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Analysis of stability and Hopf bifurcation for a delay-differential equation model of HIV infection of CD4+ T-cells

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  • Jiang, Xiaowu
  • Zhou, Xueyong
  • Shi, Xiangyun
  • Song, Xinyu

Abstract

A delay differential mathematical model that described HIV infection of CD4+ T-cells is analyzed. The stability of the non-negative equilibria and the existence of Hopf bifurcation are investigated. A stability switch in the system due to variation of delay parameter has been observed, so is the phenomena of Hopf bifurcation and stable limit cycle. The estimation of the length of delay to preserve stability has been calculated. Using the normal form theory and center manifold argument, the explicit formulaes which determine the stability, the direction and the periodic of bifurcating period solutions are derived. Numerical simulations are carried out to explain the mathematical conclusions.

Suggested Citation

  • Jiang, Xiaowu & Zhou, Xueyong & Shi, Xiangyun & Song, Xinyu, 2008. "Analysis of stability and Hopf bifurcation for a delay-differential equation model of HIV infection of CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 447-460.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:2:p:447-460
    DOI: 10.1016/j.chaos.2006.11.026
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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. 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. Nath, Bhagya Jyoti & Sadri, Khadijeh & Sarmah, Hemanta Kumar & Hosseini, Kamyar, 2024. "An optimal combination of antiretroviral treatment and immunotherapy for controlling HIV infection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 226-243.
    3. 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.
    4. Shi, Ruiqing & Lu, Ting & Wang, Cuihong, 2021. "Dynamic analysis of a fractional-order model for HIV with drug-resistance and CTL immune response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 509-536.

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