Models order reduction and equivalence: Paradox of enrichment is a 3-dim bacteriophages dynamics model as case study

Abstract

The paradox of enrichment in a three-dimensional model for bacteriophage dynamics with a free infection stage of the phage and bilinear incident rate is considered. An application of the technique of singular perturbation theory allow us to demonstrate why the paradox arises in this three-dimensional model despite the fact that it has a bilinear incident rate (while in two-dimensional predator-prey models it usually associated with the concavity of the attack rate). Our analysis demonstrates that the commonly applied approach of the model order reduction using the so-called quasi-steady-state approximation can lead to a loss of important properties of an original system.