Dynamical behaviors of a stochastic HIV/AIDS epidemic model with Ornstein–Uhlenbeck process

AIDS is a chronic infectious disease that has been having a major impact on human health and social stability. In this paper, based on the deterministic SIATR model, a stochastic SIATR model is developed to account for the spread of AIDS by introducing the Ornstein–Uhlenbeck process. First, the existence and uniqueness of the global positive solution of the model are investigated. Second, a threshold [Formula: see text] is set: when [Formula: see text], the disease will become extinct; when [Formula: see text], the disease will persist. Then, it is shown that there exists a stationary distribution for the model when [Formula: see text]. On this basis, we derive the exact expression for the probability density function of the model in the neighborhood of the quasi-equilibrium state. Finally, the results of the previous proof are verified by several numerical simulations.