Hepatitis B remains a persistent public health challenge due to its chronic nature and transmission complexity. In this study, we propose a novel fractional-order model using the Atangana Baleanu Caputo (ABC) derivative to explore the transmission dynamics of Hepatitis B, incorporating the impact of government intervention, social behavior, and public response. The model integrates realistic features such as memory effects and non-local interactions, which are essential in capturing long-term behavioral and epidemiological trends. We conduct a detailed mathematical analysis, including the existence and uniqueness of solutions, positivity and boundedness of compartments, and Ulam-Hyers (UH) and generalized Ulam-Hyers (GUH) stability, to establish the model's theoretical robustness. The basic reproduction number R₀ is derived, the Hepatitis B free equilibrium and Hepatitis B present equilibrium are obtained, and their local stability is analyzed. and the global stability of the Hepatitis B present equilibrium is also established. Sensitivity analysis reveals the most influential parameters affecting disease spread, emphasizing the importance of behavioral awareness and intervention strategies. Using a numerical scheme based on two-step Lagrange polynomial interpolation tailored to the ABC operator. We simulate the model to investigate how changes in fractional order and key parameters influence disease progression. The results demonstrate that strengthening public awareness, government response, and behavioral adherence can significantly reduce disease transmission. This is one of the first studies to explore Hepatitis B dynamics using an ABC fractional framework that integrates socio-behavioral influences, offering new insights into effective disease control strategies under uncertainty and memory effects.
Sinha et al. (2025) studied this question.