On the dynamics of hepatitis B virus disease

Hepatitis B is a serious liver infection caused by hepatitis B virus (HBV). In this paper, we review the deterministic model of HBV proposed by Emerenini and Inyama in 2018 to carry out a rigorous mathematical analysis. The analysis of the model reveals that an endemic equilibrium exists in addition to the disease free equilibrium (DFE) point. The vaccinated reproduction number, Rv is derived and revealed that if Rv <1> 1, while the endemic equilibrium point (EEP) is the only asymptotic stable equilibrium point when Rv > 1. The global asymptotic stability of both the disease free equilibrium and endemic equilibrium points are proved using Lyapunov function in conjunction with LaSalles’ Invariance Principle. Furthermore, we obtain the minimum value of the fraction of newborn babies required to be vaccinated for effective disease control.