(untitled) (Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2024)
This research focuses on the mathematical modeling of Hepatitis B virus (HBV) dynamics using optimal control theory to enhance understanding of transmission patterns and optimize intervention strategies. An ordinary differential equation (ODE) model is proposed, capturing the dynamics of HBV transmission through distinct compartments: susceptible, exposed, infected, liver cirrhosis, and removed. Advanced liver cirrhosis, a severe stage of chronic liver disease caused by sustained and progressive damage, has emerged as a critical non-communicable health concern. The study employs mathematical simulations to analyze the impact of various control measures in mitigating HBV spread. Through the application of optimal control theory and the Hamiltonian principle, the research identifies effective strategies, such as vaccination, treatment, and awareness campaigns, to manage and limit HBV transmission. The primary objective is to minimize the number of individuals in the infected and cirrhotic stages while reducing associated intervention costs. By targeting HBV, a leading cause of cirrhosis, the study aims to lower the incidence of chronic liver disease. The findings highlight the importance of vaccination, effective treatment protocols, and public awareness in curbing the progression of HBV and reducing its long-term health impacts. This research provides crucial insights for public health policies and the development of targeted strategies to combat HBV and its complications.