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Weak Convergence of a Mass-Structured Individual-Based Model

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 washout). 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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https://hal.inria.fr/hal-01090727
Contributor : Alain Rapaport <>
Submitted on : Thursday, December 4, 2014 - 9:43:19 AM
Last modification on : Wednesday, February 10, 2021 - 3:35:06 AM

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Fabien Campillo, Coralie Fritsch. Weak Convergence of a Mass-Structured Individual-Based Model. Applied Mathematics and Optimization, Springer Verlag (Germany), 2015, 72 (1), pp.37-73. ⟨10.1007/s00245-014-9271-3⟩. ⟨hal-01090727⟩

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