Optimal control strategies for diabetes population management using mathematical models

Abstract

Diabetes is a long-lasting medical condition that affects the entire world. In the present paper, we modify and analyze an existing mathematical model for diabetes population dynamics, considering control strategies. We presented two models, and the first model was developed with the assumption that the total population grows logistically. The second model was constructed by employing strategies in pursuit of controlling the growth of the diabetic population. Using Pontryagin’s maximum principle, we characterized the optimal controls. The optimality systems were solved using the forward-backward sweep iteration with the fourth-order Runge-Kutta method. This shows that the incidence rate of pre-diabetes is a crucial factor in estimating the burden of diabetes. It can also be concluded that by applying control strategies such as awareness of diet plans and regular testing, the number of incidences of pre-diabetes decreases by nearly 45% and the number of diabetes incidences, with and without complications, declined by approximately 75% over the period of 50 years.