Analysis of amensalistic bacteria biocontrol models
We present a mathematical model for growth and control of facultative anaerobic bacterial biofilms in the context of an amensalistic microbial systems. The growth of the microbial population is limited by protonated acids and the local pH value, which in return are altered as the microbial population changes. The process is described by a system of five coupled non-linear differential equations for the dependent variables biomass densities, acid concentration, pH and malate. We present an extensive model in chemostat format of this bio control model and study the effect of initial values and flow rate for the dynamics of pathogens and control agent. Using a nonlinear master equation a diffusion-reaction model for biofilms is derived. The equation for bacterial biomass shows two non-linear diffusion effects, a power law degeneracy as the dependent variable vanishes and a singularity in the diffusion coefficient as the dependent variable approaches its a priori known threshold. The interaction of both effects describes the spatial spreading of the biofilm. The interface between regions where the solution is positive and where it vanishes is the biofilm/bulk interface. We adapt a numerical method to explicitly track this interface in 'x-t' space, based on the weak formulation of the biofilm model in a moving mesh frame. Morever we present numerical simulations of the spatio-temporal amensalistic biofilm model, applied to a probiotic biofilm control scenario. An existence of solution and 2D simulation was carried out in appendix B for dual species setup.