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Mathematical Biosciences and Engineering

2016, Volume 13, Issue 1: 1-18. doi: 10.3934/mbe.2016.13.1
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Competitive exclusion and coexistence in a two-strain pathogen model with diffusion

  • 1.
    Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010
  • 2.
    Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504
  • Received: 01 December 2014 Accepted: 29 June 2018 Published: 01 October 2015

  • MSC : Primary: 92D30, 91D25; Secondary: 35K57, 37N25, 35B40.

  • We consider a two-strain pathogen model described by a system of reaction-diffusion equations. We define a basic reproduction number R0 and show that when the model parameters are constant (spatially homogeneous), if R0>1 then one strain will outcompete the other strain and drive it to extinction, but if R0≤1 then the disease-free equilibrium is globally attractive. When we assume that the diffusion rates are equal while the transmission and recovery rates are heterogeneous, then there are two possible outcomes under the condition R0>1: 1) Competitive exclusion where one strain dies out. 2) Coexistence between the two strains. Thus, spatial heterogeneity promotes coexistence.

    Citation: Azmy S. Ackleh, Keng Deng, Yixiang Wu. Competitive exclusion and coexistence in a two-strain pathogen model with diffusion[J]. Mathematical Biosciences and Engineering, 2016, 13(1): 1-18. doi: 10.3934/mbe.2016.13.1

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  • We consider a two-strain pathogen model described by a system of reaction-diffusion equations. We define a basic reproduction number R0 and show that when the model parameters are constant (spatially homogeneous), if R0>1 then one strain will outcompete the other strain and drive it to extinction, but if R0≤1 then the disease-free equilibrium is globally attractive. When we assume that the diffusion rates are equal while the transmission and recovery rates are heterogeneous, then there are two possible outcomes under the condition R0>1: 1) Competitive exclusion where one strain dies out. 2) Coexistence between the two strains. Thus, spatial heterogeneity promotes coexistence.


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