Competition in the presence of a lethal external inhibitor

Analysis of Prey-Predator Model in Chemostat When the Predator Produces Inhibitor

“…So, it is quite natural that it should be used as a model for studying detoxification problems. Many authors have studied those models [6][7][8][9][10][11][12]. Recently, the inhibitor has been introduced in the models for prey -predator in chemostat when the prey produces unaffected inhibitor which is lethal to neither predator nor nutrient [1].…”

One bug, two drugs : A mathematical model of resistance dynamics in the ICU.

“…Many ecological models are based on the chemostat; for instance, the chemostat has been used to model wastewater treatment problems [45]. The chemostat has gained widespread acceptance as a useful model in ecology [46,47]. F.M.…”

“…The growth-inhibiting substance is input into the environment from an external source, as opposed to being produced by one of the competing species. The former scenario is called an external inhibitor problem, while the latter is an internal inhibitor problem [47]. The internal inhibitor problem will not be addressed here.…”

“…While the inhibitor in the model by Lenski and Hattingh lessens the reproductive rate of the susceptible organism, Hsu, Li, and Waltman present a chemostat model in [47] with a slightly different type of inhibitor. In this model, two organisms compete for nutrient in the presence of an inhibitor which is lethal to the susceptible organism (rather than merely limiting its reproductive rate) but is taken up by the resistant organism with no damaging effect.…”

“…We denote the nutrient as S, the susceptible organism as X, the resistant organism as y, and the inhibitor as P; the model for this type of chemostat follows (adapted from [47]). The leu is similar to the chemostat with inhibitor described by Hsu, Li, and Waltman in several respects, which justifies its use as a basis for the model.…”