Stability of an adaptive immunity viral infection model with multi-stages of infected cells and two routes of infection

N. H. AlShamrani; A. M. Elaiw; N. H. AlShamrani; A. M. Elaiw

doi:10.3934/mbe.2020030

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 1: 575-605. doi: 10.3934/mbe.2020030

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Research article

Stability of an adaptive immunity viral infection model with multi-stages of infected cells and two routes of infection

N. H. AlShamrani ^1,2,
A. M. Elaiw ^{1
,
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1.
Department of Mathematics, Faculty of Science, King Abdulaziz University, 21589 Jeddah, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, University of Jeddah, 21589 Jeddah, Saudi Arabia

Received: 07 May 2019 Accepted: 12 October 2019 Published: 21 October 2019

This paper studies an (n + 4)-dimensional nonlinear viral infection model that characterizes the interactions of the viruses, susceptible host cells, n-stages of infected cells, CTL cells and B cells. Both viral and cellular infections have been incorporated into the model. The well-posedness of the model is justified. The model admits five equilibria which are determined by five threshold parameters. The global stability of each equilibrium is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations.
- viral and cellular infections,
- global stability,
- adaptive immune response,
- Lyapunov function,
- multi-staged infected cells
Citation: N. H. AlShamrani, A. M. Elaiw. Stability of an adaptive immunity viral infection model with multi-stages of infected cells and two routes of infection[J]. Mathematical Biosciences and Engineering, 2020, 17(1): 575-605. doi: 10.3934/mbe.2020030

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Abstract

This paper studies an (n + 4)-dimensional nonlinear viral infection model that characterizes the interactions of the viruses, susceptible host cells, n-stages of infected cells, CTL cells and B cells. Both viral and cellular infections have been incorporated into the model. The well-posedness of the model is justified. The model admits five equilibria which are determined by five threshold parameters. The global stability of each equilibrium is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations.

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