Mathematical Biosciences and Engineering

2020, Issue 3: 2236-2271. doi: 10.3934/mbe.2020119
Research article

Discrete attachment to a cellulolytic biofilm modeled by an Itô stochastic differential equation

• Received: 28 October 2019 Accepted: 02 January 2020 Published: 15 January 2020
• We propose a mathematical framework for introducing random attachment of bacterial cells in a deterministic continuum model of cellulosic biofilms. The underlying growth model is a highly nonlinear coupled PDE-ODE system. It is regularised and discretised in space. Attachment is described then via an auxiliary stochastic process that induces impulses in the biomass equation. The resulting system is an Itô stochastic differential equation. Unlike the more direct approach of modeling attachment by additive noise, the proposed model preserves non-negativity of solutions. Our numerical simulations are able to reproduce characteristic features of cellulolytic biofilms with cell attachment from the aqueous phase. Grid refinement studies show convergence for the expected values of spatially integrated biomass density and carbon concentration. We also examine the sensitivity of the model with respect to the parameters that control random attachment.

Citation: Yousef Rohanizadegan, Stefanie Sonner, Hermann J. Eberl. Discrete attachment to a cellulolytic biofilm modeled by an Itô stochastic differential equation[J]. Mathematical Biosciences and Engineering, 2020, 17(3): 2236-2271. doi: 10.3934/mbe.2020119

Related Papers:

• We propose a mathematical framework for introducing random attachment of bacterial cells in a deterministic continuum model of cellulosic biofilms. The underlying growth model is a highly nonlinear coupled PDE-ODE system. It is regularised and discretised in space. Attachment is described then via an auxiliary stochastic process that induces impulses in the biomass equation. The resulting system is an Itô stochastic differential equation. Unlike the more direct approach of modeling attachment by additive noise, the proposed model preserves non-negativity of solutions. Our numerical simulations are able to reproduce characteristic features of cellulolytic biofilms with cell attachment from the aqueous phase. Grid refinement studies show convergence for the expected values of spatially integrated biomass density and carbon concentration. We also examine the sensitivity of the model with respect to the parameters that control random attachment.

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