# American Institute of Mathematical Sciences

January  2012, 17(1): 401-416. doi: 10.3934/dcdsb.2012.17.401

## Global stability of a five-dimensional model with immune responses and delay

 1 Key Laboratory of Eco-environments in Three Gorges Reservoir Region, School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China, China

Received  September 2010 Revised  December 2010 Published  October 2011

In this article, we study a virus model with immune responses and an intracellular delay which is relatively large compared with virus life-cycle and is an indispensable factor in understanding virus infections, such as HIV and HBV infections. By constructing suitable Liapunov functionals, the global dynamics of the model is completely determined by the reproductive numbers for viral infection $R_0$, for CTL immune response $R_1$, for antibody immune response $R_2$, for CTL immune competition $R_3$ and for antibody immune competition $R_4$. The global stability of the model precludes the existence of periodic solution and other complex dynamical behaviors.
Citation: Yincui Yan, Wendi Wang. Global stability of a five-dimensional model with immune responses and delay. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 401-416. doi: 10.3934/dcdsb.2012.17.401
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