Impacts of evolutionary vaccine games on the spread of infectious diseases

Game-theoretical study of vaccination control strategies for contagious diseases is the subject of a vigorous research effort. Within the framework of evolutionary game theory, we propose a susceptible-infected-vaccinated (SIV) model within a population, where susceptible individuals can optionally acquire vaccine-induced immunity by learning from vaccinated individuals in the vicinity according to the payoffs from the vaccine games played among them. We show that the critical thresholds for disease outbreak, as well as that for vaccine up-take, is sensitively dependent not only of the vaccine-to-therapy cost ratio, but also of the infection histories memorized by individuals under the setup of repeated games. Our findings reveal the role of memory in the game-learning based vaccination strategy, implying that it helps individuals avoid the risk from infection and thus avails to outbreak control for infectious diseases.