Numerical bifurcation analysis of delay differential equations arising from physiological modeling

This paper has a dual purpose. First, we describe numerical methods for con tinuation and bifurcation analysis of steady state solutions and periodic s olutions of systems of delay differential equations with an arbitrary numbe r of fixed. discrete delays. Second. we demonstrate how these methods can b e used to obtain insight into complex biological regulatory systems in whic h interactions occur with time delays: for this, we consider a system of tw o equations for the plasma glucose and insulin concentrations in a diabetic patient subject to a system of external assistance. The model has two dela ys: the technological delay of the external system, and the physiological d elay of the patient's liver. We compute stability of the steady state solut ion as a function of two parameters, compare with analytical results and co mpute several branches of periodic solutions and their stability. These num erical results allow to infer two categories of diabetic patients for which the external system hits different efficiency.