Competition in a chemostat with wall attachment

Eric D. Stemmons, Hal Smith

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)567-595
Number of pages29
JournalSIAM Journal on Applied Mathematics
Volume61
Issue number2
StatePublished - Aug 2000

Fingerprint

Chemostats
Chemostat
Coexistence
Invasion
Scenarios
Nutrients
Extinction
Persistence
Vessel
Dose
Mathematical models
Limiting
Unstable
Fluids
Mathematical Model
Imply
Fluid

Keywords

  • Chemostat
  • Colonization resistance
  • Competition for wall-attachment sites
  • Uniform persistence

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Competition in a chemostat with wall attachment. / Stemmons, Eric D.; Smith, Hal.

In: SIAM Journal on Applied Mathematics, Vol. 61, No. 2, 08.2000, p. 567-595.

Research output: Contribution to journalArticle

Stemmons, Eric D. ; Smith, Hal. / Competition in a chemostat with wall attachment. In: SIAM Journal on Applied Mathematics. 2000 ; Vol. 61, No. 2. pp. 567-595.
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