This work presents a physiological-based model of the process of insulin production in relationship to the presence of glucose in the intestinal tract. Insulin is secreted by pancreatic β-cells in the Islets of Langerhans and it plays a fundamental role in both the proper functioning of the energy metabolism and glucose homeostasis. This process is regulated and influenced by numerous factors, such as glucose, but there are numerous other substances that can influence the release of insulin; among these there are the GIP (glucose-dependent insulinotropic peptide) and the GLP-1 (glucagon-like peptide), hormones secreted by the intestine as a response to the nutrients ingested. These two polypeptides are called ”incretins”, and they have an ”insulinotropic” effect, increasing the insulin production while suppressing glucagon. The effects of these two incretin hormones are the cause of greater insulin blood concentrations during an Oral Glucose Tolerance Test in comparison to what is observed after an Intra-Venous Glucose Tolerance Test. This work presents a mathematical model constituted by eight ordinary differential equations aiming to reproduce both the insulin production modulated by the incretins as well as their time course over time following a bolus of oral-administered glucose. The proposed model adapts very well to the observations and a sensitivity analysis was employed to assess the most sensitive parameters in determining the trend of the variables of interest.