Distributed-delays models of the glucose-insulin homeostasis and asymptotic state observation

In this paper the problem of the real-time reconstruction of plasma insulin concentration by using only blood glucose measurements is investigated. This is an interesting problem because the knowledge of the time course of the glucose and insulin concentrations in an individual provides precious informations concerning its health state, and may assume the role of a clinical instrument. For the purpose of the reconstruction of the insulinemia a dynamical model of the glucose-insuline homeostasis is required. The present work considers distributed delay models. Such models have been preferred in recent papers with respect to the standard Minimal Models, available in literature from 70's, because they allow to couple the glucose and insulin dynamics in a unique extended system, whose solutions have been proven to be positive, bounded, and globally asymptotically stable around the basal values of the equilibrium point. Data are acquired according to the Intra Venous Glucose Tolerance Test (IVGTT). Simulation results are reported in order to validate the developed theory