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

Fabien Campillo 1, 2, * Coralie Fritsch 1, 2, 3
* Corresponding author
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.
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Submitted on : Thursday, November 7, 2013 - 11:56:35 AM
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  • HAL Id : hal-00850959, version 3
  • ARXIV : 1308.2411

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

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