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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.


    [1]  Journal of Mathematical Biology, 47 (2003), 153-168.
    [2]  Discrete and Continuous Dynamical Systems Series B, 5 (2005), 175-188.
    [3]  Journal of Mathematical Biology, 68 (2014), 453-475.
    [4]  Journal of Differential Equations, 33 (1979), 201-225.
    [5]  Mathematical Biosciences, 186 (2003), 191-217.
    [6]  SIAM Journal on Applied Mathematics, 67 (2007), 1283-1309.
    [7]  Discrete and Continuous Dynamical Systems, 21 (2008), 1-20.
    [8]  Journal Mathematical Biology, 35 (1997), 825-842.
    [9]  Journal of Theoretical Biology, 177 (1995), 159-165.
    [10]  Science, 287 (2000), 650-654.
    [11]  Journal of Mathematical Biology, 27 (1989), 179-190.
    [12]  Rocky Mountain Journal of Mathematics, 26 (1996), 1-35.
    [13]  Wiley, Chichester, West Sussex, UK, 2003.
    [14]  SIAM Journal on Applied Mathematics, 56 (1996), 494-508.
    [15]  Journal of Mathematical Biology, 35 (1997), 503-522.
    [16]  submitted.
    [17]  Bulletin of the Australian Mathematical Society, 44 (1991), 79-94.
    [18]  American Mathematical Society, Providence, 1988.
    [19]  Springer-Verlag, New York, 1981.
    [20]  Transactions of the American Mathematical Society, 348 (1996), 4083-4094.
    [21]  Mathematical Biosciences and Engineering, 7 (2010), 51-66.
    [22]  SIAM Journal on Mathematical Analysis, 35 (2003), 453-491.
    [23]  Journal of Differential Equations, 211 (2005), 135-161.
    [24]  Funkcialaj Ekvacioj, 32 (1989), 191-213.
    [25]  Journal of Differential Equations, 223 (2006), 400-426.
    [26]  Journal of Differential Equations, 230 (2006), 720-742.
    [27]  Journal of Biological Dynamics, 3 (2009), 235-251.
    [28]  Plenum Press, New York, 1992.
    [29]  Nonlinear Analysis, 71 (2009), 239-247.
    [30]  Journal of Differential Equations, 247 (2009), 1096-1119.
    [31]  Nonlinearity, 25 (2012), 1451-1471.
    [32]  Physica D, 259 (2013), 8-25.
    [33]  Journal of Biological Dynamics, 6 (2012), 406-439.

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