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Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells

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  • Tongqian Zhang
  • Junling Wang
  • Yi Song
  • Zhichao Jiang

Abstract

In this paper, a delayed viral dynamical model that considers two different transmission methods of the virus and apoptosis of bystander cells is proposed and investigated. The basic reproductive number of the model is derived. Based on the basic reproductive number, we prove that the disease-free equilibrium is globally asymptotically stable for by constructing suitable Lyapunov functional. For , by regarding the time delay as bifurcation parameter, the existence of local Hopf bifurcation is investigated. The results show that time delay can change the stability of endemic equilibrium and cause periodic oscillations. Finally, we give some numerical simulations to illustrate the theoretical findings.

Suggested Citation

  • Tongqian Zhang & Junling Wang & Yi Song & Zhichao Jiang, 2020. "Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells," Complexity, Hindawi, vol. 2020, pages 1-12, August.
    • Handle: RePEc:hin:complx:2313102
    DOI: 10.1155/2020/2313102
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    Cited by:

    1. Meng Li & Ke Guo & Wanbiao Ma, 2022. "Uniform Persistence and Global Attractivity in a Delayed Virus Dynamic Model with Apoptosis and Both Virus-to-Cell and Cell-to-Cell Infections," Mathematics, MDPI, vol. 10(6), pages 1-16, March.

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