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We propose a model of chemostat where the bacterial population isindividually-based, each bacterium is explicitly represented and has a massevolving continuously over time. The substrate concentration is represented asa conventional ordinary differential equation. These two components are coupledwith the bacterial consumption. Mechanisms acting on the bacteria areexplicitly described (growth, division and up-take). Bacteria interact viaconsumption. We set the exact Monte Carlo simulation algorithm of this modeland its mathematical representation as a stochastic process. We prove theconvergence of this process to the solution of an integro-differential equationwhen the population size tends to infinity. Finally, we propose severalnumerical simulations.

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