Understanding Hepatitis B with chronic infection therapy and data analysis requires developing a mathematical model of the dynamical system. This study aims to examine the S \(I_{A}I_{C}\) R model with chronic infection therapy and data analysis worldwide and its actual implications. The boundedness and uniqueness solution of such an HBV model are confirmed, and Banach space is used to look for bounded discoveries. The developed system’s uniqueness is investigated to verify if it has a unique solution. A recently developed method for determining the stable location of the S \(I_{A}I_{C}\) R system is analyzed quantitatively and qualitatively to confirm its actual state. Furthermore, to comprehend the long-term impacts, the flip bifurcation of the constructed system has been confirmed using chaos. To determine the rate of change impact on HBV resulting from chronic infections and its data analysis, global stability is studied. The fractal fractional, a sophisticated technique for reliable bounded solutions, is used to find the solution of the suggested system using different fractional values. Owing to the early detection procedure, simulations have been created to examine the actual behavior and long-term impacts of HBV in the community, as well as data analysis and therapy. This study will help analyze the losses incurred by the individual due to a chronic stage infection, including actual data analysis, and develop control strategies based on our verified conclusions.
