Math. Model. Nat. Phenom.
Volume 15, 2020
Coronavirus: Scientific insights and societal aspects
|Number of page(s)||25|
|Published online||19 June 2020|
Contact rate epidemic control of COVID-19: an equilibrium view
LAMA – UMR 8050, Université Gustave Eiffel,
2 CEREMADE – UMR 7534, Université Paris Dauphine, PSL Research University, France
* Corresponding author: firstname.lastname@example.org
Accepted: 29 May 2020
We consider the control of the COVID-19 pandemic through a standard SIR compartmental model. This control is induced by the aggregation of individuals’ decisions to limit their social interactions: when the epidemic is ongoing, an individual can diminish his/her contact rate in order to avoid getting infected, but this effort comes at a social cost. If each individual lowers his/her contact rate, the epidemic vanishes faster, but the effort cost may be high. A Mean Field Nash equilibrium at the population level is formed, resulting in a lower effective transmission rate of the virus. We prove theoretically that equilibrium exists and compute it numerically. However, this equilibrium selects a sub-optimal solution in comparison to the societal optimum (a centralized decision respected fully by all individuals), meaning that the cost of anarchy is strictly positive. We provide numerical examples and a sensitivity analysis, as well as an extension to a SEIR compartmental model to account for the relatively long latent phase of the COVID-19 disease. In all the scenario considered, the divergence between the individual and societal strategies happens both before the peak of the epidemic, due to individuals’ fears, and after, when a significant propagation is still underway.
Mathematics Subject Classification: 92D30 / 92Bxx / 91A16
Key words: COVID-19 / SARS-CoV-2 / epidemic control / SEIR model / Mean Field Games
© The authors. Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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