  Diabetes Mellitus is a metabolic disorder which may result in severe and
potentially fatal complications if not well-treated and monitored. In this
study, a quantitative analysis of the data collected using CGM (Continuous
Glucose Monitoring) devices from eight subjects with type 2 diabetes in good
metabolic control at the University Polyclinic Agostino Gemelli, Catholic
University of the Sacred Heart, was carried out. In particular, a system of
ordinary differential equations whose state variables are affected by a
sequence of stochastic perturbations was proposed and used to extract more
informative inferences from the patients' data. For this work, Matlab and R
programs were used to find the most appropriate values of the parameters
(according to the Akaike Information Criterion (AIC) and the Bayesian
Information Criterion (BIC)) for each patient. Fitting was carried out by
Particle Swarm Optimization to minimize the ordinary least squares error
between the observed CGM data and the data from the ODE model. Goodness of fit
tests were made in order to assess which probability distribution was best
suitable for representing the waiting times computed from the model parameters.
Finally, both parametric and non-parametric density estimation of the frequency
histograms associated with the variability of the glucose elimination rate from
blood were conducted and their representative parameters assessed from the
data. The results show that the chosen models succeed in capturing most of the
glucose fluctuations for almost every patient.
