  We investigate the consequences of periodic, on-off glucose infusion on the
glucose-insulin regulatory system on the basis of a system-level mathematical
model with two explicit time delays. Studying the effects of such infusion
protocols is mathematically challenging yet a promising direction for probing
the system response to infusion. We pay special attention to the interplay of
the infusion with intermediate-time-scale, ultradian oscillations that arise as
a results of the physiological response of glucose uptake and back-release into
the bloodstream. By using numerical solvers and numerical continuation
software, we investigate the response of the model to different infusion
patterns, and explore how these patterns affect the overall levels of glucose
and insulin, and can lead to entrainment. By doing so, we provide a road-map of
system responses that can potentially help identify new test strategies for
detecting abnormal responses to glucose uptake.

Dynamical Systems