Dynamical behaviors of a stochastic HIV/AIDS epidemic model with Ornstein–Uhlenbeck process
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Published:2024-06-29
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Volume:
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ISSN:1793-5245
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Container-title:International Journal of Biomathematics
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language:en
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Short-container-title:Int. J. Biomath.
Author:
Shang Jia-Xin1ORCID,
Li Wen-He12ORCID
Affiliation:
1. School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, P. R. China
2. National Key Laboratory of Continental Shale Oil, Northeast Petroleum University, Daqing 163318, P. R. China
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 [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.
Funder
Tian Yuan Mathematical Foundation
Natural Science Foundation of Heilongjiang Province
Heilongjiang Provincial Postdoctoral Science Foundation
Northeast Petroleum University Special Research Team Project
Publisher
World Scientific Pub Co Pte Ltd