Nash-MFG equilibrium in a SIR model with time dependent newborn vaccination

Emma Hubert (1) , Gabriel Turinici (1, 2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 IUF - Institut universitaire de France

We study the newborn, non compulsory, vaccination in a SIR model with vital dynamics. The evolution of each individual is modeled as a Markov chain. His/Her vaccination decision optimizes a criterion depending on the time-dependent aggregate (societal) vaccination rate and the future epidemic dynamics. We prove the existence of a Nash - Mean Field Games equilibrium among all individuals in the population. Then we propose a novel numerical approach to find the equilibrium and test it numerically.

Mots clés: vaccination games; Mean Field Games; vaccination; SIR model; Nash equilibrium; vaccination eficacy; individual vaccination

Domaines: Analyse numérique [math.NA]

Emma Hubert, Gabriel Turinici. Nash-MFG equilibrium in a SIR model with time dependent newborn vaccination. Ricerche di matematica, 2018, Demographic and temporal heterogeneity in infectious disease epidemiology, 67 (1), pp.227--246. ⟨10.1007/s11587-018-0365-0⟩. ⟨hal-01389584v2⟩