A Mathematical study on the vaccination impact on the disease dynamics of HBV

Abstract

We develop a deterministic model to understand the underlying dynamics of HBV infection at population level. The model, which incorporates the vaccination and treatment of individuals, the re-infections of latent, carrier and recovery individuals, is rigorously analyzed to gain insight into its dynamical features. The mathematical analysis reveals that the model exhibits a backward bifurcation. This phenomenon resulted due to the exogenous re-infection of HBV disease . It is shown that, in the absence of such re-infection, the model has a disease-free equilibrium (DFE) which is globally asymptotically stable (GAS) using Lyapunov function and LaSalle Invariance Principle whenever the associated reproduction threshold is less than unity. Further, the model has a unique endemic equilibrium(EEP), for a special case, whenever the associate threshold quantity exceeds unity. This EEP is shown to be GAS, for a special case, using a non-linear Lyapunov function of Goh- Volterra type.