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The vaccination against ongoing epidemics is seldom compulsory but remainsone of the most classical means to fight epidemic propagation. However recentdebates concerning the innocuity of vaccines and their risk with respect to therisk of the epidemic itself lead to severe vaccination campaign failures andnew mass behaviors appeared driven by individual self-interest. Prompted bythis context we analyze, in a Susceptible-Infected-Recovered (SIR) model,whether egocentric individuals can reach an equilibrium with the rest of thesociety. Using techniques from the "Mean Field Games" theory, we extendprevious results and show that an equilibrium exists and characterizescompletely the individual best vaccination strategy (with or withoutdiscounting). We also compare with a strategy based only on overall societaloptimization and exhibit a situation with non-negative price of anarchy.Finally, we apply the theory to the 2009-2010 Influenza A (H1N1) vaccinationcampaign in France and hint that a group of individuals stopped vaccinating atlevels that indicated a pessimistic perception of the risk of the vaccine.

Individual vaccination as Nash equilibrium in a SIR model with application to the 2009-10 Influenza A(H1N1) epidemic in France