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Global Stability of Humoral Immunity HIV Infection Models with Chronically Infected Cells and Discrete Delays

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  • A. M. Elaiw
  • N. A. Alghamdi

Abstract

We study the global stability of three HIV infection models with humoral immune response. We consider two types of infected cells: the first type is the short-lived infected cells and the second one is the long-lived chronically infected cells. In the three HIV infection models, we modeled the incidence rate by bilinear, saturation, and general forms. The models take into account two types of discrete-time delays to describe the time between the virus entering into an uninfected CD4 + T cell and the emission of new active viruses. The existence and stability of all equilibria are completely established by two bifurcation parameters, and . The global asymptotic stability of the steady states has been proven using Lyapunov method. In case of the general incidence rate, we have presented a set of sufficient conditions which guarantee the global stability of model. We have presented an example and performed numerical simulations to confirm our theoretical results.

Suggested Citation

  • A. M. Elaiw & N. A. Alghamdi, 2015. "Global Stability of Humoral Immunity HIV Infection Models with Chronically Infected Cells and Discrete Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-25, December.
    • Handle: RePEc:hin:jnddns:370968
    DOI: 10.1155/2015/370968
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    Cited by:

    1. Miao, Hui & Abdurahman, Xamxinur & Teng, Zhidong & Zhang, Long, 2018. "Dynamical analysis of a delayed reaction-diffusion virus infection model with logistic growth and humoral immune impairment," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 280-291.

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