Complete classification of global dynamics of a virus model withimmune responses

Cuicui Jiang; Wendi Wang

doi:10.3934/dcdsb.2014.19.1087

Article Contents

2014, Volume 19, Issue 4: 1087-1103. Doi: 10.3934/dcdsb.2014.19.1087

This issue Previous Article Martingale and pathwise solutions to the stochastic Zakharov-Kuznetsov equation with multiplicative noise Next Article Global stability of a multi-group SIS epidemic model for population migration

Complete classification of global dynamics of a virus model with immune responses

Cuicui Jiang^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: March 31, 2013

Revised: June 30, 2013

Published: May 2014

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Abstract

A virus dynamics model for HIV or HBV is studied, which incorporates saturation effects of immune responses and an intracellular time delay. With the aid of persistence theory and Liapunov method, it is shown that the global stability of the model is totally determined by the reproductive numbers for viral infection, for CTL immune response, for antibody immune response, for antibody invasion and for CTL immune invasion. The results preclude the complicated behaviors such as the backward bifurcations and Hopf bifurcations which may be induced by saturation factors and a time delay.

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

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