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Structured Population Models in Biology and Epidemiology pp 265–302Cite as

The Biofilm Model of Freter: A Review

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Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 1936))

R. Freter et al. (1983) developed a simple chemostat-based model of competition between two bacterial strains, one of which is capable of wall-growth, in order to illuminate the role of bacterial wall attachment on the phenomenon of colonization resistance in the mammalian gut. Together with various collaborators, we have re-formulated the model in the setting of a tubular flow reactor, extended the interpretation of the model as a biofilm model, and provided both mathematical analysis and numerical simulations of solution behavior. The present paper provides a review of the work in [4–6, 31–35, 45, 46].

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003-8001, USA

    M. Ballyk

  2. Department of Mathematics and Statistics, Arizona State University, Tempe, AZ, 85287-1804, USA

    D. Jones & H. L. Smith

Authors
  1. M. Ballyk
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  2. D. Jones
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  3. H. L. Smith
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Editor information

Editors and Affiliations

  1. University of Le Havre, 25 rue philippe Lebon, 76058, Le Havre, France

    Pierre Magal

  2. Department of Mathematics, University of Miami, Coral Gables, FL, 33124-4250, USA

    Shigui Ruan

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Ballyk, M., Jones, D., Smith, H.L. (2008). The Biofilm Model of Freter: A Review. In: Magal, P., Ruan, S. (eds) Structured Population Models in Biology and Epidemiology. Lecture Notes in Mathematics, vol 1936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78273-5_6

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