Competition between plasmid-bearing and plasmid-free organisms in a chemostat with nutrient recycling and an inhibitor

The asymptotic behavior of solutions of a model for competition between plasmid-bearing and plasmid-free organisms in the chemostat with two distributed delays and an external inhibitor is considered. The model presents a refinement of the one considered by Lu and Hadeler [Z. Lu, K.P. Hadeler, Model of plasmid-bearing plasmid-free competition in the chemostat with nutrient recycling and an inhibitor, Math. Biosci. 167 (2000) p. 177]. The delays model the fact that the nutrient is partially recycled after the death of the biomass by bacterial decomposition. Furthermore, 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. Conditions for boundedness of solutions and existence of non-negative equilibrium are given. Analysis of the extinction of the organisms, including plasmid-bearing and plasmid-free organisms, and the uniform persistence of the system are also carried out. By constructing appropriate Liapunov-like functionals, some sufficient conditions of global attractivity to the extinction equilibria are obtained and the combined effects of the delays and the inhibitor are studied. (c) 2006 Elsevier Inc. All rights reserved.