We present a mathematical model and computer simulations for the control of a pathogenic biofilm by a probiotic biofilm. This is a substantial extension of a previous model of control of a pathogenic biofilm by microbial control agents that are suspended in the aqueous bulk phase (H. Khassehkhan and H.J. Eberl, Comp. Math. Meth. Med, 9(1) (2008), pp. 47–67). The mathematical model is a system of double-degenerate diffusion–reaction equations for the microbial biomass fractions probiotics, pathogens and inert bacteria, coupled with convection–diffusion–reaction equations for two growth controlling substrates, protonated lactic acids and hydrogen ions (pH). The latter are produced by the bacteria and become detrimental at high concentrations. In simulation studies, we find that the site of attachment of probiotics in the flow channel is crucial for success and efficacy of the probiotic control mechanism.

中文翻译：

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益生菌生物膜控制系统的混合培养模型。

我们提出了通过益生菌生物膜控制病原性生物膜的数学模型和计算机模拟。这是对先前通过悬浮在水性本体相中的微生物控制剂控制病原性生物膜的模型的实质扩展（H. Khassehkhan和HJ Eberl，Comp。Math。Meth。Med，9（1）（2008） ，第47-67页）。该数学模型是针对微生物生物质组分益生菌，病原体和惰性细菌的双简并扩散反应方程式，以及对两种生长控制基质（质子化乳酸和氢离子（pH））的对流扩散反应方程式。后者由细菌产生并在高浓度时有害。在模拟研究中