|# of variables||# of modes||# of jumps|
|Type||Continuous dynamics||Guards & Invariants||Resets|
|hybrid||non-linear polynomial||linear polynomial||identity|
|Flow* Strategy I||diabetic_1.model|
|Flow* Strategy II||diabetic_2.model|
We consider a model of the glycemic control in diabetic patients such that all dynamics are defined by polynomials. The modeling ODE is given by
such that is plasma glucose concentration above the basal value and is the plasma insulin concentration above the basal value . is the insulin concentration in an interstitial chamber. The constant parameters are given by , , , , , , .
The influx of glucose after a meal is modeled as
while the insulin control strategies due to  and  are given by
We consider the initial condition , , , and the time horizon is given by .
The following figures show an over-approximation computed by Flow* for the first and the second strategies:
References S. Furler, E. Kraegen, R. Smallwood, D. Chisholm. Blood glucose control by intermittent loop closure in the basal mode: computer simulation studies with a diabetic model. In Diabetes Care, Volume 8, pages 553–561, American Diabetes Association, HighWire Press, 1985.  M. Fisher. A semiclosed-loop algorithm for the control of blood glucose levels in diabetics. In IEEE transactions on biomedical engineering, Volume 38(1), pages 57-61, IEEE,