On the properties of a piecewise affine model for glucose regulation

The last four decades have seen the development of several mathematical models describing different aspects of blood glucose regulation, mainly the dynamics of glucose metabolism and the insulin action on glucose production and utilization. One of these models, developed by Ghosh and Maka involves representation of the glucose-insulin dynamics by a (piecewise affine) PWA model. The PWA modeling allows determination of the basal values of physiological variables as well as the point of hopf bifurcation of plasma glucose without carrying out extensive simulations or solving complex transcendental equations. This paper deals with some basic properties regarding the physiological feasibility of the PWA model. Theorems on the positivity and uniqueness of the solution as well as the existence of oscillatory behavior at steady state are proved.