Deep learning-driven insights into the transmission dynamics of hepatitis B virus with treatment.

Viral infections have spread globally, profoundly affecting social and economic aspects of life and causing widespread suffering. Infection caused by the hepatitis B virus (HBV) is one of the significant global health challenges but can be effectively controlled with appropriate treatment and vaccination. In this study, we present a fractional modeling approach and novel computational technique to analyze the impact of treatment on HBV transmission dynamics using the Caputo derivative. The existence and uniqueness of solutions for the fractional model are established using fixed point theory. The local stability of the disease-free equilibrium is examined using the linearization technique, while global stability is confirmed through the Hyers-Ulam-Rassias approach. Numerical simulation of the Caputo HBV model is performed using the fractional Euler method for various fractional orders, validating the theoretical results. Furthermore, to enhance the accuracy of epidemiological modeling, we develop a novel computational technique using deep neural networks (DNNs) to solve the Caputo HBV model. To support our theoretical findings, we conduct a comprehensive evaluation of the DNN-generated solutions by benchmarking them against standard numerical results and assessing them through multiple phases of training, validation, testing, error distribution analysis, and regression evaluation. The neural network training state is visualized using the gradient value of Mu, along with validation checks and detailed curve-fitting analyses for each model equation. The precision of the proposed scheme is checked using the comparison of the outputs with best validation performances around [Formula: see text]-[Formula: see text], and minimum absolute error ranges from [Formula: see text] to [Formula: see text]. We believe that the proposed hybrid architecture enhances accuracy and computational efficiency offering a novel and effective framework not previously explored in infectious disease modeling.