Stochastic modeling of the chemostat

Abstract. In a chemostat, bacteria live in a growth container of constant volume in which liquid is injected continuously. Recently, Campillo and Fritsch introduced a massstructured individual-based model to represent this dynamics and proved its convergence to a more classic partial differential equation.In this work, we are interested in the convergence of the fluctuation process. We consider this process in some Sobolev spaces and use central limit theorems on Hilbert space to prove its convergence in law to an infinite-dimensional Gaussian process.As a consequence, we obtain a two-dimensional Gaussian approximation of the CrumpYoung model for which the long time behavior is relatively misunderstood. For this approximation, we derive the invariant distribution and the convergence to it. We also present numerical simulations illustrating our results.

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“…This is a Fellerdiffusion type approximation (see Bansaye and Méléard (2015)) and it is closer to the SDE introduced in Campillo et al (2011).…”

Section: Let Us Definementioning

confidence: 76%

Gaussian approximations for chemostat models in finite and infinite dimensions

Cloez¹,

Fritsch

2017

J. Math. Biol.

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“…In Section II we present the state-space model relying on a SDE model developed in [8] where we propose a more appropriate covariance structure. In Section III we derive the equations of the optimal filter.…”

Section: Introductionmentioning

confidence: 99%

Particle filtering for the chemostat

Benyahia¹,

Campillo

Cherki³

et al. 2012

2012 20th Mediterranean Conference on Control &Amp; Automation (MED)

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We develop a particle filter approximation of the optimal nonlinear filter in the context of the chemostat. We propose a stochastic model of the chemostat together with an observation model. One of the characteristics of applications in bioprocesses is that the time between two observations is relatively large. We account for this point in the development of the particle filter by refining the prediction step of the particle filter. We present numerical tests on simulated measurements.

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“…In addition, we require that mass balance on which (3) is based should be satisfied in mean. Campillo et al (2011) considered a similar approach to investigate the relation between models at different scales.…”

Section: Pure Jump Markov Modelmentioning

confidence: 99%

On Geometry and Scale of a Stochastic Chemostat

Joannides

Larramendy–Valverde

2013

Communications in Statistics - Theory and Methods

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A chemostat is a fixed volume bioreactor in which micro-organisms are grown in a continuously renewed liquid medium. We propose a stochastic model for the evolution of the concentrations in the single species and single substrate case. It is obtained as a diffusion approximation of a pure jump Markov process, whose increments are comparable in mean with the deterministic model. A specific time scale, related to the noise intensity, is considered for each source of variation. The geometric structure of the problem, usable by identification procedures, is preserved both in the drift and diffusion term. We study the properties of this model by numerical experiments.

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Stochastic modeling of the chemostat

Cited by 80 publications

References 17 publications

Gaussian approximations for chemostat models in finite and infinite dimensions

Gaussian approximations for chemostat models in finite and infinite dimensions

Particle filtering for the chemostat

On Geometry and Scale of a Stochastic Chemostat

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