  Hepatitis B is a potentially life-threatening liver infection caused by the
hepatitis B virus (HBV). In this paper, the transmission dynamics of hepatitis
B is formulated with a mathematical model with considerations of different
classes of individuals, namely immunized, susceptible, latent,infected and
recovered class. The role of vaccination of new born babies against hepatitis B
and the treatment of both latently and actively infected individuals in
controlling the spread are factored into the model. The model in this study is
based on the standard SEIR model. The disease-free equilibrium state of the
model was established and its stability analyzed using the Routh-Hurwitz
theorem. The result of the analysis of the stability of the disease-free
equilibrium state shows that hepatitis B can totally be eradicated if effort is
made to ensure that the sum of the rate of recovery of the latent class, the
rate at which latently infected individuals become actively infected and the
rate of natural death must have a lower bound.
