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A dynamics stochastic model with HIV infection of CD4+ T-cells driven by Lévy noise

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  • Cheng, Yan
  • Li, Mingtao
  • Zhang, Fumin

Abstract

Aim to described this strong fluctuation by introducing a Lévy jump process into the HIV dynamical modelA stochastic model that describing the interaction between the CD4+ T-cells and the free human immunodeficiency virus (HIV) is investigated, a basic biological mechanism which describe the strong fluctuation in environment be considered into the model by introducing Lévy process. First, we obtained that the stochastic model admits a unique global positive solution. Then, constructed a function to analyze the extinction of infected the CD4+ T-cells and virus particles. Next, we investigated the persistence in mean of the infected CD4+ T-cells, a sufficient condition be established. Finally, some numerical simulations are given to verify the result of theoretical analysis.

Suggested Citation

  • Cheng, Yan & Li, Mingtao & Zhang, Fumin, 2019. "A dynamics stochastic model with HIV infection of CD4+ T-cells driven by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 62-70.
    • Handle: RePEc:eee:chsofr:v:129:y:2019:i:c:p:62-70
    DOI: 10.1016/j.chaos.2019.07.054
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    References listed on IDEAS

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    1. Zhou, Yanli & Zhang, Weiguo, 2016. "Threshold of a stochastic SIR epidemic model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 204-216.
    2. Rubenthaler, Sylvain, 2003. "Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 311-349, February.
    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. Jiang, Daqing & Liu, Qun & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed & Xia, Peiyan, 2017. "Dynamics of a stochastic HIV-1 infection model with logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 706-717.
    5. Alan S. Perelson & Avidan U. Neumann & Martin Markowitz & John M. Leonard & David D. Ho, 1996. "HIV-1 Dynamics In Vivo: Virion Clearance Rate, Infected Cell Lifespan, and Viral Generation Time," Working Papers 96-02-004, Santa Fe Institute.
    6. Liu, Meng & Bai, Chuanzhi, 2016. "Dynamics of a stochastic one-prey two-predator model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 308-321.
    7. Huang, Zaitang & Yang, Qigui & Cao, Junfei, 2011. "Complex dynamics in a stochastic internal HIV model," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 954-963.
    8. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
    9. Jerome K. Percus & Ora E. Percus & Alan S. Perelson, 1993. "Predicting the Size of the T-Cell Receptor and Antibody Combining Region from Consideration of Efficient Self-Nonself Discrimination," Working Papers 93-04-019, Santa Fe Institute.
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    Cited by:

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    4. Liu, Qun & Jiang, Daqing, 2020. "Dynamical behavior of a higher order stochastically perturbed HIV/AIDS model with differential infectivity and amelioration," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

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