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

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

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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Keywords 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. Mathematical Biosciences and Engineering, 2020, 17(1): 575-605. doi: 10.3934/mbe.2020030

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