Optimal Control of a Three-State Diabetic Population Model with Interventions

Abstract

This paper studies an optimal control problem to describe the population dynamics of diabetes in the presence of intervention effects. We propose two control variables representing the interventions to reduce the incidence of diabetes, and the interventions to reduce the incidence of complications. By applying the optimal control theory, we seek to minimize the relative cost associated with the intervention efforts and to reduce the total number of people with diabetes. The solution to the optimality system is approximated by using the Forward-Backward Sweep Method. The numerical simulations show that the number of diabetics who develop complications can be reduced by adopting optimal control strategies.