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Stability and Hopf bifurcation of a within-host chikungunya virus infection model with two delays

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  • Wang, Yan
  • Liu, Xianning

Abstract

In this paper, a within-host chikungunya virus infection model with two delays is considered. The basic reproductive number R0 is formulated. If R0<1, the virus-free equilibrium is globally asymptotically stable and the disease always dies out. If R0>1, the global stability of the unique endemic equilibrium E1 is proved for the case without the time delay of antigenic stimulation, which can change the stability of E1 and lead to the existence of Hopf bifurcation. Furthermore, explicit formulae for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are established. Finally, some numerical simulations are presented to illustrate the results.

Suggested Citation

  • Wang, Yan & Liu, Xianning, 2017. "Stability and Hopf bifurcation of a within-host chikungunya virus infection model with two delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 138(C), pages 31-48.
    • Handle: RePEc:eee:matcom:v:138:y:2017:i:c:p:31-48
    DOI: 10.1016/j.matcom.2016.12.011
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    References listed on IDEAS

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    Cited by:

    1. Ahmed M. Elaiw & Aeshah A. Raezah & Matuka A. Alshaikh, 2023. "Global Dynamics of Viral Infection with Two Distinct Populations of Antibodies," Mathematics, MDPI, vol. 11(14), pages 1-26, July.
    2. De Cesare, Luigi & Sportelli, Mario, 2020. "Stability and direction of Hopf bifurcations of a cyclical growth model with two-time delays and one-delay dependent coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. A. M. Elaiw & N. H. AlShamrani & E. Dahy & A. A. Abdellatif & Aeshah A. Raezah, 2023. "Effect of Macrophages and Latent Reservoirs on the Dynamics of HTLV-I and HIV-1 Coinfection," Mathematics, MDPI, vol. 11(3), pages 1-26, January.
    4. Abraham J. Arenas & Gilberto González-Parra & Jhon J. Naranjo & Myladis Cogollo & Nicolás De La Espriella, 2021. "Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay," Mathematics, MDPI, vol. 9(3), pages 1-21, January.
    5. Salah Alsahafi & Stephen Woodcock, 2021. "Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate," Mathematics, MDPI, vol. 9(18), pages 1-18, September.
    6. Ahmed M. Elaiw & Taofeek O. Alade & Saud M. Alsulami, 2018. "Global Stability of Within-Host Virus Dynamics Models with Multitarget Cells," Mathematics, MDPI, vol. 6(7), pages 1-19, July.
    7. Wang, Yan & Li, Yazhi & Liu, Lili & Liu, Xianning, 2022. "A periodic Chikungunya model with virus mutation and transovarial transmission," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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