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Dynamics of an HIV/AIDS transmission model with protection awareness and fluctuations

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  • Zhai, Xuanpei
  • Li, Wenshuang
  • Wei, Fengying
  • Mao, Xuerong

Abstract

We establish a stochastic HIV/AIDS model involving the susceptible with protection awareness within a total population. The mechanism of dynamic behaviors of the stochastic HIV/AIDS model with protection awareness are investigated in order to control the spread of HIV/AIDS. We firstly show that the stochastic model admits a global positive solution with any initial positive values. By constructing Lyapunov functions, the ergodic stationary distribution under the condition R0s>1, and the extinction under the condition R0e<1 for the stochastic model are further obtained respectively. Moreover, by using positive preserving truncated Euler–Maruyama method (PPTEM), the related numerical simulations are performed, which demonstrate the quantitative properties of persistence and extinction of the solution. Precisely, the increasing of protection efficiency of the susceptible with protection awareness reduces the scale of the infected individuals with AIDS; and the continuous antiretroviral therapy (ART) also benefits the control of the scale of the infected individuals with HIV/AIDS; the media reports with more instructions and details such as taking post-exposure prophylaxis (PEP) within 72 h to help the individuals avoid the infection to meet the 90%–90%–90% plan of WHO.

Suggested Citation

  • Zhai, Xuanpei & Li, Wenshuang & Wei, Fengying & Mao, Xuerong, 2023. "Dynamics of an HIV/AIDS transmission model with protection awareness and fluctuations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s096007792300125x
    DOI: 10.1016/j.chaos.2023.113224
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    2. Wang, Yaping & Hu, Lin & Nie, Lin-Fei, 2026. "Stability analysis and optimal intervention design for age-structured HIV/AIDS transmission model with protective consciousness," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 494-519.
    3. Zhou, Baoquan & Shi, Ningzhong, 2024. "Analysis of a stochastic SEIS epidemic model motivated by Black–Karasinski process: Probability density function," Chaos, Solitons & Fractals, Elsevier, vol. 189(P2).
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    5. Hao, Yicheng & Luo, Yantao & Huang, Jianhua & Zhang, Long & Teng, Zhidong, 2025. "Analysis of a stochastic HIV/AIDS model with commercial heterosexual activity and Ornstein–Uhlenbeck process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 234(C), pages 50-72.
    6. Luo, Yantao & Huang, Jianhua & Teng, Zhidong & Liu, Qun, 2024. "Role of ART and PrEP treatments in a stochastic HIV/AIDS epidemic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 337-357.
    7. Yang, Ying & Zhang, Jingwen & Wang, Kaiyuan & Zhang, Guofang, 2024. "Stationary distribution, density function and extinction of a stochastic SIQR epidemic model with Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    8. Xu, Hongjie & Luo, Huantian & Fan, Xu-Qian, 2024. "Stability of stochastic delay Hopfield neural network with Poisson jumps," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    9. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2023. "An effective transport-related SVIR stochastic epidemic model with media coverage and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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