Modelling glucose-insulin feedback signal interchanges involving β-cells with delays

Abstract

In this paper, we studied a mathematical model system of delay-differential equations which describe the dynamic behavior of the glucose-insulin feedback system which involved β-cells, incorporating two time delays, one being the glucose triggered insulin production delay τg, and the other being the hepatic glucose delay τi. This secretory mechanism was governed by nonlinear and time-delayed feedforward and feedback signal interchanges. Moreover, delayed responses to the changes in β-cell density were incorporated. The model system was analyzed to investigate the effect of delays on the dynamic behavior of the system and the possibility of periodic solution which simulate sustained oscillations frequently observed in the experiments.