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.
Share and Cite
ISRP Style
Safiya F. Alshehaiween, Ahmed M. Elaiw, Global stability of delayed virus infection model including multi-target cells and B-cell impairment, Journal of Mathematics and Computer Science, 23 (2021), no. 3, 245--262
AMA Style
Alshehaiween Safiya F., Elaiw Ahmed M., Global stability of delayed virus infection model including multi-target cells and B-cell impairment. J Math Comput SCI-JM. (2021); 23(3):245--262
Chicago/Turabian Style
Alshehaiween, Safiya F., Elaiw, Ahmed M.. "Global stability of delayed virus infection model including multi-target cells and B-cell impairment." Journal of Mathematics and Computer Science, 23, no. 3 (2021): 245--262
Keywords
- Virus dynamics
- global stability
- multi-target cells
- impairment of B cells
- time delay
MSC
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