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Stationary distribution and extinction of a stochastic HIV-1 model with Beddington–DeAngelis infection rate

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  • Liu, Qun
  • Jiang, Daqing
  • Hayat, Tasawar
  • Alsaedi, Ahmed

Abstract

In this paper, we consider a stochastic HIV-1 model with Beddington–DeAngelis infection rate. By constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of a unique ergodic stationary distribution to the model. Then we obtain sufficient conditions for extinction of the disease. The existence of a stationary distribution implies stochastic weak stability.

Suggested Citation

  • Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Stationary distribution and extinction of a stochastic HIV-1 model with Beddington–DeAngelis infection rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 414-426.
    • Handle: RePEc:eee:phsmap:v:512:y:2018:i:c:p:414-426
    DOI: 10.1016/j.physa.2018.08.088
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    References listed on IDEAS

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    1. Lin, Yuguo & Jiang, Daqing & Wang, Shuai, 2014. "Stationary distribution of a stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 187-197.
    2. Peng, Shige & Zhu, Xuehong, 2006. "Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 370-380, March.
    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.
    4. Liu, Qun & Chen, Qingmei, 2015. "Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 140-153.
    5. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
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    Cited by:

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    2. 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).
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    4. El Fatini, Mohamed & Sekkak, Idriss, 2020. "Lévy noise impact on a stochastic delayed epidemic model with Crowly–Martin incidence and crowding effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    5. Chen, Zhewen & Tian, Zhuyan & Zhang, Shuwen & Wei, Chunjin, 2020. "The stationary distribution and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).

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