Modeling an artificial pancreas using retarded impulsive differential equation

The glucose-insulin regulatory system is characterized by a dynamic that includes some delays in the processes acting inside. This aspect is basically a key issue for people using open-loop or closed-loop artificial pancreas. This paper will focus on the influence that the above delays have in the latest mathematical models, and in particular on those resulting from the delivering of insulin at the subcutaneous level. Such models analyze the fluctuations in the concentration of intravenous glucose and insulin in a system regulated by an open loop or a closed loop (Artificial Pancreas). The paper introduces new features in terms of mathematical aspects to solve the problem of the actual delivering of glucose by using Retarded Differential Equations and Impulsive Differential Equations (in cases of micro-infusion), that analytically describe these dynamics.