

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Abstract

The coronavirus disease 2019 (COVID-19) pandemic markedly changed human mobility patterns, necessitating epidemiological models that can capture the effects of these changes in mobility on the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)1. Here we introduce a metapopulation susceptible–exposed–infectious–removed (SEIR) model that integrates fine-grained, dynamic mobility networks to simulate the spread of SARS-CoV-2 in ten of the largest US metropolitan areas. Our mobility networks are derived from mobile phone data and map the hourly movements of 98 million people from neighbourhoods (or census block groups) to points of interest such as restaurants and religious establishments, connecting 56,945 census block groups to 552,758 points of interest with 5.4 billion hourly edges. We show that by integrating these networks, a relatively simple SEIR model can accurately fit the real case trajectory, despite substantial changes in the behaviour of the population over time. Our model predicts that a small minority of ‘superspreader’ points of interest account for a large majority of the infections, and that restricting the maximum occupancy at each point of interest is more effective than uniformly reducing mobility. Our model also correctly predicts higher infection rates among disadvantaged racial and socioeconomic groups2,3,4,5,6,7,8 solely as the result of differences in mobility: we find that disadvantaged groups have not been able to reduce their mobility as sharply, and that the points of interest that they visit are more crowded and are therefore associated with higher risk. By capturing who is infected at which locations, our model supports detailed analyses that can inform more-effective and equitable policy responses to COVID-19.

Main

In response to the COVID-19 crisis, stay-at-home orders were enacted in many countries to reduce contact between individuals and slow the spread of the SARS-CoV-29. Since then, public officials have continued to deliberate over when to reopen, which places are safe to return to and how much activity to allow10. Answering these questions requires epidemiological models that can capture the effects of changes in mobility on virus spread. In particular, findings of COVID-19 superspreader events11,12,13,14 motivate models that can reflect the heterogeneous risks of visiting different locations, whereas well-reported disparities in infection rates among different racial and socioeconomic groups2,3,4,5,6,7,8 require models that can explain the disproportionate effect of the virus on disadvantaged groups.

To address these needs, we construct fine-grained dynamic mobility networks from mobile-phone geolocation data, and use these networks to model the spread of SARS-CoV-2 within 10 of the largest metropolitan statistical areas (hereafter referred to as metro areas) in the USA. These networks map the hourly movements of 98 million people from census block groups (CBGs), which are geographical units that typically contain 600–3,000 people, to specific points of interest (POIs). As shown in Supplementary Table 1, POIs are non-residential locations that people visit such as restaurants, grocery stores and religious establishments. On top of each network, we overlay a metapopulation SEIR model that tracks the infection trajectories of each CBG as well as the POIs at which these infections are likely to have occurred. This builds on prior research that models disease spread using aggregate15,16,17,18,19, historical20,21,22 or synthetic mobility data23,24,25; separately, other studies have analysed mobility data in the context of COVID-19, but without an underlying model of disease spread26,27,28,29,30.

Combining our epidemiological model with these mobility networks allows us to not only accurately fit observed case counts, but also to conduct detailed analyses that can inform more-effective and equitable policy responses to COVID-19. By capturing information about individual POIs (for example, the hourly number of visitors and median visit duration), our model can estimate the effects of specific reopening strategies, such as only reopening certain POI categories or restricting the maximum occupancy at each POI. By modelling movement from CBGs, our model can identify at-risk populations and correctly predict, solely from mobility patterns, that disadvantaged racial and socioeconomic groups face higher rates of infection. Our model thus enables the analysis of urgent health disparities; we use it to highlight two mobility-related mechanisms that drive these disparities and to evaluate the disparate effect of reopening on disadvantaged groups.

Mobility network model

We use data from SafeGraph, a company that aggregates anonymized location data from mobile applications, to study mobility patterns from 1 March to 2 May 2020. For each metro area, we represent the movement of individuals between CBGs and POIs as a bipartite network with time-varying edges, in which the weight of an edge between a CBG and POI represents the number of visitors from that CBG to that POI during a given hour (Fig. 1a). SafeGraph also provides the area in square feet of each POI, as well as its category in the North American industry classification system (for example, fitness centre or full-service restaurant) and median visit duration in minutes. We validated the SafeGraph mobility data by comparing the dataset to Google mobility data (Supplementary Fig. 1 and Supplementary Tables 2, 3) and used iterative proportional fitting31 to derive POI–CBG networks from the raw SafeGraph data. Overall, these networks comprise 5.4 billion hourly edges between 56,945 CBGs and 552,758 POIs (Extended Data Table 1).

Fig. 1: Model description and fit.

figure1

a, The mobility network captures hourly visits from each CBG to each POI. The vertical lines indicate that most visits are between nearby POIs and CBGs. Visits dropped markedly from March to April, as indicated by the lower density of grey lines. Mobility networks in the Chicago metro area are shown for 13:00 on two Mondays, 2 March 2020 (top) and 6 April 2020 (bottom). b, We overlaid a disease-spread model on the mobility network, with each CBG having its own set of SEIR compartments. New infections occur at both POIs and CBGs, with the mobility network governing how subpopulations from different CBGs interact as they visit POIs. c, Left, to test the out-of-sample prediction, we calibrated the model on data before 15 April 2020 (vertical black line). Even though its parameters remain fixed over time, the model accurately predicts the case trajectory in the Chicago metro area after 15 April using the mobility data (r.m.s.e. on daily cases = 406 for dates ranging from 15 April to 9 May). Right, model fit was further improved when we calibrated the model on the full range of data (r.m.s.e. on daily cases = 387 for the dates ranging from 15 April to 9 May). d, We fitted separate models to 10 of the largest US metro areas, modelling a total population of 98 million people; here, we show full model fits, as in c (right). In c and d, the blue line represents the model predictions and the grey crosses represent the number of daily reported cases; as the numbers of reported cases tend to have great variability, we also show the smoothed weekly average (orange line). Shaded regions denote the 2.5th and 97.5th percentiles across parameter sets and stochastic realizations. Across metro areas, we sample 97 parameter sets, with 30 stochastic realizations each (n = 2,910); see Supplementary Table 6 for the number of sets per metro area.

Full size image

We overlay a SEIR model on each mobility network15,20, in which each CBG maintains its own susceptible (S), exposed (E), infectious (I) and removed (R) states (Fig. 1b). New infections occur at both POIs and CBGs, with the mobility network governing how subpopulations from different CBGs interact as they visit POIs. We use the area, median visit duration and time-varying density of infectious individuals for each POI to determine the hourly infection rate of that POI. The model has only three free parameters that scale: (1) transmission rates at POIs, (2) transmission rates at CBGs and (3) the initial proportion of exposed individuals (Extended Data Table 2); all three parameters remain constant over time. We calibrate a separate model for each metro area using the confirmed case counts from The New York Times by minimizing the root mean square error (r.m.s.e.) to daily incident cases32. Our model accurately fits observed daily case counts in all 10 metro areas from 8 March to 9 May 2020 (Fig. 1c, d). In addition, when calibrated on only the case counts up to 14 April, the model predicts case counts reasonably well on the held-out time period of 15 April–9 May 2020 (Fig. 1c and Extended Data Fig. 1a). Our key technical finding is that the dynamic mobility network allows even our relatively simple SEIR model with just three static parameters to accurately fit observed cases, despite changing policies and behaviours during that period.

Mobility reduction and reopening plans

We can estimate the impact of mobility-related policies by constructing a hypothetical mobility network that reflects the expected effects of each policy, and running our SEIR model forward with this hypothetical network. Using this approach, we assess a wide range of mobility reduction and reopening strategies.

The magnitude of mobility reduction is at least as important as its timing

Mobility in the USA dropped sharply in March 2020: for example, overall POI visits in the Chicago metro area fell by 54.7% between the first week of March and the first week of April 2020. We constructed counterfactual mobility networks by scaling the magnitude of mobility reduction down and by shifting the timeline earlier and later, and applied our model to the counterfactual networks to simulate the resulting infection trajectories. Across metro areas, we found that the magnitude of mobility reduction was at least as important as its timing (Fig. 2a and Supplementary Tables 4, 5): for example, if the mobility reduction in the Chicago metro area had been only a quarter of the size, the predicted number of infections would have increased by 3.3× (95% confidence interval, 2.8–3.8×), compared with a 1.5× (95% confidence interval, 1.4–1.6×) increase had people begun reducing their mobility one full week later. Furthermore, if no mobility reduction had occurred at all, the predicted number of infections in the Chicago metro area would have increased by 6.2× (95% confidence interval, 5.2–7.1×). Our results are in accordance with previous findings that mobility reductions can markedly reduce infections18,19,33,34.

Fig. 2: Assessing mobility reduction and reopening.

figure2

The Chicago metro area is used as an example; results for all metro areas are included in Extended Data Figs. 3, 4, Supplementary Figs. 10, 15–24 and Supplementary Tables 4, 5, as indicated. a, Counterfactual simulations (left) of past reductions in mobility illustrate that the magnitude of the reduction (middle) was at least as important as its timing (right) (Supplementary Tables 4, 5). b, The model predicts that most infections at POIs occur at a small fraction of superspreader POIs (Supplementary Fig. 10). c, Left, the cumulative number of predicted infections after one month of reopening is plotted against the fraction of visits lost by partial instead of full reopening (Extended Data Fig. 3); the annotations within the plot show the fraction of maximum occupancy that is used as the cap and the horizontal red line indicates the cumulative number of predicted infections at the point of reopening (on 1 May 2020). Compared to full reopening, capping at 20% of the maximum occupancy in Chicago reduces the number of new infections by more than 80%, while only losing 42% of overall visits. Right, compared to uniformly reducing visits, the reduced maximum occupancy strategy always results in a smaller predicted increase in infections for the same number of visits (Extended Data Fig. 4). The horizontal grey line at 0% indicates when the two strategies result in an equal number of infections, and we observe that the curve falls well below this baseline. The y axis plots the relative difference between the predicted number of new infections under the reduced occupancy strategy compared to a uniform reduction. d, Reopening full-service restaurants has the largest predicted impact on infections, due to the large number of restaurants as well as their high visit densities and long dwell times (Supplementary Figs. 15–24). Colours are used to distinguish the different POI categories, but do not have any additional meaning. All results in this figure are aggregated across 4 parameter sets and 30 stochastic realizations (n = 120). Shaded regions in a–c denote the 2.5th to 97.5th percentiles; boxes in d denote the interquartile range and data points outside this range are shown as individual dots.

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A minority of POIs account for the majority of the predicted infections

We next investigated whether it matters how we reduce mobility—that is, to which POIs. We computed the number of infections that occurred at each POI in our simulations from 1 March to 2 May 2020, and found that the majority of the predicted infections occurred at a small fraction of superspreader POIs; for example, in the Chicago metro area, 10% of POIs accounted for 85% (95% confidence interval, 83–87%) of the predicted infections at the POIs (Fig. 2b and Supplementary Fig. 10). Certain categories of POIs also contributed far more to infections (for example, full-service restaurants and hotels), although our model predicted time-dependent variation in how much each category contributed (Extended Data Fig. 2). For example, restaurants and fitness centres contributed less to the predicted number of infections over time, probably because of lockdown orders to close these POIs, whereas grocery stores remained steady or even grew in their contribution, which is in agreement with their status as essential businesses.

Reopening with a reduced maximum occupancy

If a minority of POIs produce the majority of infections, then reopening strategies that specifically target high-risk POIs should be especially effective. To test one such strategy, we simulated reopening on 1 May, and modelled the effects of reducing the maximum occupancy in which the numbers of hourly visits to each POI returned to their ‘normal’ levels from the first week of March but were capped if they exceeded a fraction of the maximum occupancy of that POI35. Full reopening without reducing the maximum occupancy produced a spike in the predicted number of infections: in the Chicago metro area, our models projected that an additional 32% (95% confidence interval, 25–35%) of the population would be infected by the end of May (Fig. 2c). However, reducing the maximum occupancy substantially reduced the risk without sharply reducing overall mobility: capping at 20% of the maximum occupancy in the Chicago metro area reduced the predicted number of new infections by more than 80% but only lost 42% of overall visits, and we observed similar trends across other metro areas (Extended Data Fig. 3). This result highlights the nonlinearity of the predicted number of infections as a function of the number of visits: one can achieve a disproportionately large reduction in infections with a small reduction in visits. Furthermore, in comparison to a different reopening strategy, in which the number of visits to each POI was uniformly reduced from their levels in early March, reducing the maximum occupancy always resulted in fewer predicted infections for the same number of total visits (Fig. 2c and Extended Data Fig. 4). This is because reducing the maximum occupancies takes advantage of the time-varying visit density within each POI, disproportionately reducing visits to the POI during the high-density periods with the highest risk, but leaving visit counts unchanged during periods with lower risks. These results support previous findings that precise interventions, such as reducing the maximum occupancy, may be more effective than less targeted measures, while incurring substantially lower economic costs36.

Relative risk of reopening different categories of POIs

Because we found that certain POI categories contributed far more to predicted infections in March (Extended Data Fig. 2), we also expected that reopening some POI categories would be riskier than reopening others. To assess this, we simulated reopening each category in turn on 1 May 2020 (by returning its mobility patterns to early March levels, as above), while keeping all other POIs at their reduced mobility levels from the end of April. We found large variation in predicted reopening risks: on average across metro areas, full-service restaurants, gyms, hotels, cafes, religious organizations and limited-service restaurants produced the largest predicted increases in infections when reopened (Extended Data Fig. 5d). Reopening full-service restaurants was associated with a particularly high risk: in the Chicago metro area, we predicted an additional 595,805 (95% confidence interval, 433,735–685,959) infections by the end of May, more than triple that of the POI category with the next highest risk (Fig. 2d). These risks are summed over all POIs in the category, but the relative risks after normalizing by the number of POIs were broadly similar (Extended Data Fig. 5c). These categories were predicted to be have a higher risk because, in the mobility data, their POIs tended to have higher visit densities and/or visitors stayed there longer (Supplementary Figs. 15–24).

Demographic disparities in infections

We characterize the differential spread of SARS-CoV-2 along demographic lines by using US census data to annotate each CBG with its racial composition and median income, then tracking predicted infection rates in CBGs with different demographic compositions: for example, within each metro area, comparing CBGs in the top and bottom deciles for income. We use this approach to study the mobility mechanisms behind disparities and to quantify how different reopening strategies affect disadvantaged groups.

Predicting disparities from mobility data

Despite having access to only mobility data and no demographic information, our models correctly predicted higher risks of infection among disadvantaged racial and socioeconomic groups2,3,4,5,6,7,8. Across all metro areas, individuals from CBGs in the bottom decile for income had a substantially higher likelihood of being infected by the end of the simulation, even though all individuals began with equal likelihoods of infection (Fig. 3a). This predicted disparity was driven primarily by a few POI categories (for example, full-service restaurants); far greater proportions of individuals from lower-income CBGs than higher-income CBGs became infected in these POIs (Fig. 3c and Supplementary Fig. 2). We similarly found that CBGs with fewer white residents had higher predicted risks of infection, although results were more variable across metro areas (Fig. 3b). In the Supplementary Discussion, we confirm that the magnitude of the disparities that our model predicts is generally consistent with real-world disparities and further explore the large predicted disparities in Philadelphia, that stem from substantial differences in the POIs that are frequented by higher- versus lower-income CBGs. In the analysis below, we discuss two mechanisms that lead higher predicted infection rates among lower-income CBGs, and we show in Extended Data Fig. 6 and Extended Data Table 4 that similar results hold for racial disparities as well.

Fig. 3: Mobility patterns give rise to infection disparities.

figure3

a, In every metro area, our model predicts that people in lower-income CBGs are likelier to be infected. b, People in non-white CBGs area are also likelier to be infected, although results are more variable across metro areas. For c–f, the Chicago metro area is used as an example, but references to results for all metro areas are provided for each panel. c, The overall predicted disparity is driven by a few POI categories such as full-service restaurants (Supplementary Fig. 2). d, One reason for the predicted disparities is that higher-income CBGs were able to reduce their mobility levels below those of lower-income CBGs (Extended Data Fig. 6). e, Within each POI category, people from lower-income CBGs tend to visit POIs that have higher predicted transmission rates (Extended Data Table 3). The size of each dot represents the average number of visits per capita made to the category. The top 10 out of 20 categories with the most visits are labelled, covering 0.48–2.88 visits per capita (hardware stores–full-service restaurants). f, Reopening (at different levels of reduced maximum occupancy) leads to more predicted infections in lower-income CBGs than in the overall population (Extended Data Fig. 3). In c–f, purple denotes lower-income CBGs, yellow denotes higher-income CBGs and blue represents the overall population. Aside from d and e, which were directly extracted from mobility data, all results in this figure represent predictions aggregated over model realizations. Across metro areas, we sample 97 parameter sets, with 30 stochastic realizations each (n = 2,910); see Supplementary Table 6 for the number of sets per metro area. Shaded regions in c and f denote the 2.5th–97.5th percentiles; boxes in (a, b) denote the interquartile range; data points outside the range are shown as individual dots.

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Lower-income CBGs saw smaller reductions in mobility

A first mechanism producing disparities was that, across all metro areas, lower-income CBGs did not reduce their mobility as sharply in the first few weeks of March 2020, and these groups showed higher mobility than higher-income CBGs for most of March–May (Fig. 3d and Extended Data Fig. 6). For example, in April, individuals from lower-income CBGs in the Chicago metro area had 27% more POI visits per capita than those from higher-income CBGs. Category-level differences in visit patterns partially explained the infection disparities within each category: for example, individuals from lower-income CBGs made substantially more visits per capita to grocery stores than did those from higher-income CBGs (Supplementary Fig. 3) and consequently experienced more predicted infections for that category (Supplementary Fig. 2).

POIs visited by lower-income CBGs have higher transmission rates

Differences in visits per capita do not fully explain the infection disparities: for example, cafes and snack bars were visited more frequently by higher-income CBGs in every metro area (Supplementary Fig. 3), but our model predicted that a larger proportion of individuals from lower-income CBGs were infected at cafes and snack bars in the majority of metro areas (Supplementary Fig. 2). We found that even within a POI category, the predicted transmission rates at POIs frequented by individuals fom lower-income CBGs tended to be higher than the corresponding rates for those from higher-income CBGs (Fig. 3e and Extended Data Table 3), because POIs frequented by individuals from lower-income CBGs tended to be smaller and more crowded in the mobility data. As a case study, we examined grocery stores in further detail. In eight of the ten metro areas, visitors from lower-income CBGs encountered higher predicted transmission rates at grocery stores than visitors from higher-income CBGs (median transmission rate ratio of 2.19) (Extended Data Table 3). We investigated why one visit to the grocery store was predicted to be twice as dangerous for an individual from a lower-income CBG: the mobility data showed that the average grocery store visited by individuals from lower-income CBGs had 59% more hourly visitors per square foot, and their visitors stayed 17% longer on average (medians across metro areas). These findings highlight how fine-grained differences in mobility patterns—how often people go out and which POIs that they go to—can ultimately contribute to marked disparities in predicted infection outcomes.

Reopening plans must account for disparate effects

Because disadvantaged groups suffer a larger burden of infection, it is critical to not only consider the overall impact of reopening plans but also their disparate effects on disadvantaged groups specifically. For example, our model predicted that full reopening in the Chicago metro area would result in an additional 39% (95% confidence interval, 31–42%) of the population of CBGs in the bottom income decile being infected within a month, compared to 32% (95% confidence interval, 25–35%) of the overall population (Fig. 3f; results for all metro areas are shown in Extended Data Fig. 3). Similarly, Supplementary Fig. 4 illustrates that reopening individual POI categories tends to have a larger predicted effect on lower-income CBGs. More stringent reopening plans produce smaller absolute disparities in predicted infections—for example, we predict that reopening at 20% of the maximum occupancy in Chicago would result in additional infections for 6% (95% confidence interval, 4–8%) of the overall population and 10% (95% confidence interval, 7–13%) of the population in CBGs in the bottom income decile (Fig. 3f)—although the relative disparity remains.

Discussion

The mobility dataset that we use has limitations: it does not cover all populations, does not contain all POIs and cannot capture sub-CBG heterogeneity. Our model itself is also parsimonious, and does not include all real-world features that are relevant to disease transmission. We discuss these limitations in more detail in the Supplementary Discussion. However, the predictive accuracy of our model suggests that it broadly captures the relationship between mobility and transmission, and we thus expect our broad conclusions—for example, that people from lower-income CBGs have higher infection rates in part because they tend to visit denser POIs and because they have not reduced mobility by as much (probably because they cannot work from home as easily4)—to hold robustly. Our fine-grained network modelling approach naturally extends to other mobility datasets and models that capture more aspects of real-world transmission, and these represent interesting directions for future work.

Our results can guide policy-makers that seek to assess competing approaches to reopening. Despite growing concern about racial and socioeconomic disparities in infections and deaths, it has been difficult for policy-makers to act on those concerns; they are currently operating without much evidence on the disparate effects of reopening policies, prompting calls for research that both identifies the causes of observed disparities and suggests policy approaches to mitigate them5,8,37,38. Our fine-grained mobility modelling addresses both these needs. Our results suggest that infection disparities are not the unavoidable consequence of factors that are difficult to address in the short term, such as differences in preexisting conditions; on the contrary, short-term policy decisions can substantially affect infection outcomes by altering the overall amount of mobility allowed and the types of POIs reopened. Considering the disparate effects of reopening plans may lead policy-makers to adopt policies that can drive down infection densities in disadvantaged neighbourhoods by supporting, for example, more stringent caps on POI occupancies, emergency food distribution centres to reduce densities in high-risk stores, free and widely available testing in neighbourhoods predicted to be high risk (especially given known disparities in access to tests2), improved paid leave policy or income support that enables essential workers to curtail mobility when sick, and improved workplace infection prevention for essential workers, such as high-quality personal protective equipment, good ventilation and physical distancing when possible. As reopening policies continue to be debated, it is critical to build tools that can assess the effectiveness and equity of different approaches. We hope that our model, by capturing heterogeneity across POIs, demographic groups and cities, helps to address this need.

Methods

The Methods is structured as follows. We describe the datasets that we used in the ‘Datasets’ section and the mobility network that we derived from these datasets in the ‘Mobility network’ section. In the ‘Model dynamics’ section, we discuss the SEIR model that we overlaid on the mobility network; in the ‘Model calibration’ section, we describe how we calibrated this model and quantified uncertainty in its predictions. Finally, in the ‘Analysis details’ section, we provide details on the experimental procedures used for our analyses of mobility reduction, reopening plans and demographic disparities.

Datasets

SafeGraph

We use data provided by SafeGraph, a company that aggregates anonymized location data from numerous mobile applications. SafeGraph data captures the movement of people between CBGs, which are geographical units that typically contain a population of between 600 and 3,000 people, and POIs such as restaurants, grocery stores or religious establishments. Specifically, we use the following SafeGraph datasets.

First, we used the Places Patterns39 and Weekly Patterns (v1)40 datasets. These datasets contain, for each POI, hourly counts of the number of visitors, estimates of median visit duration in minutes (the ‘dwell time’) and aggregated weekly and monthly estimates of the home CBGs of visitors. We use visitor home CBG data from the Places Patterns dataset: for privacy reasons, SafeGraph excludes a home CBG from this dataset if fewer than five devices were recorded at the POI from that CBG over the course of the month. For each POI, SafeGraph also provides their North American industry classification system category, as well as estimates of its physical area in square feet. The area is computed using the footprint polygon SafeGraph that assigns to the POI41,42. We analyse Places Patterns data from 1 January 2019 to 29 February 2020 and Weekly Patterns data from 1 March 2020 to 2 May 2020.

Second, we used the Social Distancing Metrics dataset43, which contains daily estimates of the proportion of people staying home in each CBG. We analyse Social Distancing Metrics data from 1 March 2020 to 2 May 2020.

We focus on 10 of the largest metro areas in the United States (Extended Data Table 1). We chose these metro areas by taking a random subset of the SafeGraph Patterns data and selecting the 10 metro areas with the most POIs in the data. The application of the methods described in this paper to the other metro areas in the original SafeGraph data should be straightforward. For each metro area, we include all POIs that meet all of the following requirements: (1) the POI is located in the metro area ; (2) SafeGraph has visit data for this POI for every hour that we model, from 00:00 on 1 March 2020 to 23:00 on 2 May 2020; (3) SafeGraph has recorded the home CBGs of visitors to this POI for at least one month from January 2019 to February 2020; (4) the POI is not a ‘parent’ POI. Parent POIs comprise a small fraction of POIs in the dataset that overlap and include the visits from their ‘child’ POIs: for example, many malls in the dataset are parent POIs, which include the visits from stores that are their child POIs. To avoid double-counting visits, we remove all parent POIs from the dataset. After applying these POI filters, we include all CBGs that have at least one recorded visit to at least ten of the remaining POIs; this means that CBGs from outside the metro area may be included if they visit this metro area frequently enough. Summary statistics of the post-processed data are shown in Extended Data Table 1. Overall, we analyse 56,945 CBGs from the 10 metro areas, and more than 310 million visits from these CBGs to 552,758 POIs.

SafeGraph data have been used to study consumer preferences44 and political polarization45. More recently, it has been used as one of the primary sources of mobility data in the USA for tracking the effects of the COVID-19 pandemic26,28,46,47,48. In Supplementary Methods section 1, we show that aggregate trends in SafeGraph mobility data match the aggregate trends in Google mobility data in the USA49, before and after the imposition of stay-at-home measures. Previous analyses of SafeGraph data have shown that it is geographically representative—for example, it does not systematically overrepresent individuals from CBGs in different counties or with different racial compositions, income levels or educational levels50,51.

US census

Our data on the demographics of the CBGs comes from the American Community Survey (ACS) of the US Census Bureau52. We use the 5-year ACS data (2013–2017) to extract the median household income, the proportion of white residents and the proportion of Black residents of each CBG. For the total population of each CBG, we use the most-recent one-year estimates (2018); one-year estimates are noisier but we wanted to minimize systematic downward bias in our total population counts (due to population growth) by making them as recent as possible.

The New York Times dataset

We calibrated our models using the COVID-19 dataset published by the The New York Times32. Their dataset consists of cumulative counts of cases and deaths in the USA over time, at the state and county level. For each metro area that we modelled, we sum over the county-level counts to produce overall counts for the entire metro area. We convert the cumulative case and death counts to daily counts for the purposes of model calibration, as described in the ‘Model calibration’ section.

Data ethics

The dataset from The New York Times consists of aggregated COVID-19-confirmed case and death counts collected by journalists from public news conferences and public data releases. For the mobility data, consent was obtained by the third-party sources that collected the data. SafeGraph aggregates data from mobile applications that obtain opt-in consent from their users to collect anonymous location data. Google’s mobility data consists of aggregated, anonymized sets of data from users who have chosen to turn on the location history setting. Additionally, we obtained IRB exemption for SafeGraph data from the Northwestern University IRB office.

Mobility network

Definition

We consider a complete undirected bipartite graph G=(V,E) with time-varying edges. The vertices V are partitioned into two disjoint sets C={c1,…,cm}, representing m CBGs, and P={p1,…,pn}, representing n POIs. From US census data, each CBG ci is labelled with its population Nci, income distribution, and racial and age demographics. From SafeGraph data, each POI pj is similarly labelled with its category (for example, restaurant, grocery store or religious organization), its physical size in square feet apj, and the median dwell time dpj of visitors to pj. The weight w(t)ij on an edge (ci, pj) at time t represents our estimate of the number of individuals from CBG ci visiting POI pj at the tth hour of simulation. We record the number of edges (with non-zero weights) in each metro area and for all hours from 1 March 2020 to 2 May 2020 in Extended Data Table 1. Across all 10 metro areas, we study 5.4 billion edges between 56,945 CBGs and 552,758 POIs.

Overview of the network estimation

The central technical challenge in constructing this network is estimating the network weights W(t)={w(t)ij} from SafeGraph data, as this visit matrix is not directly available from the data. Our general methodology for network estimation is as follows.

First, from SafeGraph data, we derived a time-independent estimate W¯ of the visit matrix that captures the aggregate distribution of visits from CBGs to POIs from January 2019 to February 2020.

Second, because visit patterns differ substantially from hour to hour (for example, day versus night) and day to day (for example, before versus after lockdown), we used current SafeGraph data to capture these hourly variations and to estimate the CBG marginals U(t), that is, the number of people in each CBG who are out visiting POIs at hour t, as well as the POI marginals V(t), that is, the total number of visitors present at each POI pj at hour t.

Finally, we applied the iterative proportional fitting procedure (IPFP) to estimate an hourly visit matrix W(t) that is consistent with the hourly marginals U(t) and V(t) but otherwise ‘as similar as possible’ to the distribution of visits in the aggregate visit matrix W¯, in terms of Kullback–Leibler divergence.

IPFP is a classic statistical method31 for adjusting joint distributions to match prespecified marginal distributions, and it is also known in the literature as biproportional fitting, the RAS algorithm or raking53. In the social sciences, it has been widely used to infer the characteristics of local subpopulations (for example, within each CBG) from aggregate data54,55,56. IPFP estimates the joint distribution of visits from CBGs to POIs by alternating between scaling each row to match the hourly row (CBG) marginals U(t) and scaling each column to match the hourly column (POI) marginals V(t). Further details about the estimation procedure are provided in Supplementary Methods section 3.

Model dynamics

To model the spread of SARS-CoV-2, we overlay a metapopulation disease transmission model on the mobility network defined in the ‘Mobility Network’ section. The transmission model structure follows previous work15,20 on epidemiological models of SARS-CoV-2 but incorporates a fine-grained mobility network into the calculations of the transmission rate. We construct separate mobility networks and models for each metropolitan statistical area.

We use a SEIR model with susceptible (S), exposed (E), infectious (I) and removed (R) compartments. Susceptible individuals have never been infected, but can acquire the virus through contact with infectious individuals, which may happen at POIs or in their home CBG. They then enter the exposed state, during which they have been infected but are not infectious yet. Individuals transition from exposed to infectious at a rate inversely proportional to the mean latency period. Finally, they transition into the removed state at a rate inversely proportional to the mean infectious period. The removed state represents individuals who can no longer be infected or infect others, for example, because they have recovered, self-isolated or died.

Each CBG ci maintains its own SEIR instantiation, with S(t)ci, E(t)ci, I(t)ci and R(t)ci representing how many individuals in CBG ci are in each disease state at hour t, and Nci=S(t)ci+E(t)ci+I(t)ci+R(t)ci. At each hour t, we sample the transitions between states as follows:

N(t)S

¿Esto es el kernel de Windows?

No lo citeis mas que si no la pagina se hace horrible

Y eso que Eric no le ha dado dos veces al botón.

Muy interesante

**disturbiau**- Mensajes : 31343

Fecha de inscripción : 11/04/2016

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@morley escribió:@iontxu escribió:@morley escribió:Puto fetichismo del dato, ni en las grandes guerras habría partes diarios de bajas.

Datos para asustar y concienciar a una sociedad egoísta que hasta que no les toca de cerca no son conscientes de lo peligroso que es y seguramente que a muchos les importa bien poco que su familia muera o se contagie.

Veo muchas variantes del egoísmo en los tiempos que corren, qué queréis que os diga

**Godofredo**- Mensajes : 122000

Fecha de inscripción : 25/03/2008

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Poisonblade escribió:@Toro escribió:@Reckoner escribió:Lo he leído en el Zorreo.

Es oficial si, lo han transmitido en rueda de prensa.

No entiendo la excusa de que el cierre a las 19 va vinculado al toque de queda, no le veo el sentido, si lo quieres hacer lo puedes hacer, y no estoy diciendo que haya que hacerlo, hablo de que nos están mareando y diría que intencionadamente.

Es que el cierre a las 19h es una consecuencia del toque de queda a las 20h, por eso no lo han puesto.

Si pero a lo que me refiero, que entonces no quieren poner cierre a las 19. Quieren poner toque de queda a las 20, y punto.

Consecuencia de eso cerrarían los negocios a las 19, pero llevamos un par de días mareando con lo de las 19, y no es ninguna medida que quieran poner...

Es que quieren toque de queda a las 20 y lo que conlleve y ya... porque cerrar a las 19 pueden ordenarlo.

Es como si antes del cierre municipal dijeran que querían cerrar los municipios a las 20, y luego no hay toque de queda a las 20 y dicen, no, los dejamos abiertos hasta las 22, entonces no quieres cerrar municipios a las 20, no nos marees...

Que a lo mejor quien están mareando son los medios y no ellos eh! que todo puede ser

**Toro**- Mensajes : 20775

Fecha de inscripción : 14/05/2010

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

A Eric como mucho citadle en spoiler por Dio!!

**Toro**- Mensajes : 20775

Fecha de inscripción : 14/05/2010

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

Santo dios un quote más a eric sachs y me implota el móvil

**Eristoff**- Mensajes : 5672

Fecha de inscripción : 23/11/2017

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Toro escribió:@Reckoner escribió:Lo he leído en el Zorreo.

Es oficial si, lo han transmitido en rueda de prensa.

No entiendo la excusa de que el cierre a las 19 va vinculado al toque de queda, no le veo el sentido, si lo quieres hacer lo puedes hacer, y no estoy diciendo que haya que hacerlo, hablo de que nos están mareando y diría que intencionadamente.

Cuando habla de Hosteleria y restauración cierre a las ocho, quiere decir que también el take awy a las ocho? Porque les mata a ciertos restaurantes que podrían seguir viviendo.

En octubre si lo hicieron, luego lo llevaron hasta las nueve recoger el locar y nueve y media con servicio a domicilio (creo).

**Abuelo81**- Mensajes : 7735

Fecha de inscripción : 21/11/2017

## Re: ☣ CORONAVIRUS ☣ - Minuto y Reconfinado - Vol.121: Surfeando La Tercera Ola

@Toro escribió:@Poisonblade escribió:@Reckoner escribió:Lo he leído en el Zorreo.

Es oficial si, lo han transmitido en rueda de prensa.

No entiendo la excusa de que el cierre a las 19 va vinculado al toque de queda, no le veo el sentido, si lo quieres hacer lo puedes hacer, y no estoy diciendo que haya que hacerlo, hablo de que nos están mareando y diría que intencionadamente.

Es que el cierre a las 19h es una consecuencia del toque de queda a las 20h, por eso no lo han puesto.

Si pero a lo que me refiero, que entonces no quieren poner cierre a las 19. Quieren poner toque de queda a las 20, y punto.

Consecuencia de eso cerrarían los negocios a las 19, pero llevamos un par de días mareando con lo de las 19, y no es ninguna medida que quieran poner...

Es que quieren toque de queda a las 20 y lo que conlleve y ya... porque cerrar a las 19 pueden ordenarlo.

Es como si antes del cierre municipal dijeran que querían cerrar los municipios a las 20, y luego no hay toque de queda a las 20 y dicen, no, los dejamos abiertos hasta las 22, entonces no quieres cerrar municipios a las 20, no nos marees...Que a lo mejor quien están mareando son los medios y no ellos eh! que todo puede ser

Puede ser, no he visto las ruedas de prensa de estos días.

**Poisonblade**- Mensajes : 49856

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