One of the characteristics of HBV transmission is the age structure of the host population and the vertical transmission of the disease. That is the infection is transmitted directly from infected mother to an embryo, fetus, or baby during pregnancy or childbirth (the perinatal infection). We formulated an age-structured model for the transmission dynamics of HBV with differential infectivity: symptomatic and asymptomatic infections. The model without intervention strategies is completely analyzed. We compute the basic reproduction number which determines the outcome of the disease. We also compute equilibria and study their stability. The sensitivity analysis of the initial model parameters is performed (to determine the impact of control-related parameters on outbreak severity). Using optimal control theory, we determine the cost-effective balance of three interventions methods which minimizes HBV-related deaths as well as the costs associated with intervention.
Keywords: Age structure; HBV; Non-linear dynamical system; Optimal control; Stability.