TITLE:
On the Dynamics of a Stochastic Ratio-Dependent Predator-Prey System with Infection for the Prey
AUTHORS:
Jiying Ma, Haimiao Ren
KEYWORDS:
Stochastic Predator-Prey Model, Ratio-Dependent, Stationary Distribution, Extinction
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.11 No.4,
April
21,
2021
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 for the infected prey population, that is, the disease will tend to extinction if > 1. 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.