On Switched Models of Glucose-insulin Dynamics for Type 1 Diabetes Mellitus

Abstract

This paper investigates two mathematical models of the glucose-insulin dynamics for type 1 diabetes mellitus. In particular, we propose two switched models, which are the linear switched model and the bilinear switched model. The switching parameters, which give significant effects to the resulting time responses of the switched systems, are determined by using the metabolic parameters of each subject. The time responses of the proposed switched models are evaluated by comparing with the one that is obtained from the UVA/Padova model, which is accepted by the United States Food and Drug Administration as a substitute to animal trials for the pre-clinical testing. As a validation, the metabolic parameters of ten subjects are used to evaluate the resulting glucose time responses.