1. Dynamical behaviors of a stochastic HIV/AIDS epidemic model with Ornstein–Uhlenbeck process.
- Author
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Shang, Jia-Xin and Li, Wen-He
- Abstract
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 R0E is set: when R0E < 1, the disease will become extinct; when R0E > 1, the disease will persist. Then, it is shown that there exists a stationary distribution for the model when R0E > 1. 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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