Stability Analysis and Bifurcation of a Predator-prey Model with Time Delay in Prey and Diseases in Predator

Abstract. In this paper, we present a predator-prey model with time delay, in which predator can be infected. The epidemics cannot be transmitted between prey and predator by predation. The predation ability of susceptible predators is stronger than infected ones. Based on the assumptions above, we study the stability and bifurcation of some equilibrium points, where the time delay is regarded as a parameter. It is found that there are stability switches, and Hopf bifurcation occurs when the delay passes through a sequence of critical values. We provide numerical results to illustrate our conclusion about stability and obtain the properties of Hopf bifurcation. In addition, we also discuss some interesting biological cases that our model exhibits.