Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function.

Yu Yang,Shigui Ruan,Dongmei Xiao

doi:10.3934/mbe.2015.12.859

Abstract

In this paper, we study an age-structured virus dynamics model with Beddington-DeAngelis infection function. An explicit formula for the basic reproductive number R0 of the model is obtained. We investigate the global behavior of the model in terms of R0: if R0 ≤ 1, then the infection-free equilibrium is globally asymptotically stable, whereas if R0 > 1, then the infection equilibrium is globally asymptotically stable. Finally, some special cases, which reduce to some known HIV infection models studied by other researchers, are considered.

Highlights

Various mathematical models of within-host virus dynamics with or without delay have been studied by many authors over the past two decades (Culshaw and Ruan[4], De Leenheer and Smith [8], Huang et al [13], Li and Shu [17], Nowak and Bangham [25], Nowak and May [26], Perelson and Nelson [27])
Nelson et al [24] proposed an age-structured model for HIV-1 infection with bilinear interactions between the uninfected target cells and the virus, which is a generalization of the standard delay differential equation models previously used
We aim to study the global behavior of the following age-structured virus dynamics model with Beddington-DeAngelis infection function:

Summary

Introduction

Various mathematical models of within-host virus dynamics with or without delay have been studied by many authors over the past two decades (Culshaw and Ruan[4], De Leenheer and Smith [8], Huang et al [13], Li and Shu [17], Nowak and Bangham [25], Nowak and May [26], Perelson and Nelson [27]). Nelson et al [24] proposed an age-structured model for HIV-1 infection with bilinear interactions between the uninfected target cells and the virus, which is a generalization of the standard delay differential equation models previously used. Virus dynamics model, infection equilibrium, Liapunov function, global stability. Research of DX was supported by National Natural Science Foundation of China (Nos.11371248 & 11431008)

Objectives

Conclusion