Dynamic modeling of the glucose–insulin system with inhibitors impulsive control

Abstract

Pulse injection of insulin analogues is an important strategy to control glucose concentrations and can be combined with ‐glucosidase inhibitors to reduce adverse effects to improve glucose control. To elucidate this combination therapy strategy, we assumed dietary intake in the form of pulse glucose injection and proposed a novel mathematical model incorporating pulse injection insulin and ‐glucosidase inhibitors. In type 1 diabetes, the existence and uniqueness of the positive periodic solution is confirmed utilizing the Lambert W function. The global asymptotic stability of the positive periodic solution is achieved through the application of Floquet multiplier theory and the comparison principle. Furthermore, in type 2 diabetes, the permanence of the system is also confirmed through the comparison theorem. Numerical analysis validated the theoretical calculations, highlighting the significance of insulin injection dosage and frequency, as well as ‐glucosidase inhibitor therapy. Additionally, we systematically assessed a rational approach for diabetes treatment combined with ‐glucosidase inhibitors, providing more practical clinical strategies. This facilitates the extension of our model to encompass other drugs that may be utilized in future clinical interventions.