Abstract:
We deal with a stochastic predator-prey model with stage structure and ratio-dependent in the effect of disease. Firstly, a unique global positive solution for the model with any positive initial value is proved. Then, by constructing an appropriate Lyapunov function, we investigate that the model has an ergodic stationary distribution under certain parametric restrictions. Further, sufficient conditions for populations extinction are obtained by using Itô formula and differential inequality scaling. Finally, numerical simulations have been carried out to validate the feasibility of our theoretical results.