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Home  >  Volume 35

Mathematical Model for the Detection and Control of Diabetes by Lubem Matthew Kwaghkor, a *and Tersoo Luga, b (pages 253-260)
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Abstract

Diabetes mellitus is a chronic condition in which the body cannot make or use available insulin effectively. Diabetes is one of the biggest diseases in western world today. Many millions suffer from it and do not know they have the disease. This work presents an extension of an earlier model for the detection of diabetes in the blood. The new model incorporates physical exercise which facilitates the utilization of glucose, the effectiveness of insulin and the release of epinephrine concentrations in the blood. The existence and stability of the equilibria of the model is investigated and the only equilibrium state was found to be uniformly asymptotically stable. It is shown using Ackerman criteria for detecting diabetes that, the new model can be used for the interpretation of the result from a Glucose Tolerance Test (GTT). A computer program is also developed to simulate the null-clines of the model equations to study the effect of physical exercise on glucose, insulin and epinephrine concentrations in the blood, and it is found that as the rate of physical exercise increases, the excess glucose, insulin and epinephrine concentrations returned to their equilibrium levels with time. The above results confirm that physical exercise is useful in the control of diabetes and is therefore recommended for diabetic patients.

Keywords:Diabetes; Glucose; Insulin; Epinephrine; Glucose Tolerance Test; Physical Exercise.

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