Dynamical impact of virus carrier screening and actively seeking treatment on a stochastic HIV/AIDS infection model with log-normal Ornstein–Uhlenbeck process

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-06-09 DOI:10.1016/j.cnsns.2025.109005

Shengnan Jiang, Wenjie Zuo, Daqing Jiang

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引用次数: 0

Abstract

A stochastic HIV/AIDS model with a log-normal Ornstein–Uhlenbeck process is investigated, which incorporates screened disease carriers and active treatment. First, the global asymptotic stability of endemic equilibrium of the corresponding deterministic system is obtained when

R_{0} > 1

. Second, the existence of stationary distribution is examined by constructing a suitable Lyapunov function, which determines the critical value. In addition, sufficient conditions for the persistence and extinction of the diseases are given. Moreover, an exact expression of the density function near the quasi-endemic equilibrium is derived by solving a seven-dimensional Fokker–Planck equation, and unknown parameters of the probability density function are estimated by using maximum likelihood estimation. Finally, numerical simulations and sensitivity analysis are illustrated to offer crucial insights for AIDS treatment strategies.

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病毒携带者筛选和积极寻求治疗对具有对数正态Ornstein-Uhlenbeck过程的HIV/AIDS随机感染模型的动态影响

研究了一个具有对数正态Ornstein-Uhlenbeck过程的HIV/AIDS随机模型，该模型包含筛选的疾病携带者和积极的治疗。首先，在R0>；1时，得到了相应确定性系统的局部平衡点的全局渐近稳定性。其次，通过构造一个合适的Lyapunov函数来检验平稳分布的存在性，该函数确定了临界值。此外，还给出了疾病存在和消灭的充分条件。此外，通过求解一个七维的Fokker-Planck方程，导出了准局部平衡附近密度函数的精确表达式，并利用极大似然估计估计了概率密度函数的未知参数。最后，数值模拟和敏感性分析为艾滋病治疗策略提供了重要的见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.