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Stability and Hopf bifurcation in a delayed model for HIV infection of CD4+T cells

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  • Cai, Liming
  • Li, Xuezhi

Abstract

In this paper, we consider a delayed mathematical model for the interactions of HIV infection and CD4+T cells. We first investigate the existence and stability of the Equilibria. We then study the effect of the time delay on the stability of the infected equilibrium. Criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. Moreover, by applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Finally by using a delay τ as a bifurcation parameter, the existence of Hopf bifurcation is also investigated. Numerical simulations are presented to illustrate the analytical results.

Suggested Citation

  • Cai, Liming & Li, Xuezhi, 2009. "Stability and Hopf bifurcation in a delayed model for HIV infection of CD4+T cells," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 1-11.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:1-11
    DOI: 10.1016/j.chaos.2008.04.048
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    References listed on IDEAS

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    1. Dehghan, Mehdi & Nasri, Mostafa & Razvan, Mohammad Reza, 2007. "Global stability of a deterministic model for HIV infection in vivo," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1225-1238.
    2. David D. Ho & Avidan U. Neumann & Alan S. Perelson & Wen Chen & John M. Leonard & Martin Markowitz, 1995. "Rapid Turnover of Plasma Virions and CD4 Lymphocytes in HIV-1 Infection," Working Papers 95-01-002, Santa Fe Institute.
    3. Wang, Kaifa & Wang, Wendi & Liu, Xianning, 2006. "Viral infection model with periodic lytic immune response," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 90-99.
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    1. Jajarmi, Amin & Baleanu, Dumitru, 2018. "A new fractional analysis on the interaction of HIV with CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 221-229.
    2. Bai, Ning & Xu, Rui, 2022. "Backward bifurcation and stability analysis in a within-host HIV model with both virus-to-cell infection and cell-to-cell transmission, and anti-retroviral therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 162-185.
    3. Tanvi, & Aggarwal, Rajiv, 2020. "Stability analysis of a delayed HIV-TB co-infection model in resource limitation settings," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Zhang, Huaqiao & Chen, Hong & Jiang, Cuicui & Wang, Kaifa, 2017. "Effect of explicit dynamics of free virus and intracellular delay," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 827-834.

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