Analysis of an eco‐epidemiological system with Lévy noise

Abstract

An eco‐epidemiological system with Lévy noise and white noise is proposed. In this prey–predator system, assume that the predator population is infected by disease and divided into two classes: susceptible predator and infected predator. The existence of global positive solution is derived. Threshold conditions of extinction and persistence in the mean for prey and predator population are given by Itô's formula and comparison theorem for stochastic model. The long‐time behavior of this random system is also discussed by constructing suitable Lyapunov function, which shows the relationship between the solution of stochastic system and the equilibria of corresponding deterministic system. Finally, these results are verified by numerical simulation. Our results illustrate whether Lévy noise and white noise are both unfavorable to the population size of species.