Chemostats and epidemics: Competition for nutrients/hosts

Hal Smith, Horst Thieme

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


In a chemostat, several species compete for the same nutrient, while in an epidemic, several strains of the same pathogen may compete for the same susceptible hosts. As winner, chemostat models predict the species with the lowest break-even concentration, while epidemic models predict the strain with the largest basic reproduction number. We show that these predictions amount to the same if the per capita functional responses of consumer species to the nutrient concentration or of infective individuals to the density of susceptibles are proportional to each other but that they are different if the functional responses are nonproportional. In the second case, the correct prediction is given by the break-even concentrations. In the case of nonproportional functional responses, we add a class for which the prediction does not only rely on local stability and instability of one-species (strain) equilibria but on the global outcome of the competition. We also review some results for nonautonomous models.

Original languageEnglish (US)
Pages (from-to)1635-1650
Number of pages16
JournalMathematical Biosciences and Engineering
Issue number5-6
StatePublished - Oct 2013


  • Basic reproduction number
  • Break-even concentrations
  • Coexistence
  • Competitive exclusion
  • Cross immunity
  • Cross protection
  • Evolution of virulence
  • Global stability
  • Lyapunov functions
  • Seasonality

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Agricultural and Biological Sciences
  • Computational Mathematics
  • Applied Mathematics


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