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Mathematical Biosciences and Engineering

2006, Volume 3, Issue 1: 219-235. doi: 10.3934/mbe.2006.3.219
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Competing species models with an infectious disease

  • 1.
    Applied Mathematical and Computational Sciences, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242
  • Received: 01 January 2005 Accepted: 29 June 2018 Published: 01 November 2005

  • MSC : 92D30, 92D40.

  • The frequency-dependent (standard) form of the incidence is used for the transmission dynamics of an infectious disease in a competing species model. In the global analysis of the SIS model with the birth rate independent of the population size, a modified reproduction number R1 determines the asymptotic behavior, so that the disease dies out if R1≤1 and approaches a globally attractive endemic equilibrium if R1>1. Because the disease- reduced reproduction and disease-related death rates are often different in two competing species, a shared disease can change the outcome of the competition. Models of SIR and SIRS type are also considered. A key result in all of these models with the frequency-dependent incidence is that the disease must either die out in both species or remain endemic in both species.

    Citation: Roberto A. Saenz, Herbert W. Hethcote. Competing species models with an infectious disease[J]. Mathematical Biosciences and Engineering, 2006, 3(1): 219-235. doi: 10.3934/mbe.2006.3.219

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  • The frequency-dependent (standard) form of the incidence is used for the transmission dynamics of an infectious disease in a competing species model. In the global analysis of the SIS model with the birth rate independent of the population size, a modified reproduction number R1 determines the asymptotic behavior, so that the disease dies out if R1≤1 and approaches a globally attractive endemic equilibrium if R1>1. Because the disease- reduced reproduction and disease-related death rates are often different in two competing species, a shared disease can change the outcome of the competition. Models of SIR and SIRS type are also considered. A key result in all of these models with the frequency-dependent incidence is that the disease must either die out in both species or remain endemic in both species.


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