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Modelling a stochastic HIV model with logistic target cell growth and nonlinear immune response function

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  • Wang, Yan
  • Jiang, Daqing
  • Alsaedi, Ahmed
  • Hayat, Tasawar

Abstract

A stochastic HIV viral model with both logistic target cell growth and nonlinear immune response function is formulated to investigate the effect of white noise on each population. The existence of the global solution is verified. By employing a novel combination of Lyapunov functions, we obtain the existence of the unique stationary distribution for small white noises. We also derive the extinction of the virus for large white noises. Numerical simulations are performed to highlight the effect of white noises on model dynamic behaviour under the realistic parameters. It is found that the small intensities of white noises can keep the irregular blips of HIV virus and CTL immune response, while the larger ones force the virus infection and immune response to lose efficacy.

Suggested Citation

  • Wang, Yan & Jiang, Daqing & Alsaedi, Ahmed & Hayat, Tasawar, 2018. "Modelling a stochastic HIV model with logistic target cell growth and nonlinear immune response function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 276-292.
    • Handle: RePEc:eee:phsmap:v:501:y:2018:i:c:p:276-292
    DOI: 10.1016/j.physa.2018.02.040
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    References listed on IDEAS

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    3. Wang, Yan & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "A stochastic HIV infection model with T-cell proliferation and CTL immune response," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 477-493.
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    Cited by:

    1. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    2. Chinnadurai, M. & Fatini, Mohamed El & Rathinasamy, A., 2023. "Stochastic perturbation to 2-LTR dynamical model in HIV infected patients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 473-497.
    3. Li, Qiuyue & Cong, Fuzhong & Liu, Tianbao & Zhou, Yaoming, 2020. "Stationary distribution of a stochastic HIV model with two infective stages," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    4. 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).
    5. Akdim, Khadija & Ez-zetouni, Adil & Danane, Jaouad & Allali, Karam, 2020. "Stochastic viral infection model with lytic and nonlytic immune responses driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).

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