Modeling the nonlinear behavior of glucose by using the nonlinear step-functions

Abstract

From a sample of 20 type 2 diabetes patients with evidence of exhibiting nonlinear behavior of glucose, we have proposed a mathematical model based on the convolution of the so-called step-function and a full nonlinear function. For this end, we have performed successive measurements of glucose in order to construct the histograms as function of time. With this statistics we have applied a 5-parameters fitting in order to identify the parameters characterized with a high sensitivity on the morphology of the curves of glucose. Data have exhibited abnormal behavior in their glucose's evolution for a period of 60 days. Thus, we have identified the curve pattern so that a 5-parameters fitting was performed. The fit function has turned out to have the morphology of the so-called step-function roughly. However, data exhibits also disturbs which can be attributed to the patient's behavior mainly related to their alimentary habits or others psychological factors. Under the assumption that the patients are exhibiting a certain unpredictable policy of alimentary habits and are not following a strict policy of pharmacology, the model has yielded predictions in a confidence of order of 85% ± 10%, where at least one of 5 patients of the sample (20 patients) might acquire a disorder in their glucose's evolutions for subsequent 10 weeks.