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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 654507, 11 pages
http://dx.doi.org/10.1155/2015/654507
Research Article

Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral Immunity

1School of Mathematical Science, Heilongjiang University, Harbin 150080, China
2School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received 13 July 2014; Revised 8 September 2014; Accepted 10 September 2014

Academic Editor: Zhen Jin

Copyright © 2015 Xinxin Tian and Jinliang Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We formulate a ()-dimensional viral infection model with humoral immunity, classes of uninfected target cells and   classes of infected cells. The incidence rate of infection is given by nonlinear incidence rate, Beddington-DeAngelis functional response. The model admits discrete time delays describing the time needed for infection of uninfected target cells and virus replication. By constructing suitable Lyapunov functionals, we establish that the global dynamics are determined by two sharp threshold parameters: and . Namely, a typical two-threshold scenario is shown. If , the infection-free equilibrium is globally asymptotically stable, and the viruses are cleared. If , the immune-free equilibrium is globally asymptotically stable, and the infection becomes chronic but with no persistent antibody immune response. If , the endemic equilibrium is globally asymptotically stable, and the infection is chronic with persistent antibody immune response.