Extinction and Permanence Analysis of Stochastic Predator-Prey Model With Disease, Ratio-Dependent Type Functional Response and Nonlinear Incidence Rate

Abstract

This paper is aimed to investigate a stochastic predator-prey model with disease in both species, which is also considered with ratio-dependent type functional response and nonlinear incidence rate. First, the existence and uniqueness of positive solution is discussed. Then, some sufficient conditions are established to ensure the solution is stochastically ultimate boundedness and permanent. Also, the extinction of susceptible prey, infected prey, susceptible predator and infected predator are analyzed, respectively. Furthermore, the boundedness of moments and upper-growth rate estimation are investigated. Finally, numerical simulations are given to illustrate our main results.