Delboni RR, Yang HM. Mathematical Model of Interaction Between Bacteriocin-Producing Lactic Acid Bacteria and Listeria. Part 1: Steady States and Thresholds.
Bull Math Biol 2017;
79:1637-1661. [PMID:
28597170 DOI:
10.1007/s11538-017-0302-5]
[Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2016] [Accepted: 05/24/2017] [Indexed: 11/24/2022]
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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