Dynamic analysis of a hepatitis B model with three-age-classes

Based on the fact that the likelihood of becoming chronically infected is dependent on age at primary infection Kane (1995) [2], Edmunds et al. (1993) [3], Medley et al. (2001) [4], and Ganem and Prince (2004) [6], we formulate a hepatitis B transmission model with three age classes. The reproduction number, R 0 is defined and the dynamical behavior of the model is analyzed. It is proved that the disease-free equilibrium is globally stable if R 0 < 1 , and there exists at least one endemic equilibrium and that the disease is uniformly persistent if R 0 > 1 . The unique endemic equilibrium and its global stability is obtained in a special case. Simulations are also conducted to compare the dynamical behavior of the model with and without age classes.