Global analysis and numerical simulations of a novel stochastic eco-epidemiological model with time delay

In this paper, a new stochastic eco-epidemiological model is proposed and investigated, and the high dimensional model includes time delay and a general incidence rate which make the study more complex. First, the existence and uniqueness of the global positive solution with any positive initial value are verified. Second, using stochastic analysis methods and some differential inequality techniques, we explore the long-time asymptotic properties of the stochastic delayed system. Furthermore, we prove that the solution of the stochastic delayed system has a unique stationary distribution and it has ergodic property. Third, the sufficient conditions of permanence in mean or extinction for the ecological populations are obtained. Finally, we introduce a series of computer simulations to show the performance of the theoretical results.