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Mathematical Biosciences and Engineering

2016, Volume 13, Issue 5: 935-968. doi: 10.3934/mbe.2016024
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Dynamics of a diffusive age-structured HBV model with saturating incidence

  • 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
  • Published: 01 July 2016

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

  • 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.

    Citation: Xichao Duan, Sanling Yuan, Kaifa Wang. Dynamics of a diffusive age-structured HBV model with saturating incidence[J]. Mathematical Biosciences and Engineering, 2016, 13(5): 935-968. doi: 10.3934/mbe.2016024

    Related Papers:

  • 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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