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Analysis of an HIV/AIDS treatment model with a nonlinear incidence

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  • Cai, Liming
  • Wu, Jingang

Abstract

An HIV/AIDS treatment model with a nonlinear incidence is formulated. The infectious period is partitioned into the asymptotic and the symptomatic phases according to clinical stages. The constant recruitment rate, disease-induced death, drug therapies, as well as a nonlinear incidence, are incorporated into the model. The basic reproduction number R0 of the model is determined by the method of next generation matrix. Mathematical analysis establishes that the global dynamics of the spread of the HIV infectious disease are completely determined by the basic reproduction number R0. If R0⩽1, the disease always dies out and the disease-free equilibrium is globally stable. If R0>1, the disease persists and the unique endemic equilibrium is globally asymptotically stable in the interior of the feasible region.

Suggested Citation

  • Cai, Liming & Wu, Jingang, 2009. "Analysis of an HIV/AIDS treatment model with a nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 175-182.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:175-182
    DOI: 10.1016/j.chaos.2007.11.023
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    References listed on IDEAS

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    Cited by:

    1. Cai, Liming & Guo, Shumin & Li, XueZhi & Ghosh, Mini, 2009. "Global dynamics of a dengue epidemic mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2297-2304.
    2. 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).
    3. Zhou, Baoquan & Jiang, Daqing & Dai, Yucong & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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