Analysis and simulations of the initial phase in multispecies biofilm formation

The work presents a mathematical modelling approach to study dynamic competition during the attachment phenomena in the initial phase of biofilm growth. Biofilm development is described by a set nonlinear hyperbolic partial differential equations. Diffusion of substrates through biofilm is modeled by a set of semilinear parabolic partial differential equations. The two sets of equations are mutually connected. The resulting mathematical problem is a free boundary value problem, which is essentially hyperpolic. A characteristic-like method is introduced to convert differential equations to integral equations. Fixed-point theorem is used to obtain existence, uniqueness and properties of solutions. The model has been applied to the biological competition of heterotrophic-autotrophic bacteria in a multi-specie biofilm. The effects of different attachment rates on the biofilm dynamic performances predicting biofilm thickness, volume fractions of bacterial species and substrate concentration trends have been investigated. The simulations show that the different attachment rates influence biofilm thickness, of course. However, the volume fractions of bacterial species mainly depend on biofilm internal dynamics and substrate concentration trends. The bulk concentrations of microbial species play a relative important role only in the outermost layers of biofilm.