Author : Venkatesha P. 1
Date of Publication :23rd November 2017
Abstract: A complete description of the response of man to large doses of glucose involves the use of more than sixteen rate constants the response of blood-glucose concentration (G) as a function of time (t) can be represented adequately by an equation involving only four constants in the equation: G=G0+Ae−αt sin ωt. The values of these four constants are defined by the four measurements usually made in an ordinary glucose-tolerance test. A new mathematical model for Blood Glucose Regulatory System(BGRS) which includes epinephrine as a third variable in the form, Y˙ = AY, and whose solution has been analysed for equilibrium and stability to provide the blood glucose concentrations for diabetics and non-diabetics. The glucose-insulin regulatory system in relation to diabetes is given, enhanced with a survey on available software. The models are in the form of ordinary differential, partial differential, delay differential and integro-differential equations. The human body needs continuous and stable glucose supply for maintaining its biological functions. Stable glucose supply comes from the homeostatic regulation of the blood glucose level, which is controlled by various glucose consuming or producing organs. Commonly observed combinations of parameter values, the coupled model would not admit equilibrium and the concentration of active insulin in the “distant†compartment would be predicted to increase without bounds. For comparison, a simple delay-differential model is introduced, is demonstrated to be globally asymptotically stable around a unique equilibrium point corresponding to the pre -bolus conditions, and is shown to have positive and bounded solutions for all times
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