## Classification

# of variables | # of modes | # of jumps |
---|---|---|

4 | 6,9 | 10,18 |

Type | Continuous dynamics | Guards & Invariants | Resets |
---|---|---|---|

hybrid | non-linear polynomial | linear polynomial | identity |

## Download

Flow* Strategy I | diabetic_1.model |

Flow* Strategy II | diabetic_2.model |

## Model description

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 [1] and [2] are given by

respectively.

## Reachability settings

We consider the initial condition , , , and the time horizon is given by .

## Results

The following figures show an over-approximation computed by Flow* for the first and the second strategies:

## References

[1] 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. [2] 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,

1991.