Modelling drinking water biofilms: Bacterial adhesion and Legionella pneumophila necrotrophic growth

We propose a mathematical model to simulate the establishment and growth of a drinking water distribution system biofilm, focusing on the influence of ionic strength on bacterial adhesion and persistence of Legionella pneumophila. Specifically, we consider how ionic strength affects interaction energies during the initial phase of biofilm formation and we include the dependence of the attachment flux, modelled as a linear rate with respect to free floating cells, on it. The model also incorporates a novel necrotrophic kinetics to simulate the Legionella pneumophila metabolism. The biofilm is modelled as a 1D free boundary domain, and its evolution is governed by hyperbolic-parabolic PDEs. The initial attachment phase is modelled by considering a vanishing initial value for the free boundary. The model is investigated numerically highlighting the impact of the necrotrophic kinetic parameters, the influence of ionic strength on the initial stage of biofilm formation through bacterial attachment, and how variations in nutrient levels affect system dynamics. The numerical results demonstrate that: the ionic strength mainly governs bacterial adhesion for young biofilms and affects the biofilm ecology also in presence of a biocide; the necrotrophic metabolism of Legionella pneumophila favours its persistence in oligotrophic biofilms.