Abstract
Recently, the stochastic theta-threshold method has been proposed to analyze the impact of secondorder perturbations on disease persistence. In this paper, considering the complexity of the environmental variations in the actual situation, we construct and study a stochastic staged progression HIV/AIDS infection model with third-order perturbations. First, we generalize the stochastic theta-threshold method to eliminate the effect of third-order perturbation of the stochastic model and obtain a critical value R-0(S) related to the basic reproduction number R-0 of its deterministic model. By constructing several suitable theta-Lyapunov functions, it is theoretically proved that the stochastic model has a unique ergodic stationary distribution if R-0(S) > 1. In a biological interpretation, the existence of a stationary distribution implies the long-term persistence of HIV/AIDS. Moreover, for some small perturbations, by means of the exponential martingale inequality, we establish sufficient condition rho(0) < 0 for disease extinction. Then, for some large perturbations, another sufficient condition R-0(C) < 1 for disease extinction of the stochastic model is also derived. For completeness, we provide some examples and numerical simulations to verify our analytical results. What is more, the generalized stochastic theta-threshold method can be successfully applied to the dynamical analysis of other complex high-dimensional epidemic modelswith nonlinear perturbations.