Genetic algorithms for the optimal control of a continuous model of a Diabetic Population

Diabetes is a global disease with a huge and growing socio-economic burden, affecting individuals, families and society. In this paper we present the mathematical model with optimal control approache proposed to deal with the dynamics of a diabetic population and the numerical methods that have been used to control the risks of diabetes. We will discuss the most dynamic mathematical models that exist, and the role of the control in the process of reducing the risks of diabetes and the incidence of diabetes. We will also discuss the existence and uniqueness of solution for the system and the use of Pontryagin’s maximum principle to characterize the optimal controls and we will present a comparison between the Gumel method proposed in [19] and Genetic algorithm (GA) to search for an optimal control, and finally numerical simulations are performed to verify the theoretical analysis using Matlab.