Competitive exclusion and coexistence in a two-strain pathogen model with diffusion

Azmy S. Ackleh; Keng Deng; Yixiang  Wu

doi:10.3934/mbe.2016.13.1

Mathematical Biosciences and Engineering, 2016, 13(1): 1-18. doi: 10.3934/mbe.2016.13.1. Primary: 92D30, 91D25; Secondary: 35K57, 37N25, 35B40.

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Competitive exclusion and coexistence in a two-strain pathogen model with diffusion

Azmy S. Ackleh, Keng Deng, Yixiang Wu

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

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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 $R_0$ and show that when the model parameters are constant (spatially homogeneous), if $R_0 >1$ then one strain will outcompete the other strain and drive it to extinction, but if $R_0 \le 1$ 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 $R_0 >1$: 1) Competitive exclusion where one strain dies out. 2) Coexistence between the two strains. Thus, spatial heterogeneity promotes coexistence.

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Keywords: coexistence; homogeneous environment; heterogeneous environment.; competitive exclusion; Multiple-strain pathogen model; basic reproduction number

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

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Copyright Info: 2016, Azmy S. Ackleh, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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