Optimal Control in an SDC Mathematical Model for Diabetes Complications at a Hospital in Lamongan Regency - Alvina Wiliyanti; Awawin Mustana Rohmah; Muhammad Syaiful Pradana (Journal of Mathematics Education and Science, 2026)
Diabetes is a chronic disease whose prevalence continues to increase and has the potential to cause serious complications if not properly managed. This study aims to analyze the dynamics of diabetes progression and its complications, as well as to determine optimal control strategies using a mathematical model based on data from a hospital in Lamongan Regency. The model used is a compartmental SDC (Susceptible–Diabetes–Complication) model formulated as a system of ordinary differential equations with two time-dependent control variables. The optimal control is determined using Pontryagin’s Maximum Principle, while the numerical simulations are solved using the fourth-order Runge–Kutta (RK4) method. Model parameters are obtained from the literature and epidemiological data, and then calibrated to match the characteristics of real-world cases. The simulation results show that without control, the susceptible population decreases from approximately 1500 to about 200 individuals, while the complication population increases to around 1700 individuals. With the implementation of optimal control, the susceptible population increases to approximately 1250 individuals, the number of diabetic patients decreases to around 820 individuals, and the complication population is reduced to about 980 individuals. These results indicate that control strategies focused on diabetic patients are effective in suppressing disease progression and preventing complications, and contribute to the development of data-driven mathematical models for local healthcare policy planning.