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A stochastic SICA model for HIV/AIDS transmission

Author

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  • Tan, Yiping
  • Cai, Yongli
  • Sun, Xiaodan
  • Wang, Kai
  • Yao, Ruoxia
  • Wang, Weiming
  • Peng, Zhihang

Abstract

In this paper, we present a stochastic HIV/AIDS model with standard incidence rate to investigate the impact of random fluctuations on the HIV viral dynamics. Firstly, the sufficient conditions for the stochastic extinction of the disease are obtained. Secondly, after defining the threshold parameter Rs, we prove that the model has a unique ergodic stationary distribution when Rs>1, which reveals that the disease will persist almost surely. Subsequently, we give the exact expression of the probability density function around a quasi-equilibrium point by applying four-dimensional Fokker–Planck equation. Finally, through the numerical simulations of several examples, we not only verify the correctness of the theoretical results, but also explore how the disease goes for the case of not giving clear results theoretically. Epidemiologically, we find that increasing the noise intensities may be conducive to control the spread of the HIV.

Suggested Citation

  • Tan, Yiping & Cai, Yongli & Sun, Xiaodan & Wang, Kai & Yao, Ruoxia & Wang, Weiming & Peng, Zhihang, 2022. "A stochastic SICA model for HIV/AIDS transmission," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s096007792200947x
    DOI: 10.1016/j.chaos.2022.112768
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    1. 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.
    2. 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).

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