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Rapport (Rapport De Recherche) Année : 2013

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

Résumé

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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Dates et versions

hal-00850959 , version 1 (09-08-2013)
hal-00850959 , version 2 (10-08-2013)
hal-00850959 , version 3 (07-11-2013)

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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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