Abstract
We propose a discrete-time viral model with antibody and cell-mediated immune responses. Two types of infected cells are incorporated into the model, namely latently infected and actively infected. The incidence rate of infection as well as the production and removal rates of all compartments are modeled by general nonlinear functions. The model contains three types of intracellular time delays. We utilize nonstandard finite difference (NSFD) method to discretize the continuous-time model. We prove that NSFD preserves the positivity and boundedness of the solutions of the model. Based on four threshold parameters, the existence of the five equilibria of the model is established. We perform global stability of all equilibria of the model by using Lyapunov approach. Numerical simulations are carried out to illustrate our theoretical results. The impact of time delay on the viral dynamics is established.
Highlights
Mathematical modeling and analysis of within host human viral infections have provided useful insights into the understanding of interplay between three main compartments: viruses, target cells, and infected cells
We first show that the solutions of the discrete-time model are positive and bounded, we prove the global stability of the equilibria by constructing Lyapunov functions
We perform numerical simulations to support the global stability results. The achievements in this present paper look ahead to research perspectives focused on pattern formation induced by the action of the external environments, for instance, by Keller Segel dynamics [52]
Summary
Mathematical modeling and analysis of within host human viral infections have provided useful insights into the understanding of interplay between three main compartments: viruses, target cells, and infected cells. Delayed viral infection models have been constructed and analyzed in several works (see, e.g., [19,20,21,22,23,24,25,26,27,28,29,30,31,32]) To incorporate both cell-mediated and antibody immune responses as well as the time delay into the virus dynamics, Wodarz [33] has proposed the following model:. The impact of both antibody and cell-mediated immune responses on the discrete-time virus infection model has not been investigated before. The aim of the present paper is to formulate and analyze a discrete-time viral infection model with both antibody and cell-mediated immune responses.
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