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

This paper analyzes 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 individual decisions a natural question is whether an equilibrium between the individual decisions and the epidemic evolution exists. We show that the answer is positive.