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A nonlinear density-dependent system of diffusion-reaction equations describing the spatial spreading of biomass during the development of microbial films is analysed. It comprises two non-standard diffusion effects, degeneracy as in the porous medium equation and fast diffusion. The existence of a unique bounded solution and a global attractor is proved in(More)
A mathematical model is presented that describes the disinfection of microbial biofilms by antibiotics. It is the first multi-species/multi-substrate generalization of a continuous prototype biofilm model comprising degenerating as well as fast diffusion. The boundedness of the model solution is established. The dynamic model behaviour in dependence of(More)
BACKGROUND Biofilms are microbial communities encased in a layer of extracellular polymeric substances (EPS). The EPS matrix provides several functional purposes for the biofilm, such as protecting bacteria from environmental stresses, and providing mechanical stability. Quorum sensing is a cell-cell communication mechanism used by several bacterial taxa to(More)
A finite difference scheme is presented for a density-dependent diffusion equation that arises in the mathematical modelling of bacterial biofilms. The peculiarity of the underlying model is that it shows degeneracy as the dependent variable vanishes, as well as a singularity as the dependent variable approaches its a priori known upper bound. The first(More)
Certain bacteria develop iron chelation mechanisms that allow them to scavenge dissolved iron from the environment and to make it unavailable to competitors. This is achieved by producing siderophores that bind the iron which is later liberated internally in the cell. Under conditions of iron limitation, siderophore producing bacteria have therefore an(More)
The morphology of biofilms received much attention in the last years. Several concepts to explain the development of biofilm structures have been proposed. We believe that biofilm structure formation depends on physical as well as general and specific biological factors. The physical factors (e.g. governing substrate transport) as well as general biological(More)
A benchmark problem was defined to evaluate the performance of different mathematical biofilm models. The biofilm consisted of heterotrophic bacteria degrading organic substrate and oxygen. Mathematical models tested ranged from simple analytical to multidimensional numerical models. For simple and more or less flat biofilms it was shown that analytical(More)
Iron is required by many microorganisms for growth. Although it is the most abundant transition metal on earth, its solubility is very low and therefore its bioavailability is poor. To overcome this limitation, many microorganisms have developed iron chelating mechanisms that enable them to bind the metal to organic molecules from which they are later(More)
A previously introduced degenerate diffusion-reaction model of biofilm growth and disinfection is extended to account for convective transport of oxygen and disinfectants in an aqueous environment. To achieve this in a computationally efficient manner we employ a thin-film approximation to the (Navier)-Stokes equations that can be solved analytically. In(More)
Most bacteria live in biofilm communities, which offer protection against harmful external impacts. This makes treatment of biofilm borne bacterial infections with antibiotics difficult. We discuss a dynamic mathematical model that focuses on the diffusive resistance that a growing biofilm exerts against penetration of antibiotics. This allows bacteria in(More)