A Mathematical Model for Type 1 Diabetes Regulation Using a Smart Insulin Patch: In Silico Validation Based on Published Rat Data

This work introduces a new mathematical model designed to describe the glucose–insulin dynamics associated with a glucose-responsive smart microneedle patch reported in the literature. The model captures the complete sequence of the patch behavior, from detecting glucose changes to controlled transdermal insulin delivery and gradually restoring blood glucose levels to the normal range. Our simulations show that the patch can effectively manage glucose not only during fasting conditions but also after single and multiple meals, restoring glucose levels to healthy levels within a short period. The model predictions are consistent with experimentally reported trends in previously published studies, which strengthens confidence in the biological realism of the proposed mechanism. Because some parameters in such systems are difficult to measure directly, we also performed a comprehensive sensitivity analysis to understand how variations in key parameters influence system stability. The results highlight the central role of the insulin release rate and the five glucose–regulation parameters examined in the sensitivity analysis, providing clear guidance on the most critical aspects of patch design for reliable performance. Overall, this study provides a simplified yet robust mathematical framework that makes the behavior of a glucose-responsive microneedle patch easy to understand and analyze. It lays the groundwork for future refinement of control strategies and optimization of patch design, improving control strategies, and developing more advanced systems that can maintain healthy glucose levels naturally and intuitively.