A mass-structured individual-based model of the chemostat: convergence and simulation

Fabien Campillo 1, 2, * Coralie Fritsch 1, 2, 3
* Auteur correspondant
1 MODEMIC - Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme
CRISAM - Inria Sophia Antipolis - Méditerranée , MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
Abstract : We propose a model of chemostat where the bacterial population is individually-based, each bacterium is explicitly represented and has a mass evolving continuously over time. The substrate concentration is represented as a conventional ordinary differential equation. These two components are coupled with the bacterial consumption. Mechanisms acting on the bacteria are explicitly described (growth, division and up-take). Bacteria interact via consumption. We set the exact Monte Carlo simulation algorithm of this model and its mathematical representation as a stochastic process. We prove the convergence of this process to the solution of an integro-differential equation when the population size tends to infinity. Finally, we propose several numerical simulations.
Liste complète des métadonnées

Littérature citée [31 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00850959
Contributeur : Fabien Campillo <>
Soumis le : jeudi 7 novembre 2013 - 11:56:35
Dernière modification le : samedi 27 janvier 2018 - 01:30:43
Document(s) archivé(s) le : vendredi 7 avril 2017 - 22:44:29

Fichiers

chemostat_ibm.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00850959, version 3
  • ARXIV : 1308.2411

Citation

Fabien Campillo, Coralie Fritsch. A mass-structured individual-based model of the chemostat: convergence and simulation. [Research Report] 2013. 〈hal-00850959v3〉

Partager

Métriques

Consultations de la notice

3218

Téléchargements de fichiers

188