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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.

The objective of this study is to analyze a model of competition for one resource in the chemostat with general interspecific density-dependent growth rates, taking into account the predator–prey relationship. This relationship is characterized by the fact that the prey species promotes the growth of the predator species which in turn inhibits the growth of the first species. The model is a three-dimensional system of ordinary differential equations. With the same dilution rates, the model can be reduced to a planar system where the two models have the same local and even global behavior. The existence and stability conditions of all steady states of the reduced model in the plane are determined according to the operating parameters. Using the nullcline method, we present a geometric characterization of the existence and stability of all equilibria showing the multiplicity of coexistence steady states. The bifurcation diagrams illustrate that the steady states can appear or disappear only through saddle-node or transcritical bifurcations. Moreover, the operating diagrams describe the asymptotic behavior of this system by varying the control parameters and show the effect of the inhibition of predation on the emergence of the bistability region and the reduction until the disappearance of the coexistence region by increasing this inhibition parameter.

This paper considers the production of biomass of two interconnected chemostats in series with biomass mortality and a growth kinetic of the biomass described by an increasing function. A comparison is made with the productivity of a single chemostat with the same mortality rate and with volume equal to the sum of the volumes of the two chemostats. We determine the operating conditions under which the productivity of the serial configuration is greater than the productivity of the single chemostat. Moreover, the differences and similarities in the results corresponding to the case with mortality and the one without mortality, are highlighted. The mortality leads to surprising results where the productivity of a steady state where the bacteria are washed out in the first chemostat is greater than the one where the bacteria are present in both chemostats.