Chemostats and epidemics: Competition for nutrients/hosts

Hal L. Smith; Horst R. Thieme

doi:10.3934/mbe.2013.10.1635

Article Contents

2013, Volume 10, Issue 5&6: 1635-1650. Doi: 10.3934/mbe.2013.10.1635 open access

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Chemostats and epidemics: Competition for nutrients/hosts

Hal L. Smith^1, and
Horst R. Thieme^2,

1.
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804
2.
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287

Received: January 31, 2013

Revised: March 31, 2013

Published: July 2013

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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.

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Mathematics Subject Classification: Primary: 92D15, 92D25, 92D30; Secondary: 34D23, 37B25, 93D30.

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