Equilibrium in an individual -societal SIR vaccination model in presence of discounting and finite vaccination capacity

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

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

This paper analyses individual optimal vaccination strategies for a Susceptible-Infected-Recovered (SIR) model. The individuals vaccinate according to a criterion taking into account the risk of infection, the possible side effects of the vaccine and the overall epidemic course. We treat the situation when the vaccination capacity is limited and the individual discounts the future at some rate D > 0. Since the course of the epidemic is determined by the sum of invididual decisions a natural question is whether an equilibrium between the individual decisions and the epidemic evolution exists. We show that the answer is positive.

Mots clés: optimal vaccination; SIR model; mean field games

Domaines: Analyse numérique [math.NA]; Vaccinologie; Maladies infectieuses

Laetitia Laguzet, Gabriel Turinici, Ghozlane Yahiaoui. Equilibrium in an individual -societal SIR vaccination model in presence of discounting and finite vaccination capacity. 2015. ⟨hal-01222450v1⟩