  The mathematical modelling of biological systems has historically followed
one of two approaches: comprehensive and minimal. In comprehensive models, the
involved biological pathways are modelled independently, then brought together
as an ensemble of equations that represents the system being studied, most
often in the form of a large system of coupled differential equations. This
approach often contains a very large number of tuneable parameters (> 100)
where each describes some physical or biochemical subproperty. As a result,
such models scale very poorly when assimilation of real world data is needed.
Furthermore, condensing model results into simple indicators is challenging, an
important difficulty in scenarios where medical diagnosis is required. In this
paper, we develop a minimal model of glucose homeostasis with the potential to
yield diagnostics for pre-diabetes. We model glucose homeostasis as a closed
control system containing a self-feedback mechanism that describes the
collective effects of the physiological components involved. The model is
analyzed as a planar dynamical system, then tested and verified using data
collected with continuous glucose monitors (CGMs) from healthy individuals in
four separate studies. We show that, although the model has only a small number
(3) of tunable parameters, their distribution across subjects has a consistent
distribution both for hyperglycemic and for hypoglycemic episodes.
