Competition in a chemostat with wall attachment

A mathematical model of microbial competition for limiting nutrient and wall-attachment sites in a chemostat, formulated by Freter et al. in their study of the colonization resistance phenomena associated with the gut microflora, is mathematically analyzed. The model assumes that resident and invader bacterial strains can colonize the fluid environment of the vessel as well as its bounding surface, competing for a limited number of attachment sites on the latter. Although conditions for coexistence of the two strains are of interest, and are provided by some of our results, two bistable scenarios are of more relevance to the colonization resistance phenomena. In one case, each bacterial strain's single-population equilibrium, is stable against invasion by the other strain and there exists an unstable coexistence equilibrium, while in the second case the resident strain equilibrium is stable against invasion by the invader and yet a locally attracting coexistence equilibrium exists. Both scenarios imply that a threshold dose of invader is required to colonize the chemostat. Our analysis consists of finding equilibria, determining their stability properties and establishing the persistence or extinction of the various strains.