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

Hubert, Emma; Turinici, Gabriel (2018), Nash-MFG equilibrium in a SIR model with time dependent newborn vaccination, Ricerche di Matematica, 67, 1, p. 227-246. 10.1007/s11587-018-0365-0

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01389584
Date
2018
Journal name
Ricerche di Matematica
Volume
67
Number
1
Publisher
Springer
Pages
227-246
Publication identifier
Metadata
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Author(s)
Hubert, Emma
Turinici, Gabriel cc
Abstract (EN)
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.
Subjects / Keywords
Nash equilibrium; SIR model; vaccination eficacy; individual vaccination; vaccination games; vaccination; Mean Field Games