Individual vaccination as Nash equilibrium in a SIR model: the interplay between individual optimization and societal policies

Laetitia Laguzet (1) , Gabriel Turinici (2, 1)

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

The vaccination against non recurrent 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.

Mots clés: individual vaccination; mean field games; vaccine scares; SIR model; epidemic control; Nash equilibrium

Domaines: Optimisation et contrôle [math.OC]; Santé publique et épidémiologie; Vaccinologie; Analyse numérique [math.NA]

Laetitia Laguzet, Gabriel Turinici. Individual vaccination as Nash equilibrium in a SIR model: the interplay between individual optimization and societal policies. 2015. ⟨hal-01100579v2⟩