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Uniform persistence and periodic solution of chemostat-type model with antibiotic
A system of functional differential equations is used to model
the single microorganism in the chemostat environment with a
periodic nutrient and antibiotic input. Based on the technique
of Razumikhin, we obtain the sufficient condition for uniform
persistence of the microbial population. For general periodic
functional differential equations, we obtain a sufficient
condition for the existence of periodic solution, therefore,
the existence of positive periodic solution to the chemostat-type
model is verified.