Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods

Abstract

Most mathematical models used to understand the dynamical patterns seen in the incidence of childhood viral diseases, such as measles, employ a simple, but epidemiologically unrealistic, description of the infection and recovery process. The inclusion of more realistic descriptions of the recovery process is shown to cause a significant destabilization of the model. When there is seasonal variation in disease transmission this destabilization leads to the appearance of complex dynamical patterns with much lower levels of seasonality than previously predicted. More generally this study illustrates how detailed dynamical properties of a model may depend in an important way on the assumptions made in the formulation of the model.