Memory‐Driven Dynamics of Hepatitis B Transmission Incorporating Media Awareness

ABSTRACT In this study, we develop a novel fractal‐fractional mathematical model for the transmission dynamics of Hepatitis B virus (HBV) incorporating treatment and media‐driven awareness. The model is formulated using the Atangana–Baleanu–Caputo fractal‐fractional operator, which effectively captures both memory effects and the heterogeneous (fractal) nature of disease transmission. Unlike classical integer‐order models, this approach provides a more realistic description of HBV dynamics by accounting for nonlocal interactions and long‐term dependencies. The proposed model is analyzed qualitatively by establishing key mathematical properties, including positivity, boundedness, existence, and uniqueness of solutions. The basic reproduction number is derived to examine the threshold behavior of the system, and the stability of equilibrium points is investigated. Numerical simulations are carried out to illustrate the impact of key parameters on disease progression. The results show that increasing media awareness significantly reduces the susceptible and infected populations by promoting preventive behavior, while improved treatment rates enhance recovery. Moreover, the fractal‐fractional framework reveals persistent memory effects, indicating that past disease states play an important role in shaping current dynamics. These findings highlight the importance of combining treatment strategies with awareness programs to effectively control HBV transmission and provide useful insights for public health policy design.