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

TL;DR

This paper introduces a detailed individual-based chemostat model with bacterial mass dynamics, coupling stochastic simulation with mathematical analysis, and demonstrates convergence to an integro-differential equation.

Contribution

It presents a novel mass-structured stochastic model of the chemostat with a proven convergence to a deterministic limit, along with simulation algorithms.

Findings

Model accurately captures bacterial mass evolution.

Simulation algorithm converges to the mathematical solution.

Numerical results validate the model's behavior.

Abstract

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.