A Statistical Model for Describing the Response of Diabetic Patients to Insulin

In this paper we develop a model for the response of a diabetic patient to medical therapy. The main tools for the model development come from elementary concepts of statistical theory. calculus. and differential equations. Using a simple step function as the input. the response of apatient to therapy is shown to be the solution of a first order differential equation. The presence of random variation caused by differences between patients and by random fluctuations in a patient's physiology and environment are accounted for in the model. Least squares techniques are used to fit the model to data taken from a set of diabetic dogs. The model is shown to do an adequate job of describing the responses of the animals.