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Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence

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  • Liu, Qun
  • Jiang, Daqing
  • Hayat, Tasawar
  • Ahmad, Bashir

Abstract

In this paper, a stochastic delayed HIV-1 infection model with nonlinear incidence is proposed and investigated. First of all, we prove that there is a unique global positive solution as desired in any population dynamics. Then by constructing some suitable Lyapunov functions, we show that if the basic reproduction number R0≤1, then the solution of the stochastic system oscillates around the infection-free equilibrium E0, while if R0>1, then the solution of the stochastic system fluctuates around the infective equilibrium E∗. Sufficient conditions of these results are established. Finally, we give some examples and a series of numerical simulations to illustrate the analytical results.

Suggested Citation

  • Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 867-882.
    • Handle: RePEc:eee:phsmap:v:486:y:2017:i:c:p:867-882
    DOI: 10.1016/j.physa.2017.05.069
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    References listed on IDEAS

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    1. Artalejo, J.R. & Economou, A. & Lopez-Herrero, M.J., 2015. "The stochastic SEIR model before extinction: Computational approaches," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1026-1043.
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    Cited by:

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    2. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2019. "Dynamic threshold probe of stochastic SIR model with saturated incidence rate and saturated treatment function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution and extinction of a stochastic staged progression AIDS model with staged treatment and second-order perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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    7. Kiouach, Driss & El-idrissi, Salim El Azami & Sabbar, Yassine, 2023. "An improvement of the extinction sufficient conditions for a higher-order stochastically disturbed AIDS/HIV model," Applied Mathematics and Computation, Elsevier, vol. 447(C).
    8. He, Lingyun & Banihashemi, Seddigheh & Jafari, Hossein & Babaei, Afshin, 2021. "Numerical treatment of a fractional order system of nonlinear stochastic delay differential equations using a computational scheme," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    9. Rathinasamy, A. & Chinnadurai, M. & Athithan, S., 2021. "Analysis of exact solution of stochastic sex-structured HIV/AIDS epidemic model with effect of screening of infectives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 213-237.

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