International Journal of Differential Equations

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

Adnane Boukhouima, Khalid Hattaf, and Noura Yousfi

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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.

Article information

Source
Int. J. Differ. Equ., Volume 2018, Special Issue (2018), Article ID 1019242, 12 pages.

Dates
Received: 9 September 2018
Accepted: 7 November 2018
First available in Project Euclid: 10 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1547089232

Digital Object Identifier
doi:10.1155/2018/1019242

Mathematical Reviews number (MathSciNet)
MR3892176

Citation

Boukhouima, Adnane; Hattaf, Khalid; Yousfi, Noura. A Fractional Order Model for Viral Infection with Cure of Infected Cells and Humoral Immunity. Int. J. Differ. Equ. 2018, Special Issue (2018), Article ID 1019242, 12 pages. doi:10.1155/2018/1019242. https://projecteuclid.org/euclid.ijde/1547089232


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