Ergodic stationary distribution and extinction of a staged progression HIV/AIDS infection model with nonlinear stochastic perturbations.

Recently, the stochastic θ -threshold method has been proposed to analyze the impact of second-order 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 θ -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 θ -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 ϱ 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 θ -threshold method can be successfully applied to the dynamical analysis of other complex high-dimensional epidemic models with nonlinear perturbations. [ABSTRACT FROM AUTHOR]