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

Pulse injection of insulin analogues is an important strategy to control blood glucose concentrations and can be combined with α – glucosidase inhibitors to reduce adverse effects to improve glucose control. We propose a novel mathematical models with pulse injection insulin and α – glucosidase inhibitors , eating in the form of pulse blood glucose injection. The existence and uniqueness of the positive periodic solution is confirmed In type 1 diabetes, which is globally asymptotically stable. Further, the permanence of the system is given in type 2 diabetes. The numerical analysis verified the correctness of the theoretical calculation results, and show that the period and the dose of insulin injections and α – glucosidase inhibitors are crucial for insulin therapies. In addition, we systematically evaluated a reasonable strategy to treat diabetes combined with α – glucosidase inhibitors, which can provide more reasonable clinical strategies.