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Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays
Author(s) -
Elaiw Ahmed M.,
AlShamrani Noura H.
Publication year - 2018
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.5182
Subject(s) - mathematics , ctl* , lyapunov function , bounded function , latency (audio) , pathogen , nonlinear system , control theory (sociology) , stability (learning theory) , immune system , dynamics (music) , mathematical analysis , immunology , biology , computer science , physics , telecommunications , control (management) , quantum mechanics , artificial intelligence , machine learning , acoustics , cd8
We incorporate three distributed time delays into the model of pathogen dynamics with antibody and Cytotoxic T Lymphocyte (CTL) immune responses. We consider both actively and latently infected cells. The pathogen‐target incidence rate, production/proliferation, and removal rates of the cells and pathogens are represented by general nonlinear functions. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive four threshold parameters that fully determine the existence and stability of the five steady states of the model. Using Lyapunov functionals, we established the global stability of the steady states of the model. The theoretical results are confirmed by numerical simulations.