A Mathematical Model of the Dynamics of Glucose, Insulin, β-cells Mass, and Insulin Receptors in Diabetes Mellitus Disease Type 2

Abstract

The diabetes mellitus is a disease in glucose-insulin regulatory system, which is referred to as hyperglikemia. Most cases are categorized as type 2 of the diabetes mellitus (T2DM), which are characterized by high blood glucose levels. The T2DM is associated with a deficit in the mass of β-cells. If the blood glucose consentration level is high, then the β-cells release insulin into the pancreas. The aim of this research is to study the glucose-insulin dynamics. A βIG model was proposed to describe the glucose-insulin dynamics. This model provide a pathway for diabetes development through the introduction of a 3rd dynamical variable, the β-cell mass. The addition of insulin receptor is an important factor in this quantitative improvement in order to make the model more realistic. Incorporation of the insulin receptor into the existing mathematical model gives a four dimensional system of nonlinear ordinary differential equations, which is introduced as the modified model. Both of the models have two stable equilibria representing physiological steady state and pathological steady state. Furthermore the third steady state is found to be a saddle point. Nevertheless the average mass of β-cell in the modified model is quantitatively more reasonable and therefore better then βIG models.

Diabetes melitus tipe 2 (DMT2) merupakan penyakit gangguan kesehatan akibat kadar glukosa yang tinggi terus menerus sehingga mengakibatkan penurunan fungsi sel-β penghasil insulin. Hampir sebagian besar kasus diabetes adalah DMT2, yang disebabkan karena pola hidup tidak sehat. DMT2 awalnya ditandai dengan penurunan sensitivitas insulin (kepekaan terhadap insulin) dan peningkatan resistansi insulin (perlawanan terhadap insulin), dan jika kondisi ini secara signifikan meningkat terus maka akan terjadi hiperglikemia akut yang mengakibatkan komplikasi dan kematian. DMT2 merupakan penyakit global yang banyak diidap penduduk dunia, dan Indonesia berada pada peringkat ke-4 setelah Cina, India, dan Amerika.