Mathematical Biosciences and Engineering (MBE)

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

Pages: 859 - 877, Volume 12, Issue 4, August 2015      doi:10.3934/mbe.2015.12.859

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Yu Yang - School of Science and Technology, Zhejiang International Studies University, Hangzhou 310012, China (email)
Shigui Ruan - Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250, United States (email)
Dongmei Xiao - Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China (email)

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 $\mathcal{R}_{0}$ of the model is obtained. We investigate the global behavior of the model in terms of $\mathcal{R}_{0}$: if $\mathcal{R}_{0}\leq1$, then the infection-free equilibrium is globally asymptotically stable, whereas if $\mathcal{R}_{0}>1$, 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.

Keywords:  Age structure, virus dynamics model, infection equilibrium, Liapunov function, global stability.
Mathematics Subject Classification:  Primary: 35L60, 92C37; Secondary: 35B35, 34K20.

Received: April 2014;      Accepted: December 2014;      Available Online: April 2015.