KONTROL OPTIMAL PADA MODEL POPULASI PENDERITA DIABETES MELITUS

Abstract

In this final project is discussed the optimal control problem of a population model of diabetes mellitus. Model of diabetes mellitus population illustrates the flow of development a person suffering diabetes mellitus from pre-diabetes stage, diabetes without complications stage, diabetes with complications stage, until recovered stage. Optimal control aims to minimize the number of diabetics without complications, and the number of diabetics with complications through the implementation of the treatment control ( ) and glucose diet therapy ( ). Moreover, the goal of optimal control is also to minimize the cost of treatment and diet therapy glucose. Optimal control is obtained by applying Pontryagin minimum principle. Optimal control which is obtained from the calculation then simulated to see the effect of the treatment control and glucose diet therapy which is given. Keywords: Diabetes Mellitus, Optimal Control, Pontryagin Minimum Principle