Weak Convergence of a Mass-Structured Individual-Based Model
Authored by Fabien Campillo, Coralie Fritsch
Date Published: 2015
DOI: 10.1007/s00245-014-9271-3
Sponsors:
French national network of complex systems (RNSC)
Platforms:
No platforms listed
Model Documentation:
Other Narrative
Pseudocode
Mathematical description
Model Code URLs:
Model code not found
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 washout).
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.
Tags
Adaptation
Dynamics
Chemostat