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. KEYWORDS adaptive immune response, global stability, intracellular delay, Lyapunov function, pathogen infection Math Meth Appl Sci. 2018;41:6645-6672.wileyonlinelibrary.com/journal/mma
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 infectedsusceptible 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. KEYWORDS adaptive immune response, global stability, Lyapunov function, multistaged infected cells, viral and cellular infections CLASSIFICATION 34D20; 34D23; 37N25; 92B05
In this paper, we consider two nonlinear models for viral infection with humoral immunity. The first model contains four compartments; uninfected target cells, actively infected cells, free virus particles and B cells. The second model is a modification of the first one by including the latently infected cells. The incidence rate, removal rate of infected cells, production rate of viruses and the latent-to-active conversion rate are given by more general nonlinear functions. We have established a set of conditions on these general functions and determined two threshold parameters for each model which are sufficient to determine the global dynamics of the models. The global asymptotic stability of all equilibria of the models has been proven by using Lyapunov theory and applying LaSalle's invariance principle. We have performed some numerical simulations for the models with specific forms of the general functions. We have shown that, the numerical results are consistent with the theoretical results.
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