Epidemiological models and vaccinations: From Bernoulli to today

In this review, we recall the basic models of mathematical epidemiology and present some of their recent advances in the context of behavioral epidemiology. Such new models allow to mathematically represent the decision-making process ruling the immunization choices. In particular, a SIRV (Susceptibles - Infectious - Removed - Vaccinated) model is considered, where vaccine uptake levels can depend on imitation processes (as in game theory) or on the (past and present) available information about the disease status. Finally, an optimal control problem is discussed in order to identify the temporal profile of persuasive campaigns for vaccination that public health systems can implement.