A modeling approach of the chemostat

TL;DR

This paper explores a combined deterministic and stochastic modeling framework for microbial population dynamics in chemostats, highlighting the mathematical links and simulation approaches to better capture biological complexity.

Contribution

It introduces a novel approach integrating stochastic formalisms with classic deterministic models for chemostat dynamics, enhancing modeling accuracy.

Findings

Stochastic models complement deterministic equations in chemostat dynamics.

Mathematical analysis clarifies links between stochastic and deterministic representations.

Simulations demonstrate improved modeling of microbial population variability.

Abstract

Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit this approach by complementing these classic formalisms by stochastic formalisms and to explain the links between these representations in terms of mathematical analysis but also in terms of modeling and numerical simulations. We illustrate this approach on the model of chemostat.