Michaelis–Menten kinetics as a model of doctoral supervisor–supervisee relationship

Abstract

The process of turning a doctoral student into an independent researcher is usually guided by a professor. In this work, the supervisor–supervisee relationship is represented by a scheme inspired by Michaelis–Menten kinetics, which has been used to determine the rate of enzyme-catalysed reactions. Here, the time evolution of the number of supervisors with k supervisees is modelled by a system of linear ordinary differential equations. The long-term behaviour of these equations is analytically examined and illustrated by a numerical simulation. This model related to the PhD formation catalysed by a professor can be presented in a class on differential equations or chemical kinetics.