A stochastic HIV model based on population mobility

Juhui Yan; Wanqin Wu; Xuewen Tan; Juhui Yan; Wanqin Wu; Xuewen Tan

doi:10.3934/math.20251184

AIMS Mathematics

2025, Volume 10, Issue 11: 26926-26957. doi: 10.3934/math.20251184

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Research article

A stochastic HIV model based on population mobility

Department of Mathematics, Yunnan Minzu University, Kunming 650031, China

Received: 03 September 2025 Revised: 01 November 2025 Accepted: 14 November 2025 Published: 20 November 2025
MSC : 60G10, 60H10

This paper established a stochastic HIV model that incorporates population mobility to analyze the role of stochastic noise in HIV dynamics. First, the existence and uniqueness of a globally positive solution for the stochastic system were proven, and sufficient conditions for the stochastic extinction of the disease were derived. Second, by constructing a Lyapunov function, it was demonstrated that the stochastic system possesses a unique ergodic stationary distribution when $ \hat{R_0^s } > 1 $. Finally, theoretical findings were illustrated through numerical simulations. From an epidemiological perspective, our study reveals that an increased response to infection risks and higher white noise intensity appear advantageous for limiting HIV transmission.
- HIV infection,
- population mobility,
- extinction,
- stationary distribution
Citation: Juhui Yan, Wanqin Wu, Xuewen Tan. A stochastic HIV model based on population mobility[J]. AIMS Mathematics, 2025, 10(11): 26926-26957. doi: 10.3934/math.20251184

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Abstract

This paper established a stochastic HIV model that incorporates population mobility to analyze the role of stochastic noise in HIV dynamics. First, the existence and uniqueness of a globally positive solution for the stochastic system were proven, and sufficient conditions for the stochastic extinction of the disease were derived. Second, by constructing a Lyapunov function, it was demonstrated that the stochastic system possesses a unique ergodic stationary distribution when $ \hat{R_0^s } > 1 $. Finally, theoretical findings were illustrated through numerical simulations. From an epidemiological perspective, our study reveals that an increased response to infection risks and higher white noise intensity appear advantageous for limiting HIV transmission.

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