Global stability of a five-dimensional model with immune responsesand delay

Yincui Yan; Wendi Wang

doi:10.3934/dcdsb.2012.17.401

Article Contents

2012, Volume 17, Issue 1: 401-416. Doi: 10.3934/dcdsb.2012.17.401

This issue Previous Article Stability and Hopf bifurcations for a delayed diffusion system in population dynamics Next Article Traveling wave solutions in an integro-differential competition model

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

Yincui Yan^1, and
Wendi Wang^1,

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

Received: September 2010

Revised: December 2010

Published: January 2012

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: Primary: 92D30; Secondary: 34K20.

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