Analysis of a stochastic eco-epidemiological model with modified Leslie–Gower functional response

Abstract In this paper, the deterministic and stochastic eco-epidemiological models with modified Leslie–Gower functional response are studied. For a deterministic system, the stability of disease-free equilibrium and positive equilibrium is studied. For a stochastic system, we verify that the system admits a unique positive global solution starting from any positive initial value, and we establish the conditions of extinction for infected prey population and strong persistence in mean for all species. We also show the system has a stationary distribution under some conditions. Finally, some numerical simulations are carried out to illustrate the main results.