# Optimality of Unconstrained Pulse Inputs to the Bergman Minimal Model

## TL;DR

This paper characterizes the optimality of rectangular bolus insulin inputs in the Bergman minimal model, ensuring plasma glucose levels stay above a minimum, with numerical illustrations using the Hovorka model.

## Contribution

It provides a theoretical framework for determining optimal insulin bolus inputs under specific constraints in glucose regulation models.

## Key findings

- Optimal bolus inputs are rectangular under given constraints.
- The model ensures plasma glucose remains above a minimum level.
- Numerical examples demonstrate the theoretical results.

## Abstract

We characterise optimality of bolus insulin inputs, to the Bergman minimal model, by the predicted behaviour of the plasma glucose concentration for a given disturbance. The result is derived subject to the constraints that the plasma glucose concentration must attain but not go below a specified minimum value and the bolus input is rectangular. We give numerical examples of the results for the Hovorka model.