Canonical modeling of anticipatory vaccination behavior and long term epidemic recurrence

Vaccination is one of humanity's main tools to fight epidemics. In most countries and for most diseases, vaccination is offered on a voluntary basis. Hence, the spread of a disease can be described as two interacting opposite dynamic systems: contagion is determined by past vaccination, while individuals decide whether to vaccinate based on beliefs regarding future disease prevalence. In this study, we show how the interplay between such anticipating behavior and the otherwise biological dynamics of a disease may lead to the emergence of recurrent patterns. We provide simulation results for (i) a Measles-like outbreak, (ii) canonical fully rational and far-sighted individuals, (iii) waning vaccine efficacy and vital dynamics, and (iv) long periods of time, i.e. long enough to observe several vaccination peaks. For comparison, we conducted a similar analysis for individuals with adaptive behavior. As an extension, we investigated the case where part of the population has an anti-vaccination stance.