A SEI model for hepatitis B is constructed where the susceptibility and other crucial transmission probabilities depend on the chronological age and the basic reproduction rate R₀ is derived. Under suitable (biological and mathematical) assumptions in a closed population, results of Houpa D. D. E. et al. [1] are extended from constant case of p and q to age-dependent case: the disease-free equilibrium is globally asymptotically stable (GAS) if R₀ < 1. On the other hand, R₀ > 1 induces that endemic equilibrium is GAS and the system is uniformly persistent.