A mass-structured individual-based model of the chemostat: convergence and simulation
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.
Keywords
Cite
@article{arxiv.1308.2411,
title = {A mass-structured individual-based model of the chemostat: convergence and simulation},
author = {Fabien Campillo and Coralie Fritsch},
journal= {arXiv preprint arXiv:1308.2411},
year = {2013}
}