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Global stability of delay‐distributed viral infection model with two modes of viral transmission and B‐cell impairment
Author(s) -
Elaiw A. M.,
Alshehaiween S. F.
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.6408
Subject(s) - mathematics , basic reproduction number , stability (learning theory) , transmission (telecommunications) , invariance principle , lyapunov function , viral replication , viral infection , function (biology) , cell , exponential stability , virus , control theory (sociology) , virology , computer science , biology , microbiology and biotechnology , nonlinear system , physics , control (management) , population , philosophy , artificial intelligence , linguistics , sociology , genetics , telecommunications , quantum mechanics , machine learning , demography
This paper formulates a virus dynamics model with impairment of B‐cell functions. The model incorporates two modes of viral transmission: cell‐free and cell‐to‐cell. The cell‐free and cell‐cell incidence rates are modeled by general functions. The model incorporates both, latently and actively, infected cells as well as three distributed time delays. Nonnegativity and boundedness properties of the solutions are proven to show the well‐posedness of the model. The model admits two equilibria that are determined by the basic reproduction number R 0 . 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. The effect of impairment of B‐cell functions and time delays on the virus dynamics are studied. We have shown that if the functions of B‐cell is impaired, then the concentration of viruses is increased in the plasma. Moreover, we have observed that increasing the time delay will suppress the viral replication.