Dynamical behavior and numerical simulation of a stochastic eco-epidemiological model with Ornstein–Uhlenbeck process

Abstract

As the spread of diseases among species becomes more and more common, our society pays increasingly more attention to the harm caused by the disease. Research on eco-epidemiological models will not only promote the development of biology and ecology, but also have important impacts on the economy and health of the society. This paper deals with a stochastic eco-epidemiological model which contains three species and is governed by Ornstein–Uhlenbeck (OU) process. Two common approaches to incorporate the effects of environmental perturbations in stochastic systems are first discussed and compared analytically and computationally. Based on the existence and uniqueness of the global solution to the model, several sharp conditions for the persistence and extinction of the species are established. Then, a criteria for the existence of the stationary distribution to the system is established by constructing suitable Lyapunov functions. Furthermore, the analytical expression of the probability density function of the model around the quasi-equilibrium is obtained. Finally, the impact of the main parameters on the dynamical behaviors and the noise perturbation effect are analysed in the numerical simulations section to illustrate the theoretical results.