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Stability of a general adaptive immunity virus dynamics model with multistages of infected cells and two routes of infection
Author(s) -
Elaiw Ahmed,
AlShamrani Noura
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5923
Subject(s) - ctl* , mathematics , lyapunov function , invariance principle , exponential stability , nonlinear system , dynamics (music) , virus , stability (learning theory) , function (biology) , viral infection , virology , immune system , biology , immunology , microbiology and biotechnology , physics , computer science , linguistics , philosophy , quantum mechanics , machine learning , acoustics , cd8
This paper studies an ( n +4)‐dimensional nonlinear virus dynamics model that characterizes the interactions of the viruses, susceptible host cells, n ‐stages of infected cells, B cells and cytotoxic T lymphocyte (CTL) cells. Both viral and cellular infections have been incorporated into the model. The infected‐susceptible and virus‐susceptible infection rates as well as the generation and removal rates of all compartments are described by general nonlinear functions. Five threshold parameters are computed, which insure the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established, which is sufficient to investigate the global dynamics of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions.