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# A discrete-delayed model with plasmid-bearing, plasmid-free competition in a chemostat

• A discrete-delayed model of plasmid-bearing, plasmid-free organisms competing for a single-limited nutrient in a chemostat is established. Rigorous mathematical analysis of the asymptotic behavior of this model is presented. An interesting method to analyze the local stability of interior equilibrium is developed. The argument is also applicable to a model of plasmid-bearing, plasmid-free organisms competing for two complementary nutrients in a chemostat.
Mathematics Subject Classification: 34D05, 34K25, 92D25.

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