DDE models of the glucose-insulin system: a useful tool for the artificial pancreas

Delay differential equations arewidely adopted in life sciences: including delays explicitly in mathematical models allows to simulate the systems under investigation more accurately, without the use of auxiliary fictitious compartments. This work deals with Delay Differential Equation (DDE) models exploited in the specific framework of the glucose-insulin regulatory system, and a brief review of the DDE models available in the literature is presented. Furthermore, recent results on the closed loop control of plasma glycemia, based on DDE models of the individual glucose-insulin system are summarized. Indeed, DDE models revealed to be particularly suited to simulate the pancreatic insulin delivery rate, thereby allowing to treat in a unified fashion both Type 1, where no endogenous insulin release is available, and Type 2 diabetic patients, where the exogenous insulin administration adds up to the endogenous insulin production.