title: Paradox of enrichment and system order reduction: bacteriophages dynamics as case study.
abstract: 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.
authors.affiliation: Centre de Recerca Matemática, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Barcelona, Spain and Departament de Matemátiques, Universitat Autónoma de Barcelona, 08193 Bellaterra, Barcelona, Spain akorobeinikov@crm.cat.
authors.forename: Andrei
authors.initials: A
authors.lastname: Korobeinikov
authors.affiliation: Samara State Aerospace University (SSAU), 34, Moskovskoye shosse, Samara 443086, Russia.
authors.forename: Elena
authors.initials: E
authors.lastname: Shchepakina
authors.affiliation: Samara State Aerospace University (SSAU), 34, Moskovskoye shosse, Samara 443086, Russia.
authors.forename: Vladimir
authors.initials: V
authors.lastname: Sobolev
mesh_terms: D001435:Bacteriophages; D017753:Ecosystem; D008962:Models, Theoretical
keywords: Hopf bifurcation; bacteriophage; limit cycle; model order reduction; self-sustained oscillations; singular perturbations; stability; the paradox of enrichment