Math. Model. Nat. Phenom.
Volume 15, 2020
Coronavirus: Scientific insights and societal aspects
|Number of page(s)||18|
|Published online||14 July 2020|
Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model
CEREMADE (CNRS UMR n° 7534), PSL university, Université Paris-Dauphine, Place de Lattre de Tassigny,
* Corresponding author: email@example.com
Accepted: 28 June 2020
We study variants of the SEIR model for interpreting some qualitative features of the statistics of the Covid-19 epidemic in France. Standard SEIR models distinguish essentially two regimes: either the disease is controlled and the number of infected people rapidly decreases, or the disease spreads and contaminates a significant fraction of the population until herd immunity is achieved. After lockdown, at first sight it seems that social distancing is not enough to control the outbreak. We discuss here a possible explanation, namely that the lockdown is creating social heterogeneity: even if a large majority of the population complies with the lockdown rules, a small fraction of the population still has to maintain a normal or high level of social interactions, such as health workers, providers of essential services, etc. This results in an apparent high level of epidemic propagation as measured through re-estimations of the basic reproduction ratio. However, these measures are limited to averages, while variance inside the population plays an essential role on the peak and the size of the epidemic outbreak and tends to lower these two indicators. We provide theoretical and numerical results to sustain such a view.
Mathematics Subject Classification: 92C60 / 92D30 / 34C60
Key words: Epidemic models / disease control / heterogeneous populations / basic reproduction ratio / equilibrium solutions
© The authors. Published by EDP Sciences, 2020
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