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.
Highlights
The research of eco-epidemiology involving ecological and epidemiological models is a significant field in mathematical biology
We investigate the dynamics of a stochastic predator-prey model with ratio-dependent functional response and disease in the prey
We obtain the threshold R0s for the infected prey population, that is, the disease will tend to extinction if R0s < 1, and it will exist in the long time if R0s > 1
Summary
The research of eco-epidemiology involving ecological and epidemiological models is a significant field in mathematical biology. Anderson and May were the first to study the spread and persistence of infectious diseases by formulating an eco-epidemiological prey-predator model [1]. Li et al [10] analyzed a stochastic predator-prey model with disease in the predator and Beddington-DeAngelis functional response. They showed that the stochastic system has a similar property to the corresponding deterministic system when the white noise is small enough. The predator-prey models with ratio-dependent functional responses have been proposed and mathematically studied [12] [13] [14] [15]. We propose an eco-epidemiological model with infection in the prey and ratio-dependent functional responses as follows.
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