Fatal SIR diseases and rational exemption to vaccination

A challenge to disease control in modern societies is the spread of rational exemption to vaccination as a consequence of the rational comparison between the steadily declining risk of infection and the risk of side effects from the vaccine. Here, we consider rational exemption in an susceptible-infectious-removed (SIR) model with information-dependent vaccination where individuals use information on the disease's mortality as their information set. Using suitable assumptions on the dynamics of the population, we show the dynamic implications of the interaction between rational exemption, current and delayed information and the risk of death by the disease. In particular, we illustrate the onset of the long cycles caused by rational exemption when vaccination decisions are based on delayed informations.