Global stability of a delayed humoral immunity virus dynamics model with nonlinear incidence and infected cells removal rates

Article

Abstract

In this paper, we investigate the dynamical behavior of a nonlinear model for viral infection with humoral immune response and two discrete delays. The model is a four-dimensional system which describes the interactions of the virus, uninfected target cells, infected cells and B cells. We assume that the incidence rate and removal rate of infected cells are given by general nonlinear functions. We derive two threshold parameters, the basic reproduction number \(R_{0}\) and the humoral immunity number \(R_{1}\). Utilizing Lyapunov functionals and LaSalle’s invariance principle, the global asymptotic stability of the steady states of the model has been studied. We have established a set of sufficient conditions which guarantee the global stability of the model. We have proven that (1) if \(R_{0}\le 1\), then the infection-free steady state is globally asymptotically stable (GAS), (2) if \(R_{1}\le 1<R_{0}\), then the chronic-infection steady state without humoral immune response is GAS, (3) if \(R_{1}>1\), then the chronic-infection steady state with humoral immune response is GAS. We introduce an example and conduct some numerical simulations to confirm our theoretical results.

Keywords

Virus dynamics Intracellular delay Global stability Humoral immune response Lyapunov functional 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

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