title: Dynamics of a diffusive age-structured HBV model with saturating incidence.
abstract: 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 Ω ⊂ Rn 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 R0 ≤ 1, 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.
authors: School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China. email: xcduan82@126.com.
authors: Xichao
authors: X
authors: Duan
authors: Sanling
authors: S
authors: Yuan
authors: Kaifa
authors: K
authors: Wang
mesh_terms: D017677:Age Distribution; D003198:Computer Simulation; D006509:Hepatitis B / Q000453:epidemiology*; D006515:Hepatitis B virus; D006801:Humans; D015994:Incidence; D008954:Models, Biological