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Mathematical Biosciences and Engineering

2015, Volume 12, Issue 4: 859-877. doi: 10.3934/mbe.2015.12.859
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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: 01 April 2014 Accepted: 29 June 2018 Published: 01 April 2015

  • MSC : Primary: 35L60, 92C37; Secondary: 35B35, 34K20.

  • 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.

    Citation: Yu Yang, Shigui Ruan, Dongmei Xiao. Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function[J]. Mathematical Biosciences and Engineering, 2015, 12(4): 859-877. doi: 10.3934/mbe.2015.12.859

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  • 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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