On an Age-Structured Hepatitis B Virus Infection Model with HBV DNA-Containing Capsids

Abstract

In this paper, we study an age-structured hepatitis B virus model with DNA-containing capsids. We obtain the well-posedness of the model by reformulate the model as an abstract Cauchy problem, and we find a threshold number $$\mathfrak {R}_0$$ for the existence of the steady states. The local stability of each steady states is established by linearizing the system and analyze the corresponding characteristic equation. Furthermore, we investigate the uniform persistence of the system and constructing Lyapunov functionals to show the global stability of each steady states. We observe that the virus-free steady state is globally asymptotically stable when $$\mathfrak {R}_0<1$$ , while the infection steady state is globally asymptotically stable when $$\mathfrak {R}_0>1$$ . Numerical simulations are also presented to support the analytical results.