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

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Contact_rate_epidemic_control_of_COVID_19__an_equilibrium_view__1_.pdf (651.1Kb)
Date
2020
Publisher city
Paris
Dewey
Analyse
Sujet
COVID-19; SARS-CoV-2; Epidemic control; SIR model; Mean Field Games
Journal issue
Mathematical Modelling of Natural Phenomena
Volume
15
Number
35
Publication date
2020
Article pages
25
DOI
http://dx.doi.org/10.1051/mmnp/2020022
URI
https://basepub.dauphine.fr/handle/123456789/20842
Collections
  • CEREMADE : Publications
Metadata
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Author
Elie, Romuald
1004422 Laboratoire Analyse et Mathématiques Appliquées [LAMA]
Hubert, Emma
1004422 Laboratoire Analyse et Mathématiques Appliquées [LAMA]
Turinici, Gabriel
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
We consider the control of the COVID-19 pandemic, modeled by a standard SIR com-partmental model. The control of the epidemic is induced by the aggregation of individuals' decisions to limit their social interactions: on one side, when the epidemic is ongoing, an individual is encouraged to diminish his/her contact rate in order to avoid getting infected, but, on the other side, 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. However, it is not clear that the individual's interest aligns with that of the society. We prove that the equilibrium exists and compute it numerically. The 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. We show that the divergence between the individual and societal strategies happens after the epidemic peak but while significant propagation is still underway.

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