Existence and longtime behavior of a biofilm model

Math Methods in App Sciences

2015

Abstract. Bacterial biofilms are microbial depositions on immersed surfaces. Their mathematical description leads to degenerate diffusion-reaction equations with two non-Fickian effects:(i) a porous medium equation like degeneracy where the biomass density vanishes, and (ii) a super-diffusion singularity if the biomass density reaches its threshold density. In the case of multi-species interactions, several such equations are coupled, both in the reaction terms and in the nonlinear diffusion operator. In this paper we generalize previous work on existence and uniqueness of solutions of this type of models and give a general, relatively easy to apply criterion for well-posedness. The use of the criterion is illustrated in several examples from the biofilm modeling literature.

Section: Introductionsupporting

confidence: 59%

On the well‐posedness of mathematical models for multicomponent biofilms

Sonner

Efendiev

Math Methods in App Sciences

2015

“…Thus the model includes both finite speed of interface propagation (between biofilm and aqueous phase) and volume filling features. For visualizations of biofilm growth simulations of this density-dependent diffusion model in 2D or 3D we refer to [12,15,18].…”

Section: Biofilm Modelmentioning

confidence: 99%

A Mixed‐Culture Model of a Probiotic Biofilm Control System

Computational and Mathematical Methods in Medicine

Khassehkhan

Demaret

2009

We present a mathematical model and computer simulations for the control of a pathogenic biofilm by a probiotic biofilm. This is a substantial extension of a previous model of control of a pathogenic biofilm by microbial control agents that are suspended in the aqueous bulk phase (H. Khassehkhan and H.J. Eberl, Comp. Math. Meth. Med, 9(1) (2008), pp. 47-67). The mathematical model is a system of double-degenerate diffusion-reaction equations for the microbial biomass fractions probiotics, pathogens and inert bacteria, coupled with convection-diffusion-reaction equations for two growth controlling substrates, protonated lactic acids and hydrogen ions (pH). The latter are produced by the bacteria and become detrimental at high concentrations. In simulation studies, we find that the site of attachment of probiotics in the flow channel is crucial for success and efficacy of the probiotic control mechanism.

“…We recall that indeed many computer simulations of the underlying biofilm model have shown that in the interior of a growing biofilm R ≈ 1, cf [25,29,43], while other biofilm models, such as [39] are based on the model assumption of an always completely compressed biofilm. Thus the model parameter Σ of the boundary condition (7) can be related to model parameters and the target biofilm thickness λ by…”

Section: Mathematical Modelmentioning

confidence: 99%

A modeling and simulation study of siderophore mediated antagonism in dual-species biofilms

Collinson

2009

Theor Biol Med Model

BackgroundSeveral bacterial species possess chelation mechanisms that allow them to scavenge iron from the environment under conditions of limitation. To this end they produce siderophores that bind the iron and make it available to the cells later on, while rendering it unavailable to other organisms. The phenomenon of siderophore mediated antagonism has been studied to some extent for suspended populations where it was found that the chelation ability provides a growth advantage over species that do not have this possibility. However, most bacteria live in biofilm communities. In particular Pseudomonas fluorescens and Pseudomonas putida, the species that have been used in most experimental studies of the phenomenon, are known to be prolific biofilm formers, but only very few experimental studies of iron chelation have been published to date for the biofilm setting. We address this question in the present study.MethodsBased on a previously introduced model of iron chelation and an existing model of biofilm growth we formulate a model for iron chelation and competition in dual species biofilms. This leads to a highly nonlinear system of partial differential equations which is studied in computer simulation experiments.Conclusions(i) Siderophore production can give a growth advantage also in the biofilm setting, (ii) diffusion facilitates and emphasizes this growth advantage, (iii) the magnitude of the growth advantage can also depend on the initial inoculation of the substratum, (iv) a new mass transfer boundary condition was derived that allows to a priori control the expect the expected average thickness of the biofilm in terms of the model parameters.