The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat

Tewfik Sari; Miled El Hajji; Jérôme Harmand; Tewfik Sari; Miled El Hajji; Jérôme Harmand

doi:10.3934/mbe.2012.9.627

Mathematical Biosciences and Engineering

2012, Volume 9, Issue 3: 627-645. doi: 10.3934/mbe.2012.9.627

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The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat

1.
Irstea, UMR ITAP, 361 rue Jean-François Breton 34196 Montpellier, & Modemic (Inra/Inria), UMR Mistea, 2 place Viala, 34060 Montpellier
2.
ISSATSO (Université de Sousse) Cité Taffala, 4003 Sousse, & LAMSIN-ENIT, Université Tunis El-manar BP 37, 1002 Tunis
3.
INRA UR0050, Laboratoire de Biotechnologie de l’Environnement, Avenue des Étangs, 11100 Narbonne, and Modemic (Inra/Inria), UMR Mistea, 2 place Viala, 34060 Montpellier

Received: 01 November 2011 Accepted: 29 June 2018 Published: 01 July 2012
MSC : Primary: 92A15, 92A17; Secondary: 34C15, 34C35.

Abstract
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A mathematical model involving a syntrophic relationship between two populations of bacteria in a continuous culture is proposed. A detailed qualitative analysis is carried out as well as the analysis of the local and global stability of the equilibria. We demonstrate, under general assumptions of monotonicity which are relevant from an applied point of view, the asymptotic stability of the positive equilibrium point which corresponds to the coexistence of the two bacteria. A syntrophic relationship in the anaerobic digestion process is proposed as a real candidate for this model.
- global asymptotic stability,
- syntrophic relationship,
- coexistence,
- Chemostat,
- anaerobic digestion.
Citation: Tewfik Sari, Miled El Hajji, Jérôme Harmand. The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat[J]. Mathematical Biosciences and Engineering, 2012, 9(3): 627-645. doi: 10.3934/mbe.2012.9.627

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Abstract

A mathematical model involving a syntrophic relationship between two populations of bacteria in a continuous culture is proposed. A detailed qualitative analysis is carried out as well as the analysis of the local and global stability of the equilibria. We demonstrate, under general assumptions of monotonicity which are relevant from an applied point of view, the asymptotic stability of the positive equilibrium point which corresponds to the coexistence of the two bacteria. A syntrophic relationship in the anaerobic digestion process is proposed as a real candidate for this model.

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