Rabies remains an important human health and wildlife management concern worldwide. Currently, there is significant underreporting of human deaths from rabies in many parts of the world. Concerning foxes in Europe, the proportion of all cases that are observed is likely to be as low as 2−10%. Consequently predictive models have been developed to estimate the mortality attributable to rabies. When rabies penetrates a new area, there is a peak in reported cases among foxes. These pulse like events causing the spread of rabies, often due to migration, mating and other seasonal behaviors are often absent from a rabies model. We present a model which modifies an existing continuous rabies model with the addition of a discrete kick via the Dirac distribution. Furthermore noting the observed complexities in the literature and the data we study the level of complexity of the presented model and use an algorithm to demonstrate the existence of chaos via Taylor expansions and curve fitting for the stable and unstable manifold of a fixed point at the origin.
Ippolito A Stephen, Naudot Vincent