Stationary Patterns of a Cross-Diffusion Epidemic Model
We investigate the complex dynamics of cross-diffusion SI epidemic model. We first give the conditions of the local and global stability of the nonnegative constant steady states, which indicates that the basic reproduction number determines whether there is an endemic outbreak or not. Furthermore,...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/852698 |
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| _version_ | 1832550769354604544 |
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| author | Yongli Cai Dongxuan Chi Wenbin Liu Weiming Wang |
| author_facet | Yongli Cai Dongxuan Chi Wenbin Liu Weiming Wang |
| author_sort | Yongli Cai |
| collection | DOAJ |
| description | We investigate the complex dynamics of cross-diffusion SI epidemic model. We first give the conditions of the local and global stability of the nonnegative constant steady states, which indicates that the basic reproduction number determines whether there is an endemic outbreak or not. Furthermore, we prove the existence and nonexistence of the positive nonconstant steady states, which guarantees the existence of the stationary patterns. |
| format | Article |
| id | doaj-art-b346db495d9a4235b3188ab74801e327 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b346db495d9a4235b3188ab74801e3272025-02-03T06:05:51ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/852698852698Stationary Patterns of a Cross-Diffusion Epidemic ModelYongli Cai0Dongxuan Chi1Wenbin Liu2Weiming Wang3School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, ChinaDepartment of Applied Mathematics, Shanghai Finance University, Shanghai 201209, ChinaCollege of Physics and Electronic Information Engineering, Wenzhou University, Wenzhou 325035, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaWe investigate the complex dynamics of cross-diffusion SI epidemic model. We first give the conditions of the local and global stability of the nonnegative constant steady states, which indicates that the basic reproduction number determines whether there is an endemic outbreak or not. Furthermore, we prove the existence and nonexistence of the positive nonconstant steady states, which guarantees the existence of the stationary patterns.http://dx.doi.org/10.1155/2013/852698 |
| spellingShingle | Yongli Cai Dongxuan Chi Wenbin Liu Weiming Wang Stationary Patterns of a Cross-Diffusion Epidemic Model Abstract and Applied Analysis |
| title | Stationary Patterns of a Cross-Diffusion Epidemic Model |
| title_full | Stationary Patterns of a Cross-Diffusion Epidemic Model |
| title_fullStr | Stationary Patterns of a Cross-Diffusion Epidemic Model |
| title_full_unstemmed | Stationary Patterns of a Cross-Diffusion Epidemic Model |
| title_short | Stationary Patterns of a Cross-Diffusion Epidemic Model |
| title_sort | stationary patterns of a cross diffusion epidemic model |
| url | http://dx.doi.org/10.1155/2013/852698 |
| work_keys_str_mv | AT yonglicai stationarypatternsofacrossdiffusionepidemicmodel AT dongxuanchi stationarypatternsofacrossdiffusionepidemicmodel AT wenbinliu stationarypatternsofacrossdiffusionepidemicmodel AT weimingwang stationarypatternsofacrossdiffusionepidemicmodel |