Finite-time control of plasma glucose in insulin therapies for diabetes

Abstract

To study the finite-time control of plasma glucose for diabetic patients with impulsive injections of insulin, we propose an impulsive differential equation model with initial and boundary conditions. The goal of glucose control is supposed to be achieved if the system has a solution, otherwise the goal cannot be achieved. By constructing two comparison systems and using a comparison principle, several conditions under which the system has a solution are obtained. Furthermore, some numerical simulations are given. The results show that a relatively higher initial insulin level is beneficial for the glucose control. For a predefined finite time, injection dose and injection period are two important adjustable factors which can guarantee the achievement of the control goal.