@article{Zhang2026, 
author = {Zhongyuan Zhang and Qiqi Zheng and Mingzhan Huang},
title = {Dynamical analysis of impulsive insulin delivery in a glucose-insulin system with insulin-degrading enzyme effects},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {4},
pages = {2433-2461},
keywords = {glucose-insulin model, impulsive injection, periodic solution, stability},
url = {https://www.sciopen.com/article/10.3934/era.2026112},
doi = {10.3934/era.2026112},
abstract = {This paper investigated impulsive insulin therapy within an extended glucose-insulin regulatory system that included insulin-degrading enzyme dynamics. Two treatment modes were examined: periodic delivery and state-dependent feedback. For the periodic model, we established solution positivity and boundedness, proved the global asymptotic stability of a unique positive periodic solution for type I diabetes, and derived permanence bounds along with a safe dosing region for type II diabetes. For the state-dependent model, under mild conditions, we demonstrated the existence and global orbital asymptotic stability of a unique order-1 periodic orbit within a physiologically relevant glucose range. Numerical simulations supported the theoretical results and illustrated how the choice of dosing period, bolus size, and threshold level influenced long-term glucose control. The results provided a unified theoretical framework for comparing and optimizing impulsive insulin therapies.}
}