Development, validation, and testing of algorithms for artificial pancreas (AP) systems require mathematical models for the glucose–insulin dynamics inside the body. These physiological models have been extensively studied over the past decades. Two broad types of models are available in diabetic research, each with its own unique purpose: (i) minimal models, which are relatively simple but still manages to capture the macroscopic behavior of the glucose–insulin dynamics of the body, and (ii) high-fidelity models, which are complex and precisely describe the internal dynamics of the glucose–insulin interaction in the body. The minimal models are primarily utilized for control algorithm synthesis, whereas the high-fidelity models are used as platforms for testing and validating AP systems. The most well-known variants of these physiological models are discussed in detail. In addition to these systems, data-driven models such as the auto-regressive moving average with exogenous inputs (ARMAX) models are also used widely in control algorithm synthesis for AP systems. High-fidelity models are utilized for simulating virtual diabetic patients for in silico testing and validation of artificial pancreas systems. Two currently available high-fidelity models are reviewed in this paper for completeness, including the Type-1 diabetes mellitus (T1DM) simulator approved by the food and drug administration of USA. Models accounting for exercise and also glucagon infusion (for dual-hormone AP systems) are also included, which are essential in developing control algorithms with better autonomy and minimal risk.
