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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 5&6: 1635-1650. doi: 10.3934/mbe.2013.10.1635
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Chemostats and epidemics: Competition for nutrients/hosts

  • 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: 01 February 2013 Accepted: 29 June 2018 Published: 01 August 2013

  • MSC : Primary: 92D15, 92D25, 92D30; Secondary: 34D23, 37B25, 93D30.

  • In a chemostat, several species compete for the same nutrient, whilein an epidemic, several strains of the same pathogen may competefor the same susceptible hosts. As winner, chemostat models predict the specieswith the lowest break-even concentration, while epidemicmodels predict the strain with the largest basic reproduction number.We show that these predictions amount to the same if the per capitafunctional responses of consumer species to the nutrient concentration or ofinfective individuals to the density of susceptibles are proportional to eachother 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) equilibriabut on the global outcome of the competition. We also review some results fornonautonomous models.

    Citation: Hal L. Smith, Horst R. Thieme. Chemostats and epidemics: Competition for nutrients/hosts[J]. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1635-1650. doi: 10.3934/mbe.2013.10.1635

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  • In a chemostat, several species compete for the same nutrient, whilein an epidemic, several strains of the same pathogen may competefor the same susceptible hosts. As winner, chemostat models predict the specieswith the lowest break-even concentration, while epidemicmodels predict the strain with the largest basic reproduction number.We show that these predictions amount to the same if the per capitafunctional responses of consumer species to the nutrient concentration or ofinfective individuals to the density of susceptibles are proportional to eachother 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) equilibriabut on the global outcome of the competition. We also review some results fornonautonomous models.


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