Competition in the presence of a lethal external inhibitor

The study considers two organisms competing for a nutrient in an open system in the presence of an inhibitor (or toxicant). The inhibitor is input at a constant rate and is lethal to one competitor while being taken up by the other without harm. This is in contrast to previous studies, where the inhibitor decreases the reproductive rate of one of the organisms. The mathematical result of the lethal effect, modeled by a mass action term, is that the system cannot be reduced to a monotone dynamical system of one order lower as is common with chemostat-like problems. The model is described by four non-linear, ordinary differential equations and we seek to describe the asymptotic behavior as a function of the parameters of the system. Several global exclusion results are presented with mathematical proofs. However, in the case of coexistence, oscillatory behavior is possible and the study proceeds with numerical examples. The model is relevant to bioremediation problems in nature and to laboratory bio-reactors.