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

  • Received: 01 October 2015 Accepted: 29 June 2018 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 ΩRn and obtain an explicit formula for the basic reproductive number R0 of the model. Then we investigate the global behavior of the model in terms of R0: if R01, then the uninfected steady state is globally asymptotically stable, whereas if R0>1, then the infected steady state is globally asymptotically stable. In addition, when R0>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 ±, 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

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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 ΩRn and obtain an explicit formula for the basic reproductive number R0 of the model. Then we investigate the global behavior of the model in terms of R0: if R01, then the uninfected steady state is globally asymptotically stable, whereas if R0>1, then the infected steady state is globally asymptotically stable. In addition, when R0>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 ±, we prove the existence of traveling wave solutions. Numerical simulations are provided to illustrate the theoretical results.


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