Asian Research Journal of Mathematics

In this paper, we develop and analyze a mathematical model to better understand the transmission dynamics of Hepatitis B Virus (HBV), focusing on the interaction between latent and infectious individuals. The model is designed to capture the long-term progression of the disease and to explore how different epidemiological conditions influence its persistence within a population. We derive the equilibrium states of the system and examine their stability to determine when the disease dies out or becomes endemic. The existence and stability of the endemic equilibrium are examined to understand the long–term behavior of the disease. Furthermore, the dynamics of the system near the disease–free equilibrium E₀ at the threshold R₀ = 1 are analyzed using centre manifold theory. This analysis helps determine the local stability and bifurcation behavior of the endemic equilibrium. Numerical simulations show that, without effective control measures, the infectious population rises rapidly at the early stage of the outbreak, reaches a significant peak, and then undergoes damped oscillations before settling at a stable endemic level. In contrast, the latent population remains relatively small throughout the simulation, although it follows a similar oscillatory pattern. These results suggest that even when initial outbreaks subside, HBV can persist in the population over the long term. The findings emphasize the importance of sustained public health interventions, particularly vaccination and treatment programs, in reducing transmission and preventing long-term endemicity.