Singular perturbation analysis of a model for a predator-prey system invaded by a parasite

A model of the predator-prey dynamics, as modified by the action of a parasite, is considered in which the prey population is divided into two classes, the susceptible and the infective members. The predator population is assumed to be of a social type, and have very fast dynamics, with all of its members infected by the parasite. Analysis of the model is carried out through singular perturbation arguments which allow us to derive explicit conditions on the parameters that identify different dynamic behavior of the system, and specifically ascertain the existence of a limit cycle composed of a concatenation of catastrophic transitions occurring at different speeds.