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

TL;DR

This paper models individual vaccination decisions during an epidemic using game theory, showing equilibrium strategies and applying findings to the 2009-2010 H1N1 campaign in France, revealing insights into vaccination behaviors.

Contribution

It extends Mean Field Games theory to analyze vaccination behavior in SIR models and characterizes individual strategies as Nash equilibria, including societal comparisons.

Findings

Existence of vaccination Nash equilibrium in SIR models.

Comparison between individual and societal vaccination strategies.

Application to French H1N1 data indicating vaccine risk perception.

Abstract

The vaccination against ongoing epidemics is seldom compulsory but remains one of the most classical means to fight epidemic propagation. However recent debates concerning the innocuity of vaccines and their risk with respect to the risk of the epidemic itself lead to severe vaccination campaign failures and new mass behaviors appeared driven by individual self-interest. Prompted by this context we analyze, in a Susceptible-Infected-Recovered (SIR) model, whether egocentric individuals can reach an equilibrium with the rest of the society. Using techniques from the "Mean Field Games" theory, we extend previous results and show that an equilibrium exists and characterizes completely the individual best vaccination strategy (with or without discounting). We also compare with a strategy based only on overall societal optimization and exhibit a situation with non-negative price of anarchy. Finally, we apply the theory to the 2009-2010 Influenza A (H1N1) vaccination campaign in France and hint that a group of individuals stopped vaccinating at levels that indicated a pessimistic perception of the risk of the vaccine.