Abstract

This system was proposed by \textit{H. I. Freedman} [Math. Biosci. 99, 143–155 (1990; Zbl 0698.92024)] to model the interactions between a prey population \(X\) and a predator population \(Y\) with the action of a parasite. Due to the action of the parasite, the prey population \(X\) is divided into two classes: the susceptible class \(S\) and the infective class \(I\). The predators are assumed to be all infected. We establish a uniform persistence criterion for this model.