### Mathematical Biosciences and Engineering

2015, Issue 4: 859-877. doi: 10.3934/mbe.2015.12.859

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

• 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

### Related Papers:

• 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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