Applying a Moment Approximation to a Bacterial Biofilm Individual-Based Model

We consider a 2D individual-based model of biofilm, in which bacteria can generate a polymeric substance (EPS), The coupling between polymer generation and bacteria creates a variety of biofilm structures. Then, we derive the equations of first and second moment evolution for the bacteria and EPS particle population sizes. This approximation of the dynamics is much lighter to compute than the whole IBM, hence more systematic exploration is easier particularly in case of large bacteria populations. We show that the second moment approximation predicts accurately the quantities of bacteria and polymer. Moreover, it gives relevant information about their spatial distribution.