Chemostats and epidemics: Competition for nutrients/hosts

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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
Volume10
Issue number5-6
DOIs
StatePublished - Oct 2013

Fingerprint

Chemostats
Chemostat
Nutrients
Functional Response
Basic Reproduction Number
Food
prediction
nutrients
Prediction
Chemostat Model
Pathogens
Predict
Basic Reproduction number
Epidemic Model
Local Stability
nutrient content
Lowest
pathogens
Directly proportional

Keywords

  • 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

  • Applied Mathematics
  • Modeling and Simulation
  • Computational Mathematics
  • Agricultural and Biological Sciences(all)
  • Medicine(all)

Cite this

Chemostats and epidemics : Competition for nutrients/hosts. / Smith, Hal; Thieme, Horst.

In: Mathematical Biosciences and Engineering, Vol. 10, No. 5-6, 10.2013, p. 1635-1650.

Research output: Contribution to journalArticle

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