We investigate the consequences of periodic, on–off glucose infusion on the glucose–insulin regulatory system based on 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 periodic infusion with intermediate-time-scale, ultradian oscillations that arise as a result 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, explore how these patterns affect the overall levels of glucose and insulin, and how this can lead to entrainment. By doing so, we provide a road-map of system responses that can potentially help identify new, less-invasive, test strategies for detecting abnormal responses to glucose uptake without falling into lockstep with the infusion pattern.
