Modeling of pseudo-rational exemption to vaccination for SEIR diseases

A challenge to disease control in modern societies is the spread of pseudo–rational exemption to vaccination, as a consequence of a comparison between the steadily declining risk of infection, and the perceived risk of side effects from the vaccine. Here we consider rational exemption in an SEIR model with information dependent vaccination where individuals use information on the spread of the disease as their information set. Using suitable assumptions, we show the dynamic implications of the interaction between rational exemption and current information. In particular, we show that the vaccinating behavior depending on current information can trigger oscillations, differently from the case of SIR diseases, where an information delay is needed to induce oscillations.