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.
Yuan
Sanling
S
College of Science, Shanghai University for Science and Technology, Shanghai 200093, China. yuansanling@263.net
Xiao
Dongmei
D
Han
Maoan
M
D019149:Bioreactors / Q000706:statistics & numerical data*; D001709:Biotechnology; D003470:Culture Media; D008433:Mathematics; D008829:Microbiology; D008954:Models, Biological; D010957:Plasmids / Q000235:genetics
D003470:Culture Media