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

• A model with three age classes for hepatitis B transmission is formulated.
• Theoretical results including stability and persistence are obtained.
• A special case of the model is analyzed theoretically.
• It originally compares two types of HBV models.
• Simulations are conducted to analyze the behaviors of the model.

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, R0R0 is defined and the dynamical behavior of the model is analyzed. It is proved that the disease-free equilibrium is globally stable if R0<1R0<1, and there exists at least one endemic equilibrium and that the disease is uniformly persistent if R0>1R0>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.