Abstract
In the present work a study of the dynamic insulin-glucose in a healthy person is made; the different types of diabetes are indicated as well as the symptoms that characterize each one of them. The model that simulates the insulin-glucose dynamics for a person with diabetes is presented, and for the critical case of a pair of pure imaginary eigenvalues of the matrix of the linear part of the system, the system is simplified, a qualitative study is done of the system of equations and conclusions are given on the future behavior of the disease.
Highlights
Hormones are chemicals produced by glands of the endocrine system or by specialized neurons, are of utmost importance for the control of the functioning of the human body
When the dynamic insulin-glucose is not the natural one in the human organism, it can be produced to diabetes; this disease is a metabolic syndrome of multiple origins, due to the lack of insulin and / or the inability of insulin to properly exercise its effects, causing an increase of glucose in the blood
Our goal in this work is to do a study of the dynamics of insulin-glucose for a diabetic person, indicating the corresponding model; which will be simplified to arrive at conclusions regarding the disease for the critical case in which the matrix of the linear part presents a pair of pure imaginary eigenvalues
Summary
Hormones are chemicals produced by glands of the endocrine system or by specialized neurons, are of utmost importance for the control of the functioning of the human body. Our goal in this work is to do a study of the dynamics of insulin-glucose for a diabetic person, indicating the corresponding model; which will be simplified to arrive at conclusions regarding the disease for the critical case in which the matrix of the linear part presents a pair of pure imaginary eigenvalues. Glucose stays in the blood instead of being used as energy This is the process that characterizes Type 1 diabetes, which concentrates between 5% and 10% of the total people with the disease. Type 1 usually appears in childhood or adolescence, but can be diagnosed in adults as well This variety is always treated with insulin, medications, food planning and physical activities to help control blood glucose levels. It requires the use of insulin and / or other medications to control glucose
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