Sensitivity analysis for a delay mathematical model: the glucose-insulin model

We investigate glucose-insulin regulation through a delay differential equation model formulated in Sobolev spaces. A physiologically motivated time delay is incorporated into an advanced modeling framework that builds upon the classical ordinary differential equation based model proposed by Bergman and Cobelli. The resulting system is formulated within a semigroup-theoretical setting that ensures well-posedness. Sensitivity analysis based on Fréchet derivatives is employed to quantify parameter influence, while optimal design criteria derived from the Fisher Information Matrix are used to improve parameter estimation. The findings highlight the effectiveness of Sobolev-space and semigroup techniques in providing a rigorous and adaptable foundation for modeling delayed physiological processes.