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Social heterogeneity and the COVID-19 lockdown in a multi-group SEIR model

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Date
2020-05
Collection title
Cahier de recherche du CEREMADE
Link to item file
https://doi.org/10.1101/2020.05.15.20103010
Dewey
Analyse
Sujet
Epidemic models; Disease control; Heterogeneous populations; Basic reproduction ratio; Equilibrium solutions; COVID-19
URI
https://basepub.dauphine.fr/handle/123456789/20781
Collections
  • CEREMADE : Publications
Metadata
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Author
Dolbeault, Jean
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Turinici, Gabriel
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
10
Abstract (EN)
The goal of the lockdown is to mitigate and if possible prevent the spread of an epidemic. It consists in reducing social interactions. This is taken into account by the introduction of a factor of reduction of social interactions q, and by decreasing the transmission coefficient of the disease accordingly. Evaluating q is a difficult question and one can ask if it makes sense to compute an average coefficient q for a given population, in order to make predictions on the basic reproduction rate R0, the dynamics of the epidemic or the fraction of the population that will have been infected by the end of the epidemic. On a very simple example, we show that the computation of R0 in a heterogeneous population is not reduced to the computation of an average q but rather to the direct computation of an average coefficient R0. Even more interesting is the fact that, in a range of data compatible with the Covid-19 outbreak, the size of the epidemic is deeply modified by social heterogeneity, as is the height of the epidemic peak, while the date at which it is reached mainly depends on the average R0 coefficient. This short note is an application and a summary of the technical results that can be found in J. Dolbeault and G. Turinici, Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model.

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