Open AccessA MEAN FIELD GAME ANALYSIS OF SIR DYNAMICS WITH VACCINATION
Author(s) -
Josu Doncel,
Nicolas Gast,
Bruno Gaujal
Publication year - 2020
Publication title -
probability in the engineering and informational sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.406
H-Index - 39
eISSN - 1469-8951
pISSN - 0269-9648
DOI - 10.1017/s0269964820000522
Subject(s) - convergence (economics) , monotone polygon , rate of convergence , mathematics , vaccination , mathematical optimization , field (mathematics) , computer science , medicine , economics , virology , computer network , pure mathematics , economic growth , channel (broadcasting) , geometry
In this paper, we analyze a mean-field game model of SIR dynamics (Susceptible, Infected, Recovered) where players can vaccinate. This game admits a unique mean-field equilibrium: The equilibrium strategy of each player is to vaccinate until the proportion of susceptible players drops below some threshold and stop vaccinating thereafter. We also show that the vaccination strategy minimizing the total cost for the population is a different threshold strategy. This implies that, to encourage optimal vaccination behaviors, vaccination should be subsidized.
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