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A new deterministic spatio-temporal continuum model for biofilm development. (English) Zbl 0985.92009

Summary: A new mathematical model for the development of spatially heterogeneous biofilm structures is presented. Unlike previous hybrid discrete/continuum models it is a continuum model throughout, describing the interaction of nutrient availability and biomass production. Spatial biomass spreading is described by a nonlinear density-dependent diffusion mechanism. The diffusion operator degenerates for small biomass densities and is singular at the biomass density bound. The model can be interpreted as a predator-prey model for biomass and nutrients. First numerical simulations show that the model is able to predict experimentally observed cluster-and-channel biofilm structures. The results are reliable and in qualitatively good agreement with experimental expectations.

MSC:

92C05 Biophysics
92D40 Ecology
65C20 Probabilistic models, generic numerical methods in probability and statistics
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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