Adaptive dynamics for individual payoff game-theoretic models of vaccination

Vaccination is widely recognised as one of the most effective forms of public health interventions. Individuals decisions regarding vaccination creates a complex social dilemma between individual and collective interests, where each person's decision affects the overall public health outcome. In this paper, we study the adaptive dynamics for the evolutionary dynamics of strategies in a fundamental game-theoretic model of vaccination. We show the existence of an (Nash) equilibrium and analyse the stability and bifurcations when varying the relevant parameters. We also demonstrate our analytical results by several concrete examples.