Globale Stability in a Viral Infection Model with Beddington-DeAngelis Functional Response

Wang Zhanwei,He Xia

doi:10.2174/1874070701509010027

Abstract

The stability of a mathematical model for viral infection with Beddington-DeAngelis functional response is considered in this paper. If the basic reproduction number R ≤1, by the Routh-Hurwitz criterion and Lyapunov function, the uninfected equilibrium E is globally asymptotically stable. Then, the global stability of the infected equilibrium E is obtained by the method of Lyapunov function

Highlights

Human Immunodeficiency Virus and Acquired Immune Deficiency Syndrome (AIDS) have received much attention from the first case of AIDS was diagnosed on December 1st in 1981
It is proven to be valuable in understanding the population dynamics of viral load in vivo with mathematical models
Many mathematical models have been developed to describe the infection with Human Immunodeficiency virus (HIV)

Summary

INTRODUCTION

Human Immunodeficiency Virus and Acquired Immune Deficiency Syndrome (AIDS) have received much attention from the first case of AIDS was diagnosed on December 1st in 1981. Many mathematical models have been developed to describe the infection with Human Immunodeficiency virus (HIV) (see[1,2,3,4,5,6,7,8,9]). In model (1.1), it is assumed that healthy CD4 T-cells are input at a constant rate , and die at a rate dx. The infection rate is bilinear in most HIV-I models with the virus v and healthy CD4 T- cells x , actual incidence rates are probably not linear over the entire range of v and x. We consider a HIV-I model with Beddington-DeAngelis function response as follows: x '. The biological meanings of these parameters are the similar to those appearing parameters in model (1.1)

EQUILIBRIA AND GLOBAL STABILITY ANALYSIS

CONCLUSION