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EDP Sciences, Mathematical Modelling of Natural Phenomena, (15), p. 35, 2020

DOI: 10.1051/mmnp/2020022



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Contact rate epidemic control of COVID-19: an equilibrium view

Journal article published in 2020 by Romuald Elie, Emma Hubert, Gabriel Turinici ORCID
This paper was not found in any repository, but could be made available legally by the author.
This paper was not found in any repository, but could be made available legally by the author.

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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.