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Stability and Hopf bifurcation in a HIV-1 infection model with delays and logistic growth

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  • Hu, Qing
  • Hu, Zhixing
  • Liao, Fucheng

Abstract

In this paper, we consider the dynamical behavior of a HIV-1 infection model with logistic growth for target cells, time delay and two predominant infection modes, namely the classical cell-free infection and the direct cell-to-cell transfer. It is proved the existence of the positive equilibrium E2 in different conditions. By analyzing the characteristic equations and using stability theory of delay differential equations, we establish the local stability of the two boundary equilibria and the infected equilibrium of the model. The time delay does not affect the stability of the boundary equilibrium, but can change the stability of E2 and lead to the occurrence of Hopf bifurcations. The direction and stability of bifurcating periodic solutions is also studied. Finally, the numerical simulations are carried out to explain our theorems.

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  • Hu, Qing & Hu, Zhixing & Liao, Fucheng, 2016. "Stability and Hopf bifurcation in a HIV-1 infection model with delays and logistic growth," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 128(C), pages 26-41.
    • Handle: RePEc:eee:matcom:v:128:y:2016:i:c:p:26-41
    DOI: 10.1016/j.matcom.2016.04.003
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    References listed on IDEAS

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    1. Tipsri, S. & Chinviriyasit, W., 2015. "The effect of time delay on the dynamics of an SEIR model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 153-172.
    2. Dong, Yueping & Huang, Gang & Miyazaki, Rinko & Takeuchi, Yasuhiro, 2015. "Dynamics in a tumor immune system with time delays," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 99-113.
    3. Avila-Vales, Eric & Chan-Chí, Noé & García-Almeida, Gerardo E. & Vargas-De-León, Cruz, 2015. "Stability and Hopf bifurcation in a delayed viral infection model with mitosis transmission," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 293-312.
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    Cited by:

    1. Sonjoy Pan & Siddhartha P. Chakrabarty, 2020. "Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1673-1695, December.
    2. Pan, Sonjoy & Chakrabarty, Siddhartha P., 2022. "Analysis of a reaction–diffusion HCV model with general cell-to-cell incidence function incorporating B cell activation and cure rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 431-450.

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