  The Glucose-Insulin-Glucagon nonlinear model [1-4] accurately describes how
the body responds to exogenously supplied insulin and glucagon in patients
affected by Type I diabetes. Based on this model, we design infusion rates of
either insulin (monotherapy) or insulin and glucagon (dual therapy) that can
optimally maintain the blood glucose level within desired limits after
consumption of a meal and prevent the onset of both hypoglycemia and
hyperglycemia. This problem is formulated as a nonlinear optimal control
problem, which we solve using the numerical optimal control package PSOPT.
Interestingly, in the case of monotherapy, we find the optimal solution is
close to the standard method of insulin based glucose regulation, which is to
assume a variable amount of insulin half an hour before each meal. We also find
that the optimal dual therapy (that uses both insulin and glucagon) is better
able to regulate glucose as compared to using insulin alone. We also propose an
ad-hoc rule for both the dosage and the time of delivery of insulin and
glucagon.
