Stability of a CTL-mediated immunity HIV infection models with silent infected cells and cellular infection
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Authors
Noura H. AlShamrani
- Department of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia.
- Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, 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, Egypt.
Abstract
This paper proposes and analyzes a CTL-mediated HIV infection model. The
susceptible CD\(4^{+}\)T cells can be infected when they are contacted by one of
the following: (i) free HIV particles, (ii) silent infected cells, and (iii)
actively infected cells. The effect of saturation infection has been
incorporated in the second model. The model is an improvement of an existing
HIV infection models which have neglected the infection due to incidence
between the silently infected cells and susceptible CD\(4^{+}\)T cells. We first
show that the models are well-posed. Each of our proposed models has three
equilibria, namely: HIV-free equilibrium, \DJ \(_{0}\), chronic HIV infection
equilibrium with inactive {CTL-mediated }immune response, \DJ \(_{1}\), chronic
HIV infection equilibrium with active {CTL-mediated }immune response,
\DJ \(_{2}\). We derive two threshold parameters, the basic HIV reproduction
number, \(\Re_{0}\), and the CTL-mediated immunity reproduction number, \(\Re
_{1}\). These parameters determine the existence and global stability of the
equilibria of the model. We prove the global asymptotic stability of all
equilibria by utilizing the Lyapunov function and LaSalle's invariance principle.
We have proven the following: (i) if \(\Re_{0}\leq1\), then \DJ \(_{0}\) is
globally asymptotically stable (G.A.S), (ii) if \(\Re_{1}\leq1<\Re_{0}\), then
\DJ \(_{1}\) is G.A.S, and (iii) if \(\Re_{1}>1\), then \DJ \(_{2}\) is G.A.S. We
have illustrated the theoretical results via numerical simulations. We have
studied the effects of cell-to-cell (CTC) transmission and saturation on the
dynamical behaviour of the system. We have shown that\ inclusion of CTC
transmission decreases the concentration of susceptible CD4\(^{+}\) T cells and
increases the concentrations of infected cells and free HIV particles. While
the inclusion of saturation increases the concentration of susceptible
CD4\(^{+}\) T cells and reduces the concentrations of infected cells and free
HIV particles.
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ISRP Style
Noura H. AlShamrani, Ahmed M. Elaiw, Stability of a CTL-mediated immunity HIV infection models with silent infected cells and cellular infection, Journal of Mathematics and Computer Science, 22 (2021), no. 3, 216--237
AMA Style
AlShamrani Noura H., Elaiw Ahmed M., Stability of a CTL-mediated immunity HIV infection models with silent infected cells and cellular infection. J Math Comput SCI-JM. (2021); 22(3):216--237
Chicago/Turabian Style
AlShamrani, Noura H., Elaiw, Ahmed M.. "Stability of a CTL-mediated immunity HIV infection models with silent infected cells and cellular infection." Journal of Mathematics and Computer Science, 22, no. 3 (2021): 216--237
Keywords
- HIV infection
- viral and cellular infections
- global stability
- silent infected cells
- CTL-mediated immune response
- Lyapunov function
MSC
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