A novel fractional mathematical model for the impact of media awareness on Hepatitis B

Hepatitis B is one of the most severe viral infections, transmitted through contact with infected blood, sexual interaction, bodily fluids, and from mother to child during delivery. In this study, we develop a nonlinear fractional-order mathematical model of the Hepatitis B virus (HBV) using the Caputo fractional derivative operator. The use of the Caputo operator is particularly significant as it captures memory and hereditary properties of disease progression, providing a more realistic representation compared to classical integer-order models. For numerical simulations, we employ the Homotopy Analysis Transform Method (HATM), which combines the homotopy analysis method, homotopy polynomials, and the Laplace transform. Furthermore, the existence and uniqueness of the solution are established, and stability analysis is carried out using fixed-point theory. Sensitivity analysis is performed to identify the most influential parameters affecting HBV transmission. Numerical results, obtained using MATLAB, indicate that increasing media awareness significantly reduces the spread of HBV. Additionally, the inclusion of fractional-order dynamics enhances the model's capability as an effective tool for controlling disease transmission. The findings of this study provide valuable insights for the healthcare sector and can assist in predicting disease outcomes and designing effective treatment and prevention strategies.