Modeling of hunting strategies of the predators in susceptible and infected prey

•Both disease for prey and staged structure for predator are considered.•A threshold dynamics of system determined by predator’s net reproductive number is investigated.•Predator’s hunting strategies for maximum surviving rate and maximum density are studied.

A predator–prey model with epidemic prey and staged structure in the predators, where the predators are assumed to keep constant preference probability of predation on susceptible/infected prey, is formulated to study the hunting strategies of predators for maximum surviving rate as well as maximum density. Given that the disease is endemic among prey before the invasion of predators, global dynamics of the model are obtained and threshold dynamics determined by the predator’s net reproductive number RH are established: the predators go extinct if RH < 1; and predators persist if RH > 1. As an application, the hunting strategies of the predators for the maximum RH are studied, and it is shown that the predators should only hunt the susceptible prey when the disease is just slightly endemic, while if the disease is seriously endemic, they should only hunt the infected prey. Numerical simulations are performed to verify/support the theoretical results and to consider the hunting strategies of predators for their maximum density, for which it is shown that the predators should keep some proper preference probability on both susceptible and infected prey.