Computational analysis of parameter uncertainties in a two-dimensional mixed-culture biofilm model
Bacterial biofilms are complex microbial depositions on immersed interfaces that form wherever the environmental conditions sustain microbial growth. In recent years a variety of mathematical concepts have been introduced to model these spatially structured microbial populations. These are complex two- or three-dimensional models that combine population and resource dynamics, mass transfer and fluid dynamics. Regardless of the type of model, they all have, even for microbially relatively simple systems, many parameters which generally are known at most approximately. We investigate the effect of uncertainties in model parameters on the solutions of a nonlinear diffusion model for a biofilm in which two species compete for a shared nutrient. This is done in computer simulations that use a Nonstandard Finite Difference Scheme. We show the convergence of the method by grid refinement and study some qualitative properties of the numerical solution. The method is shown to scale well on shared memory computers. In an extensive computational experiment we find that model parameter uncertainties affect ecological output parameters much heavier than morphological output parameters that measure biofilm structure.