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

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 gettin...

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Bibliographic Details
Published inMathematical modelling of natural phenomena Vol. 15; p. 35
Main Authors Elie, Romuald, Hubert, Emma, Turinici, Gabriel
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 2020
SeriesCoronavirus: Scientific insights and societal aspects
Subjects
Biodiversity
Coronaviruses
COVID-19
Disease control
Disease transmission
Divergence
Epidemics
Life Sciences
Mathematical models
Mathematics
Optimization
Optimization and Control
Pandemics
Populations and Evolution
Sensitivity analysis
Social factors
Social interactions
Viral diseases
Viruses
COVID-19
SARS-CoV-2
Epidemic control
Mean Field Games
SIR model
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Summary: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.
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ISSN:0973-5348
1760-6101
DOI:10.1051/mmnp/2020022