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

Article Contents

2015, Volume 12, Issue 4: 859-877. Doi: 10.3934/mbe.2015.12.859 open access

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

1.
School of Science and Technology, Zhejiang International Studies University, Hangzhou 310012
2.
Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250
3.
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240

Received: March 31, 2014

Revised: November 30, 2014

Published: March 2015

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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.

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Mathematics Subject Classification: Primary: 35L60, 92C37; Secondary: 35B35, 34K20.

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