Mathematical Model and Analysis of Transmission Dynamics of Hepatitis B Virus

Abstract: 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.