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
