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Title: Weak Convergence of a Mass-Structured Individual-Based Model

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.
Authors:
 [1] ;  [2]
  1. INRIA (France)
  2. Montpellier 2 University and INRA/MIA (France)
Publication Date:
OSTI Identifier:
22469890
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 72; Journal Issue: 1; Other Information: Copyright (c) 2015 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 60 APPLIED LIFE SCIENCES; ALGORITHMS; BACTERIA; COMPUTERIZED SIMULATION; CONCENTRATION RATIO; CONVERGENCE; DIFFERENTIAL EQUATIONS; INTEGRO-DIFFERENTIAL EQUATIONS; MASS; MATHEMATICAL SOLUTIONS; MONTE CARLO METHOD; STOCHASTIC PROCESSES; SUBSTRATES