Dynamic modeling of the Insulin-Glucose-Glucocorticoid impulsive control system

This paper introduces a class of insulin-glucose-glucocorticoid impulsive systems in the treatment of patients with diabetes to consider the effect of glucocorticoids. The existence and uniqueness of the positive periodic solution of the impulsive model at double fixed time is confirmed for type 1 diabetes mellitus (T1DM) using the \(Lambert\;W\) function. Further, the global asymptotic stability of the positive periodic solution is achieved following Floquet multiplier theory and comparison principle. Additionally, the permanence of the system is confirmed in type 2 diabetes mellitus (T2DM) via the comparison theorem. Numerical analysis verifies the results of theoretical calculations and indicates that combining therapeutic strategies under hormonal interactions with the dose of exogenous insulin and glucocorticoid medicines within organisms provides more reasonable clinical strategies.