An exact discretization of Michaelis–Menten type population equations

Abstract

Many single population models involve the inclusion of Michaelis–Menten type terms. We derive an exact discretization for such rational functions and demonstrate how these relations may be incorporated into more complex models representing the dynamics of single populations. The Lambert W-function plays an important role in this work.

Keywords:

• population models
• Michaelis–Menten dynamics
• numerical integration

AMS Subject Classification :

• 34A05
• 34A50
• 65L12
• 92D25

Acknowledgements

This research was supported, in part, by funds from the Clark Atlanta University, School of Arts and Sciences, Professional Development Funds. We also thank Professors Kale Oyedeji and Sandra Rucker for several valuable discussions on the topic of this paper.