Dynamic vaccination games and variational inequalities on time-dependent sets.

This paper presents a model of a dynamic vaccination game in a population consisting of a collection of groups, each of which holds distinct perceptions of vaccinating versus non-vaccinating risks. Vaccination is regarded here as a game due to the fact that the payoff to each population group depends on the so-called perceived probability of getting infected given a certain level of the vaccine coverage in the population, a level that is generally obtained by the vaccinating decisions of other members of a population. The novelty of this model resides in the fact that it describes a repeated vaccination game (over a finite time horizon) of population groups whose sizes vary with time.