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Stability of a general delay‐distributed virus dynamics model with multi‐staged infected progression and immune response
Author(s) -
Elaiw A. M.,
AlShamrani N. H.
Publication year - 2017
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.4002
Subject(s) - mathematics , invariance principle , basic reproduction number , stability (learning theory) , nonlinear system , exponential stability , immune system , lyapunov function , dynamics (music) , control theory (sociology) , computer science , immunology , physics , biology , control (management) , artificial intelligence , population , philosophy , linguistics , demography , quantum mechanics , machine learning , sociology , acoustics
In this paper, we formulate a ( n + 3)‐dimensional nonlinear virus dynamics model that considers n ‐stages of the infected cells and n + 1 distributed time delays. The model incorporates humoral immune response and general nonlinear forms for the incidence rate of infection, the generation and removal rates of the cells and viruses. Under a set of conditions on the general functions, the basic infection reproduction numberR 0 Mand the humoral immune response activation numberR 1 Mare derived. Utilizing Lyapunov functionals and LaSalle's invariance principle, the global asymptotic stability of all steady states of the model are proven. Numerical simulations are carried out to confirm the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.