A mathematical model for insulin kinetics. II. Extension of the model to include response to oral glucose administration and application to insulin-dependent diabetes mellitus (IDDM).

A generalized nonlinear mathematical model which incorporates beta-cell kinetics, a glucose-insulin feedback system and a gastrointestinal absorption term for glucose, is presented. Numerical simulations using this model lead to time variations of plasma glucose and insulin levels that are consistent with clinical observations in normal groups. The results obtained after suitable reduction in some of the parameters are in agreement with the clinical profile and laboratory data in insulin-dependent diabetes mellitus (IDDM). Linear stability analysis of the equations shows that there is a change in the nature of the stability in the transition from the normal case to IDDM, and it is the decrease in the beta cell function which causes this change.