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 from the disease, and the risks from the
vaccine. Here we consider rational exemption in an 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 decisionsare based on delayed informations.