Coexistence of a cross-diffusive West Nile virus model in a heterogenous environment
This paper is concerned with a strongly-coupled elliptic system, which describes a West Nile virus (WNv) model with cross-diffusion in a heterogeneous environment. The basic reproduction number is introduced through the next generation infection operator and some related eigenvalue problems. The exi...
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| Language: | English |
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AIMS Press
2018-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018068 |
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| author | Abdelrazig K. Tarboush Jing Ge Zhigui Lin |
| author_facet | Abdelrazig K. Tarboush Jing Ge Zhigui Lin |
| author_sort | Abdelrazig K. Tarboush |
| collection | DOAJ |
| description | This paper is concerned with a strongly-coupled elliptic system, which describes a West Nile virus (WNv) model with cross-diffusion in a heterogeneous environment. The basic reproduction number is introduced through the next generation infection operator and some related eigenvalue problems. The existence of coexistence states is presented by using a method of upper and lower solutions. The true positive solutions are obtained by monotone iterative schemes. Our results show that a cross-diffusive WNv model possesses at least one coexistence solution if the basic reproduction number is greater than one and the cross-diffusion rates are small enough, while if the basic reproduction number is less than or equal to one, the model has no positive solution. To illustrate the impact of cross-diffusion and environmental heterogeneity on the transmission of WNv, some numerical simulations are given. |
| format | Article |
| id | doaj-art-a62ef29cfbce49dd98f492c45f275a5b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-a62ef29cfbce49dd98f492c45f275a5b2025-01-24T02:41:08ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-11-011561479149410.3934/mbe.2018068Coexistence of a cross-diffusive West Nile virus model in a heterogenous environmentAbdelrazig K. Tarboush0Jing Ge1Zhigui Lin2School of Mathematical Science, Yangzhou University, Yangzhou 225002, ChinaSchool of Mathematical Science, Huaiyin Normal University, Huaian 223300, ChinaSchool of Mathematical Science, Yangzhou University, Yangzhou 225002, ChinaThis paper is concerned with a strongly-coupled elliptic system, which describes a West Nile virus (WNv) model with cross-diffusion in a heterogeneous environment. The basic reproduction number is introduced through the next generation infection operator and some related eigenvalue problems. The existence of coexistence states is presented by using a method of upper and lower solutions. The true positive solutions are obtained by monotone iterative schemes. Our results show that a cross-diffusive WNv model possesses at least one coexistence solution if the basic reproduction number is greater than one and the cross-diffusion rates are small enough, while if the basic reproduction number is less than or equal to one, the model has no positive solution. To illustrate the impact of cross-diffusion and environmental heterogeneity on the transmission of WNv, some numerical simulations are given.https://www.aimspress.com/article/doi/10.3934/mbe.2018068west nile virusstrongly-coupled elliptic systemsheterogeneous environmentbasic reproduction numbercoexistence |
| spellingShingle | Abdelrazig K. Tarboush Jing Ge Zhigui Lin Coexistence of a cross-diffusive West Nile virus model in a heterogenous environment Mathematical Biosciences and Engineering west nile virus strongly-coupled elliptic systems heterogeneous environment basic reproduction number coexistence |
| title | Coexistence of a cross-diffusive West Nile virus model in a heterogenous environment |
| title_full | Coexistence of a cross-diffusive West Nile virus model in a heterogenous environment |
| title_fullStr | Coexistence of a cross-diffusive West Nile virus model in a heterogenous environment |
| title_full_unstemmed | Coexistence of a cross-diffusive West Nile virus model in a heterogenous environment |
| title_short | Coexistence of a cross-diffusive West Nile virus model in a heterogenous environment |
| title_sort | coexistence of a cross diffusive west nile virus model in a heterogenous environment |
| topic | west nile virus strongly-coupled elliptic systems heterogeneous environment basic reproduction number coexistence |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018068 |
| work_keys_str_mv | AT abdelrazigktarboush coexistenceofacrossdiffusivewestnilevirusmodelinaheterogenousenvironment AT jingge coexistenceofacrossdiffusivewestnilevirusmodelinaheterogenousenvironment AT zhiguilin coexistenceofacrossdiffusivewestnilevirusmodelinaheterogenousenvironment |