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Hepatitis B remains a major global health challenge, requiring advanced mathematical models to understand and control its spread. This study develops a fractional-order mathematical model using the Caputo fractional derivative (CFD), incorporating awareness, vaccination, and a Beddington-DeAngelis type incidence rate to better capture disease dynamics. The model considers preventive measures by susceptible individuals and the inhibition effect of treatment on infectives, providing a realistic approach to disease transmission. The study ensures the model’s positivity and boundedness, demonstrates the existence and uniqueness of its solution, and investigates the Ulam-Hyers type stability and generalized Ulam-Hyers (GUH) type stability. It derives the Hepatitis B-free equilibrium (HBFE) and Hepatitis B-present equilibrium (HBPE) points, analyzing their local stability using the basic reproduction number and proving the global stability of the endemic equilibrium through a Lyapunov function. Sensitivity analysis identifies key parameters influencing disease transmission, offering valuable insights for control strategies. Numerical simulations use the Lagrange two-step polynomial method, effectively demonstrating parameter impacts on disease progression. The results show that higher awareness and vaccination rates reduce infection levels, emphasizing the role of public health interventions in controlling Hepatitis B.
Soni et al. (Wed,) studied this question.