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Dynamical analysis of a delayed reaction-diffusion virus infection model with logistic growth and humoral immune impairment

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  • Miao, Hui
  • Abdurahman, Xamxinur
  • Teng, Zhidong
  • Zhang, Long

Abstract

In this paper, the dynamical analysis of a delayed reaction-diffusion virus infection model with logistic growth and chemotaxis for the uninfected target cells and humoral immune impairment is studied. By analyzing corresponding characteristic equations, the local stability of the infection-free equilibrium is established. The stability properties and Turing instability of the antibody-free equilibrium and antibody-present infection equilibrium have been extensively discussed. The existence of Hopf bifurcation with antibody response delay as a bifurcation parameter at the antibody-present infection equilibrium is established. The numerical simulations are carried out in order to illustrate the dynamical behavior of the model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:110:y:2018:i:c:p:280-291
    DOI: 10.1016/j.chaos.2018.03.006
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    References listed on IDEAS

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    1. Li, Xiuling & Wei, Junjie, 2005. "On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 519-526.
    2. 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.
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    Cited by:

    1. Noura H. AlShamrani & Reham H. Halawani & Ahmed M. Elaiw, 2023. "Effect of Impaired B-Cell and CTL Functions on HIV-1 Dynamics," Mathematics, MDPI, vol. 11(20), pages 1-39, October.
    2. Luo, Yantao & Zhang, Long & Zheng, Tingting & Teng, Zhidong, 2019. "Analysis of a diffusive virus infection model with humoral immunity, cell-to-cell transmission and nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Ahmed M. Elaiw & Safiya F. Alshehaiween & Aatef D. Hobiny, 2019. "Global Properties of a Delay-Distributed HIV Dynamics Model Including Impairment of B-Cell Functions," Mathematics, MDPI, vol. 7(9), pages 1-27, September.
    4. Elaiw, Ahmed M. & Alshehaiween, Safiya F. & Hobiny, Aatef D., 2020. "Impact of B-cell impairment on virus dynamics with time delay and two modes of transmission," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    5. Elaiw, Ahmed M. & Al Agha, Afnan D., 2019. "Stability of a general HIV-1 reaction–diffusion model with multiple delays and immune response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).

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