On the Dynamics of a Stochastic Ratio-Dependent Predator-Prey System with Infection for the Prey

Abstract

In this paper, we investigate the dynamics of a stochastic predator-prey model with ratio-dependent functional response and disease in the prey. Firstly, we prove the existence and uniqueness of the positive solution for the stochastic model by using conventional methods. Then we obtain the threshold 0 s R for the infected prey population, that is, the disease will tend to extinction if 0 1 s R < , and it will exist in the long time if 0 1 s R > . Finally, the sufficient condition on the existence of a unique ergodic stationary distribution is obtained, which indicates that all the populations are permanent in the time mean sense. Numerical simulations are conducted to verify our analysis results.