Abstract:
Diabetes is a chronic disease due to problems with the insulin hormone.
Although diabetes cannot be cured, it can be managed with the right
medications, proper exercise, and a diet low in carbohydrates and sugar.
Multiple problems are exacerbated by uncontrolled diabetes. The objective of
this study is to investigate the behavior of the diabetic population dynamics
under control strategies, assuming that the total population grows logistically.
To achieve this objective, we modify an existing mathematical model, which
is a system of nonlinear ordinary differential equations for diabetic population
dynamics with optimal control strategies. We derived the necessary condition
for optimal control using Pontryagin’s maximum principle, which is usually
used to characterize the optimal control for a system of ordinary differential
equations. The optimality system was solved using the forward-backward
sweep iteration with the fourth order Runge-Kutta method. The results of our
model demonstrate that the incidence rate could not remain constant over a
long period of time. Furthermore, we can conclude that by implementing a
control, the number of cases of pre-diabetes and diabetes with and without
complications, can be reduced.
