A survey of mathematical models of competition with an inhibitor.

*(English)*Zbl 1034.92034Summary: Mathematical models of the effect of inhibitors on microbial competition are surveyed. The term inhibitor is used in a broad sense and includes toxins, contaminants, allelopathic agents, etc. This includes both detoxification where the inhibitor is viewed as a pollutant and control where the inhibitor is viewed as an aid to controlling a bioreactor. The inhibitor may be supplied externally or may be created as an anti-competitor toxin. This includes plasmid-bearing and plasmid-free competition.

The literature is spread across journals in different disciplines and with different notation. This survey attempts to present the mathematical models and the results of the corresponding analysis within a common framework and notation. Detailed mathematical proofs are not given but the methods of proof are indicated, references cited, and the results presented in tables. Open problems are indicated where there is a gap in the theory.

The literature is spread across journals in different disciplines and with different notation. This survey attempts to present the mathematical models and the results of the corresponding analysis within a common framework and notation. Detailed mathematical proofs are not given but the methods of proof are indicated, references cited, and the results presented in tables. Open problems are indicated where there is a gap in the theory.

##### MSC:

92D40 | Ecology |

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\textit{S. B. Hsu} and \textit{P. Waltman}, Math. Biosci. 187, No. 1, 53--91 (2004; Zbl 1034.92034)

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