Mathematical Biosciences and Engineering, 2016, 13(5): 935-968. doi: 10.3934/mbe.2016024

Primary: 35C07, 35K57, 35J61; Secondary: 37B25, 92D30.

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Dynamics of a diffusive age-structured HBV model with saturating incidence

Xichao Duan, Sanling Yuan, Kaifa Wang

1. School of Management, University of Shanghai for Science and Technology, Shanghai 200093
2. College of Science, Shanghai University for Science and Technology, Shanghai 200093
3. Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038

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In this paper, we propose and investigate an age-structured hepatitis B virus (HBV) model with saturating incidence and spatial diffusion where the viral contamination process is described by the age-since-infection. We first analyze the well-posedness of the initial-boundary values problem of the model in the bounded domain $\Omega\subset\mathbb{R}^n$ and obtain an explicit formula for the basic reproductive number $R_0$ of the model. Then we investigate the global behavior of the model in terms of $R_0$: if $R_0\leq1$, then the uninfected steady state is globally asymptotically stable, whereas if $R_0>1$, then the infected steady state is globally asymptotically stable. In addition, when $R_0>1$, by constructing a suitable Lyapunov-like functional decreasing along the travelling waves to show their convergence towards two steady states as $t$ tends to $\pm\infty$, we prove the existence of traveling wave solutions. Numerical simulations are provided to illustrate the theoretical results.
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