Analisis Perilaku Solusi Sistem Dinamik Glukosa-Insulin dari Model Minimal Bergman

Abstract

Abstract  Diabetes Mellitus is broadly classified into two categories, namely type 1 and type 2 diabetes. In this study, the model used was a model that interpreted the glucose-insulin dynamics in everyone, except for people who have type 1 diabetes. Bergman Minimal Model which interprets the dynamics of glucose-insulin in the human body is a non-linear autonomous system consisting of three equations and eight parameters. From the results of the study, it was concluded that in this model there is only one equilibrium point, namely x^*=(G_b,0,I_b ). This equilibrium point means that the glucose concentration over time will be as large as the basal concentration (G_b). Active insulin that is already in the body of every human being will go to zero, meaning that over time it will disappear, and the insulin that has been secreted by the pancreas will remain at the threshold (I_b). All eigenvalues of polynomials formed from the linearization process and the Jacobian matrix in the Bergman Minimal Model are of negative real value. Based on the Stability Criteria Theorem, the glucose-insulin system of the Bergman Minimal Model is asymptotically stable around its equilibrium point.  [ANALYSIS OF GLUCOSE-INSULIN DYNAMIC SYSTEM SOLUTIONS BEHAVIOR FROM THE BERGMAN MINIMAL MODEL] (J. Sains Indon., 42(1): 1-6, 2018)