Optimal control in a mathematical model of a spread of the obesity epidemic and its impact on diabetes

Abstract

The obesity epidemic is associated with several cardiovascular risk factors, including diabetes mellitus, dyslipidemia, and hypertension. Insulin resistance is believed to play a crucial role in the emergence of various health problems. Apart from genetic factors, obesity, particularly abdominal obesity, is a major contributor to the onset of diabetes. In this study, we present a mathematical model that captures the interplay between the prevalence of obesity and diabetes, and we investigate the adverse effects of excess weight on the well-being of diabetic individuals. Our approach employs Pontryagin’s maximum principle to determine the optimal control strategies, and we solve the resulting system through iterative methods. Finally, we perform numerical simulations using Matlab to validate our theoretical analysis.