Delay differential equations can be very effective in the study of complex dynamics observed. Popular ways to incorporate time delays include a constant (discrete) time delay (representing the average delay and assuming the delay variation is small) and an evenly distributed delay (when the time delay is random and bounded) over an interval preceding the current time. A more realistic way to model the time delay effect is to employ the so-called delay interval which can include these two types of time delay as special cases. Delay interval uses two parameters to describe the interval center and half-width, respectively. We present a Laplace transform-based approach to study the asymptotical stability of differential systems with delay interval. As an example, we apply this method to a model of insulin-glucose interaction based on frequently sampled intravenous glucose tolerance test (fsIVGTT) which provides a good fit to fluctuating patient data sets and removes a defect in the well-known Minimal Model which often overestimates the glucose effectiveness index.