Application of inequalities technique to dynamics analysis of a stochastic eco-epidemiology model

This paper formulates an infected predator-prey model with Beddington-DeAngelis functional response from a classical deterministic framework to a stochastic differential equation (SDE). First, we provide a global analysis including the global positive solution, stochastically ultimate boundedness, the persistence in mean, and extinction of the SDE system by using the technique of a series of inequalities. Second, by using Itô's formula and Lyapunov methods, we investigate the asymptotic behaviors around the equilibrium points of its deterministic system. The solution of the stochastic model has a unique stationary distribution, it also has the characteristics of ergodicity. Finally, we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients to illustrate the performance of the theoretical results. The results show that if the intensity of the disturbance is sufficiently large, the persistence of the SDE model can be destroyed.

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