Fractional order modeling of hepatitis B virus transmission with imperfect vaccine efficacy.

This study aims to develop and analyze a model of hepatitis B virus transmission dynamics using integer and fractional derivatives in the Caputo sense. After formulating the models, we conduct an asymptotic stability analysis of the disease-free equilibrium point of both models. The Lyapunov technique demonstrates that under specific conditions, the disease-free equilibrium point in both models remains globally asymptotically stable. The study demonstrates that both models can have at least one endemic equilibrium when [Formula: see text], using the vaccination coverage parameter to identify positive equilibrium points. The Banach contraction principle is used to establish the uniqueness and existence of each fractional model's solutions, followed by demonstrating their global stability using the Ulam-Hyers technique. The model is calibrated using reported hepatitis B cases in Nigeria, allowing for parameter estimations. The study indicates that the disease is endemic in this country, as [Formula: see text], indicating a higher level of endemicity. The Adams-Bashforth approach is used to develop a numerical scheme, which is then validated through numerical simulations and evaluated under fractional order parameter variations.