Dynamical behavior of a stochastic predator-prey model with Holling-type III functional response and infectious predator

In this paper, we formulate a stochastic predator-prey model with Holling III type functional response and infectious predator. By constructing Lyapunov functions, we prove the global existence and uniqueness of the positive solution of the model, and establish the ergodic stationary distribution of the positive solution, which indicates that both the prey and predator will coexist for a long time. We also obtain sufficient conditions for the extinction of the predator and prey population. We finally provide numerical simulations to demonstrate our main results.