Stochastic modeling of the chemostat

The chemostat is classically represented, at large population scale, as a system of ordinary differential equations. Our goal is to establish a set of stochastic models that are valid at different scales: from the small population scale to the scale immediately preceding the one corresponding to the deterministic model. At a microscopic scale we present a pure jump stochastic model that gives rise, at the macroscopic scale, to the ordinary differential equation model. At an intermediate scale, an approximation diffusion allows us to propose a model in the form of a system of stochastic differential equations. We expound the mechanism to switch from one model to another, together with the associated simulation procedures. We also describe the domain of validity of the different models.

► We establish a set of stochastic models for the chemostat that are valid at different scales (from pure jump process to diffusion models). ► The randomness emerges naturally from the demographic stochastic at microscopic scale. ► Explicit scale parameters allow to describe the difference between each model and the limit deterministic model (ODE). ► Simulation procedures are proposed for each model.