Allelopathy of plasmid-bearing and plasmid-free organisms competing for two complementary resources in a chemostat

We consider a model of competition between plasmid-bearing and plasmid-free organisms for two complementary nutrients in a chemostat. We assume that the plasmid-bearing organism produces an allelopathic agent at the cost of its reproductive abilities which is lethal to plasmid-free organism. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the organisms associated with the system cannot thrive even in the absence of competition. Local stability of the system is obtained in the absence of one or both the organisms. Also, global stability of the system is obtained in the presence of both the organisms. Computer simulations have been carried out to illustrate various analytical results.