Paradox of enrichment and system order reduction: bacteriophages dynamics as case study

The paradox of enrichment in a 3D model for bacteriophage dynamics, with a free infection stage of the phage and a bilinear incident rate, is considered. An application of the technique of singular perturbation theory allows us to demonstrate why the paradox arises in this 3D model despite the fact that it has a bilinear incident rate (while in 2D predator-prey models it is 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.