Mathematical Model for Detecting Diabetes in the Blood

Hello to all my friends of Steemit especially to the scientific community, I want to share with you a work developed by me in the study of my masters, before explaining the mathematical model used I will talk about diabetes and I will show you a graph with Which can have a better understanding of the functioning of this disease.

Diabetes is a disease that is characterized by excessive glucose in the blood stream. Currently, there is an epidemic of diabetes that has resulted from unhealthy lifestyles, which are dramatically diferent from how humans survived when they evolved from small nomadic hunter-gatherer societies, and food was di±cult to ¯nd. There are two forms of diabetes, Type 1, often called juvenile diabetes, and Type 2, often referred to as adult onset diabetes (which now occurs in children as young as 5). For our studies here, we will concentrate on Type 1 diabetes, which is an autoimmune disease, and represents only 10% of all cases of diabetes. Type 1 diabetes is a hereditary disease, which occurs in about 4-20 per 100,000 people with peak occurrence around 14 years of age.

As noted above, the glucose regulatory system in the body is very complex. However, we want to develop a simple model with a few parameters that can be fit to the data generated by the GTT. For simplicity, we create a system of diferential equations that follow the blood concentrations of glucose (G(t)) and insulin (I(t)) though the later can be thought of as the
complex soup of hormones in the body regulating blood glucose. The general model is written:

We expand the general model to linear terms with these definitions, yielding the linearized perturbation model given by:

Using the lsqnonlin command of Matlab with real data the following results are obtained:

Solving the system of equations using Newton's method programmed in Matlab gives the following results:

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