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COMPETITION BETWEEN PLASMID-BEARING AND PLASMID-FREE ORGANISMS IN A CHEMOSTAT WITH DISTINCT REMOVAL RATES AND AN EXTERNAL INHIBITOR

NABIL HAMIDI

https://orcid.org/0000-0003-0406-6958

Laboratory of Mathematics, Djillali Liabès University, Sidi Bel Abbès 22000, Algeria

E-mail Address: nabil.hamidi@univ-sba.dz

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MOHAMED DELLAL

https://orcid.org/0000-0002-4066-4093

Laboratory of Mathematics, Djillali Liabès University, Sidi Bel Abbès 22000, Algeria

Department of Mathematics, Faculty of Mathematics and Computer Science, Ibn Khaldoun University, Tiaret 14000, Algeria

E-mail Address: dellal.m48@univ-tiaret.dz

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MUSTAPHA LAKRIB

https://orcid.org/0000-0002-5998-2067

Laboratory of Mathematics, Djillali Liabès University, Sidi Bel Abbès 22000, Algeria

E-mail Address: m.lakrib@univ-sba.dz

Corresponding author.

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https://doi.org/10.1142/S0218339024500359Cited by:0 (Source: Crossref)

Abstract

A mathematical model of competition between plasmid-bearing and plasmid-free organisms for a single limiting resource in a chemostat with distinct removal rates and in the presence of an external inhibitor is analyzed. This model was previously introduced in the special case where the growth rate functions and the absorption rate of the inhibitor follow the Monod kinetics and the removal rates are the same as the dilution rate. Here, we consider the general case of monotonic growth and absorption functions, and distinct removal rates. Through the three operating parameters of the model, represented by the dilution rate, the input concentrations of the substrate and the inhibitor, we give necessary and sufficient conditions for existence and stability of all equilibria. To better understand the richness of the model’s behavior with respect to those operating parameters, we determine the operating diagram theoretically and numerically. This diagram is very useful to understand the model from both the mathematical and biological points of view.

Keywords:

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