### Mathematical Biosciences and Engineering

2016, Issue 1: 1-18. doi: 10.3934/mbe.2016.13.1

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

• 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 $R_0$ 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.

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

### Related Papers:

• 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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沈阳化工大学材料科学与工程学院 沈阳 110142

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