It is well known that Michaelis–Menten kinetics is suitable for the response function in chemical reaction, when the reaction rate does not increase indefinitely when an excess of resource is available. However, the existing models for insulin therapies assume that the response function of insulin clearance is proportional to the insulin concentration. In this paper, we propose a new model for insulin therapy for both type 1 and type 2 diabetes mellitus, in which the insulin degradation rate assumes Michaelis–Menten kinetics. Our analysis shows that it is possible to mimic pancreatic insulin secretion by exogenous insulin infusions, and our numerical simulations provide clinical strategies for insulin–administration practices.
Keywords: diabetes; glucose–insulin regulator system; insulin therapy; periodic solution; time delay.