Analysis of ivgtt glucose-insulin interaction models with time delay

In the last three decades, several models on the interaction of glucose and insulin following the intra venous glucose tolerance test (IVGTT) have appeared in the literature. One of the mostly used one is generally known as the minimal model which was first published in 1979 and modified in 1986. Recently, this minimal model has been challenged by De Gaetano and Arino [4] from both physiological and modeling aspects. Instead, they proposed a new and mathematically more reasonable model, called dynamic model . Their model makes use of certain simple and specific functions and introduces time delay in a particular way. The outcome is that the model always admits a globally asymptotically stable steady state. The objective of this paper is to find out if and how this outcome depends on the specific choice of functions and the way delay is incorporated. To this end, we generalize the dynamical model to allow more general functions and an alternative way of incorporating time delay. Our findings show that in theory, such models can possess unstable positive steady states. However, for all conceivable realistic data, such unstable steady states do not exist. Hence, our work indicates that the dynamic model does provide qualitatively robust dynamics for the purpose of clinic application. We also'perform simulations based on data from a clinic study and point out some plausible but important implications.