Global stability of delayed virus infection model including multi-target cells and B-cell impairment

Volume 23, Issue 3, pp 245--262 http://dx.doi.org/10.22436/jmcs.023.03.07

Publication Date: November 22, 2020 Submission Date: August 26, 2020 Revision Date: September 10, 2020 Accteptance Date: September 28, 2020

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Authors

Safiya F. Alshehaiween - Department of Mathematics, Faculty of Science, Taibah University, P.O. Box 344, Medina 42353, Saudi Arabia. Ahmed M. Elaiw - Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia. - Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut, Egypt.

Abstract

In this paper, we formulate a virus infection model with \(n\) classes of target uninfected cells, \(n\) classes of latent infected cells, \(n\) classes of active infected cells, virus particles, and B cells. Three types of time delays and the impairment of B cells are involved. The Well-posedness of the model is demonstrated. Basic reproduction number of infection \(\mathcal{R}_{0}>0\) is established, which determines the existence of equilibria as follows; when \(\mathcal{R}_{0}\) is greater than unity, and then the model has two equilibria. Otherwise, the model has only a single equilibrium. The global stability of equilibria is proven using Lyapunov's direct method and applying LaSalle's invariance principle. To support our theoretical results, we have performed some numerical simulations in case of \(n=2 \) where the model can describe the HIV dynamics with two types of target cells, CD\(4^{+} \) T cells and macrophages.

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Keywords

• Virus dynamics
• global stability
• multi-target cells
• impairment of B cells
• time delay

MSC

•  34D20
•  34D23
•  37N25
•  92B05

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