MODELING GLUCOSE AND INSULIN CONCENTRATION IN BLOOD OF HEALTHY PEOPLE AND DIABETICS

R. Rustam, N. Nasruddin

Abstract


The purpose of this study is to mathematically model the concentration of glucose and insulin in the blood in healthy people and diabetics. The dynamics of glucose and insulin concentration in the blood of healthy people and diabetics is assessed using mathematical approach. The model is derived from a glucose tolerance test mechanism that describes the behavior of physiological systems of both healthy and diabetics. The basic assumptions used in modeling the overall picture of the glucose and insulin regulation system in blood are the absence of oral glucose (food) input and the simplification of the interactions between glucose and insulin. The concentration of glucose and insulin in the blood of healthy people and diabetics is modeled using nonlinear differential equation system that contains several parameters. The model that has been established is determined the balance point and the system linearization around the balance point. The stability of the equilibrium point was then tested using the Hurwitz stability test. The results obtained show that in healthy people blood glucose concentration in the absence of glucose input, can still be maintained within a certain time according to the condition and endurance of each individual. However, this will not last long as the body continually performs metabolic processes to generate energy. While in diabetics, high blood glucose concentrations are not matched by high insulin concentrations resulting in a slower decrease in blood glucose concentration. As a result, blood glucose concentrations in diabetics remain high even in the absence of glucose input. The low concentration of insulin that is not able to maintain normal blood glucose concentration causes the time needed to lower blood glucose levels in diabetics tend to be very long compared to healthy people.

Keywords


Mathematical Model, Diabetics, Glucose, Insulin, Concentrations

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