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

hal.structure.identifierLaboratoire Analyse et Mathématiques Appliquées [LAMA]
dc.contributor.authorElie, Romuald*
hal.structure.identifierLaboratoire Analyse et Mathématiques Appliquées [LAMA]
dc.contributor.authorHubert, Emma
HAL ID: 175536		*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorTurinici, Gabriel
HAL ID: 16
ORCID: 0000-0003-2713-006X		*
dc.date.accessioned2020-06-08T12:22:55Z
dc.date.available2020-06-08T12:22:55Z
dc.date.issued2020
dc.identifier.issn0973-5348
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20842
dc.language.isoenen
dc.subjectCOVID-19
dc.subjectSARS-CoV-2
dc.subjectEpidemic control
dc.subjectSIR model
dc.subjectMean Field Games
dc.subject.ddc515en
dc.titleContact rate epidemic control of COVID-19: an equilibrium view
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe 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.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameMathematical Modelling of Natural Phenomena
dc.relation.isversionofjnlvol15
dc.relation.isversionofjnlissue35
dc.relation.isversionofjnldate2020
dc.relation.isversionofjnlpages25
dc.relation.isversionofdoi10.1051/mmnp/2020022
dc.subject.ddclabelAnalyseen
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dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-10-07T09:19:16Z
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