Transmission dynamics of an age-structured Hepatitis-B infection with differential infectivity

Abstract

An age-structured deterministic mathematical model describing the transmission dynamics of Hepatitis B (HBV) is proposed in this paper. The model exhibits the phenomenon of backward bifurcation in which a stable disease-free equilibrium coexists with a stable endemic equilibrium as the basic reproduction number (BRN) approaches one. The epidemiological consequence of backward bifurcation is that the requirement for making the BRN less than one is necessary but not sufficient condition for efficiently controlling the persistence of the disease in the human population. We estimate the model parameters with the help of real data from South Africa using the nonlinear least-squares curve fitting method. We also use the forward normalized sensitivity index technique to determine the most sensitive parameters. Numerical simulations confirm that reducing the transition of chronically infected children to adults through treatment is crucial to eliminating Hepatitis-B in South Africa.