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Mathematical Model of Interaction Between Bacteriocin-Producing Lactic Acid Bacteria and Listeria. Part 1: Steady States and Thresholds

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Abstract

Mathematical modeling is an important tool to assessing quantitative conjectures and to answer specific questions. In the modeling, we assume that a competitor represented by a lactic acid bacterium produces antimicrobial compounds (substances that kill microorganisms or inhibit their growth), such as lactic acid and bacteriocins, with some cost to its own growth. Bacteriocins are protein compounds with antimicrobial effect against related species and bacteria such as Listeria monocytogenes, which is foodborne pathogen that cause listeriosis. From the analysis of the model, we found the thresholds which determine the existence of multiple equilibria and we studied their stability, in order to evaluate the interaction between lactic acid bacteria and L. monocytogenes.

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Acknowledgements

We thank to anonymous reviewers for providing comments and suggestions, which contributed to improving this paper.

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Authors and Affiliations

  1. UNICAMP-IMECC-DMA, Rua Sérgio Buarque de Holanda, 651, CEP: 13083-859, Campinas, SP, Brazil

    Roberta Regina Delboni & Hyun Mo Yang

Authors
  1. Roberta Regina Delboni
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  2. Hyun Mo Yang
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Correspondence to Roberta Regina Delboni.

Additional information

Project supported by Grant from FAPESP 2008/10735-0 and CAPES.

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Delboni, R.R., Yang, H.M. Mathematical Model of Interaction Between Bacteriocin-Producing Lactic Acid Bacteria and Listeria. Part 1: Steady States and Thresholds. Bull Math Biol 79, 1637–1661 (2017). https://doi.org/10.1007/s11538-017-0302-5

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  • DOI: https://doi.org/10.1007/s11538-017-0302-5

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