Periodic oscillations in a model of the glucose-insulin interaction with delay and periodic forcing

摘要

Using degree theoretic methods, the existence of periodic solutions is established for a two-dimensional delay model representing the glucose-insulin interaction in a person with reduced insulin secretion and receiving oscillatory infusions of both insulin and glucose. For the case when the parameters are time-independent, the possibility of a periodic solution is investigated by a Hopf bifurcation analysis. The results of some numerical simulations are also presented and discussed.