Continuum and Discrete Approach in Modeling Biofilm Development and Structure: A Review

J Math Biol. 2018 Mar;76(4):945-1003. doi: 10.1007/s00285-017-1165-y. Epub 2017 Jul 24.


The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

Keywords: Biofilm; Biomass representation; Continuum models; Discrete models.

Publication types

  • Research Support, Non-U.S. Gov't
  • Review

MeSH terms

  • Biofilms / drug effects
  • Biofilms / growth & development*
  • Biomass
  • Computational Biology
  • Computer Simulation
  • Drug Resistance, Microbial
  • Humans
  • Mathematical Concepts
  • Microbial Interactions
  • Models, Biological*
  • Nonlinear Dynamics
  • Quorum Sensing
  • Systems Analysis