Dynamic analysis of a class of Insulin-Glucose-Glucocorticoid model with nonlinear pulse

Abstract

Few studies have employed nonlinear processes to characterize treatment strategies in the context of diabetes and combination drug therapy while considering the effects of drug-induced insulin resistance. Based on this, we proposed a nonlinear impulse system to describe the interaction mechanism among insulin, glucose, and glucocorticoids in diabetic patients, with a particular focus on the role of glucocorticoids in diabetes treatment. To investigate the existence of positive periodic solutions in a type 1 diabetes model with double fixed impulses, we employed the properties of the LambertW function and the Floquet multiplier theory, thereby proving the existence, uniqueness, and global asymptotic stability of the periodic solution. Furthermore, for the type 2 diabetes model, we established the permanence of the system. The findings of this study, in conjunction with treatment strategies based on hormonal interactions, provided more scientifically grounded clinical guidance for determining the appropriate dosage of exogenous insulin and glucocorticoid medications.