Dynamical analysis for a hepatitis B transmission model with immigration and infection age.

Hepatitis B virus (HBV) is responsible for an estimated 378 million infections worldwide and 620, 000 deaths annually. Safe and effective vaccination programs have been available for decades, but coverage is limited due to economic and social factors. We investigate the effect of immigration and infection age on HBV transmission dynamics, incorporating age-dependent immigration flow and vertical transmission. The mathematical model can be used to describe HBV transmission in highly endemic regions with vertical transmission and migration of infected HBV individuals. Due to the effects of immigration, there is no disease-free equilibrium or reproduction number. We show that the unique endemic equilibrium exists only when immigration into the infective class is measurable. The smoothness and attractiveness of the solution semiflow are analyzed, and boundedness and uniform persistence are determined. Global stability of the unique endemic equilibrium is shown by a Lyapunov functional for a special case.