Weak convergence of a mass-structured individual-based model. (English) Zbl 1325.60139
Appl. Math. Optim. 72, No. 1, 37-73 (2015); erratum ibid. 72, No. 1, 75-76 (2015).
Summary: We propose a model of chemostat where the bacterial population is individual-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.
MSC:
| 60J85 | Applications of branching processes |
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
| 60F05 | Central limit and other weak theorems |
| 45J05 | Integro-ordinary differential equations |
| 92D25 | Population dynamics (general) |
| 65C05 | Monte Carlo methods |
| 37N25 | Dynamical systems in biology |
Keywords:
bacterial population; mass-structured chemostat model; individual-based model; integro-differential equation; weak convergence; Markov processes; Monte Carlo simulationReferences:
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