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A Fractional Order Model for Viral Infection with Cure of Infected Cells and Humoral Immunity

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  • Adnane Boukhouima
  • Khalid Hattaf
  • Noura Yousfi

Abstract

In this paper, we study the dynamics of a viral infection model formulated by five fractional differential equations (FDEs) to describe the interactions between host cells, virus, and humoral immunity presented by antibodies. The infection transmission process is modeled by Hattaf-Yousfi functional response which covers several forms of incidence rate existing in the literature. We first show that the model is mathematically and biologically well-posed. By constructing suitable Lyapunov functionals, the global stability of equilibria is established and characterized by two threshold parameters. Finally, some numerical simulations are presented to illustrate our theoretical analysis.

Suggested Citation

  • Adnane Boukhouima & Khalid Hattaf & Noura Yousfi, 2018. "A Fractional Order Model for Viral Infection with Cure of Infected Cells and Humoral Immunity," International Journal of Differential Equations, Hindawi, vol. 2018, pages 1-12, December.
    • Handle: RePEc:hin:jnijde:1019242
    DOI: 10.1155/2018/1019242
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    Cited by:

    1. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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