Dynamics of a plasmid chemostat model with periodic nutrient input and delayed nutrient recycling

A model of competition between plasmid-bearing and plasmid-free organisms in the chemostat with periodic input of nutrient and two distributed delays is investigated. The delays model the fact that the nutrient is partially recycled after the death of the biomass by bacterial decomposition. It is assumed that there is inter-specific competition between the plasmid-bearing and plasmid-free organisms as well as intra-specific competition within each population. Analysis of the extinction of the organisms, including plasmid-bearing and plasmid-free organisms, and the permanence of the system are carried out. Furthermore, sufficient conditions ensuring the existence and global stability of the positive periodic solution are established. Numerical simulations illustrate the theoretical results. Finally, we present a procedure by which one can control the parameters of the model to keep the plasmid-bearing organism stay eventually in a desired set