Application of Optimal Control Strategies on Incidence of Medical Complications in Diabetic Patients’ Population

Abstract

Diabetes mellitus is a chronic condition characterized by elevated blood glucose levels, which can lead to severe health complications if not properly managed. The increasing prevalence of diabetes worldwide has made it a major public health concern. This study formulates and analyzes an optimal control model for diabetes management, focusing on minimizing complications and treatment costs. The model is structured around a population of diabetic patients, incorporating dynamic interactions between healthy, susceptible, diabetic, complication, and treatment populations. An objective functional is defined, integrating costs associated with complications and treatment efforts, and is subjected to optimization through control strategies aimed at enhancing patient education, regular monitoring, and comprehensive care. The application of the Pontryagin Maximum Principle provides a solid theoretical foundation for identifying optimal control strategies. Utilizing a fourth-order Runge-Kutta method, the model is simulated under varying control conditions to assess the impact of interventions. The results demonstrate that increasing control measures significantly reduces the incidence of complications while improving treatment rates. The findings highlight the importance of strategic health management interventions in mitigating the burden of diabetes-related complications and emphasize the model's applicability in real-world healthcare settings. This research provides a robust framework for policymakers and healthcare providers to devise effective strategies that enhance the quality of care for diabetic patients.