Transmission dynamics of symptom-dependent HIV/AIDS models

Wenshuang Li; Shaojian Cai; Xuanpei Zhai; Jianming Ou; Kuicheng Zheng; Fengying Wei; Xuerong Mao; Wenshuang Li; Shaojian Cai; Xuanpei Zhai; Jianming Ou; Kuicheng Zheng; Fengying Wei; Xuerong Mao

doi:10.3934/mbe.2024079

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 2: 1819-1843. doi: 10.3934/mbe.2024079

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Transmission dynamics of symptom-dependent HIV/AIDS models

1.
School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, Fujian, China
2.
Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China
3.
School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
4.
Center for Applied Mathematics of Fujian Province, Fuzhou University, Fuzhou 350116, Fujian, China
5.
Key Laboratory of Operations Research and Control of Universities in Fujian, Fuzhou University, Fuzhou 350116, Fujian, China
6.
Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK

Academic Editor: Sanling Yuan
^† These authors contributed equally to this work.

Received: 11 October 2023 Revised: 29 November 2023 Accepted: 12 December 2023 Published: 03 January 2024

In this study, we proposed two, symptom-dependent, HIV/AIDS models to investigate the dynamical properties of HIV/AIDS in the Fujian Province. The basic reproduction number was obtained, and the local and global stabilities of the disease-free and endemic equilibrium points were verified to the deterministic HIV/AIDS model. Moreover, the indicators $ R_0^s $ and $ R_0^e $ were derived for the stochastic HIV/AIDS model, and the conditions for stationary distribution and stochastic extinction were investigated. By using the surveillance data from the Fujian Provincial Center for Disease Control and Prevention, some numerical simulations and future predictions on the scale of HIV/AIDS infections in the Fujian Province were conducted.
- HIV/AIDS,
- threshold,
- stability,
- stationary distribution,
- extinction
Citation: Wenshuang Li, Shaojian Cai, Xuanpei Zhai, Jianming Ou, Kuicheng Zheng, Fengying Wei, Xuerong Mao. Transmission dynamics of symptom-dependent HIV/AIDS models[J]. Mathematical Biosciences and Engineering, 2024, 21(2): 1819-1843. doi: 10.3934/mbe.2024079

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Abstract

In this study, we proposed two, symptom-dependent, HIV/AIDS models to investigate the dynamical properties of HIV/AIDS in the Fujian Province. The basic reproduction number was obtained, and the local and global stabilities of the disease-free and endemic equilibrium points were verified to the deterministic HIV/AIDS model. Moreover, the indicators $ R_0^s $ and $ R_0^e $ were derived for the stochastic HIV/AIDS model, and the conditions for stationary distribution and stochastic extinction were investigated. By using the surveillance data from the Fujian Provincial Center for Disease Control and Prevention, some numerical simulations and future predictions on the scale of HIV/AIDS infections in the Fujian Province were conducted.

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