Competitive exclusion and coexistence in a two-strain pathogen model with diffusion
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 ex...
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AIMS Press
2015-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.1 |
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| author | Azmy S. Ackleh Keng Deng Yixiang Wu |
| author_facet | Azmy S. Ackleh Keng Deng Yixiang Wu |
| author_sort | Azmy S. Ackleh |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-80d4847038b345b09005f8fde93d9c00 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-80d4847038b345b09005f8fde93d9c002025-01-24T02:34:05ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-09-0113111810.3934/mbe.2016.13.1Competitive exclusion and coexistence in a two-strain pathogen model with diffusionAzmy S. Ackleh0Keng Deng1Yixiang Wu2Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504We 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.https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.1coexistencehomogeneous environmentheterogeneous environment.competitive exclusionmultiple-strain pathogen modelbasic reproduction number |
| spellingShingle | Azmy S. Ackleh Keng Deng Yixiang Wu Competitive exclusion and coexistence in a two-strain pathogen model with diffusion Mathematical Biosciences and Engineering coexistence homogeneous environment heterogeneous environment. competitive exclusion multiple-strain pathogen model basic reproduction number |
| title | Competitive exclusion and coexistence in a two-strain pathogen model with diffusion |
| title_full | Competitive exclusion and coexistence in a two-strain pathogen model with diffusion |
| title_fullStr | Competitive exclusion and coexistence in a two-strain pathogen model with diffusion |
| title_full_unstemmed | Competitive exclusion and coexistence in a two-strain pathogen model with diffusion |
| title_short | Competitive exclusion and coexistence in a two-strain pathogen model with diffusion |
| title_sort | competitive exclusion and coexistence in a two strain pathogen model with diffusion |
| topic | coexistence homogeneous environment heterogeneous environment. competitive exclusion multiple-strain pathogen model basic reproduction number |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.1 |
| work_keys_str_mv | AT azmysackleh competitiveexclusionandcoexistenceinatwostrainpathogenmodelwithdiffusion AT kengdeng competitiveexclusionandcoexistenceinatwostrainpathogenmodelwithdiffusion AT yixiangwu competitiveexclusionandcoexistenceinatwostrainpathogenmodelwithdiffusion |