Bacterial population dynamics are classically modeled as systems of ordinary differential equations that failed to account for certain situation where randomness could not be negelected. In the case of the chemostat model of a continuous bioreactor in which bacterial microorganisms degrade a substrate we will present an individual-based model. The population of individuals is structured in mass and the model describes discrete mechanisms (the division of cells and the uptake) and continuous mechanisms (the growth of individuals and the substrate consumption). We can compare this stochastic model with deterministic models, in particular with an integro-differential equation which also accounts for the mass structure of the population and with the classical system of ordinary differential equations which only describes dynamics of the substrate and biomass concentrations.

This work is in collaboration with Fabien Campillo and Jérôme Harmand.