Existence of Traveling Wave Solutions for Cholera Model
To investigate the spreading speed of cholera, Codeço’s cholera model (2001) is developed by a reaction-diffusion model that incorporates both indirect environment-to-human and direct human-to-human transmissions and the pathogen diffusion. The two transmission incidences are supposed to be saturate...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/201094 |
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| _version_ | 1832561869385105408 |
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| author | Tianran Zhang Qingming Gou Xiaoli Wang |
| author_facet | Tianran Zhang Qingming Gou Xiaoli Wang |
| author_sort | Tianran Zhang |
| collection | DOAJ |
| description | To investigate the spreading speed of cholera, Codeço’s cholera model (2001)
is developed by a reaction-diffusion model that incorporates both indirect
environment-to-human and direct human-to-human transmissions and the
pathogen diffusion. The two transmission incidences are supposed to be
saturated with infective density and pathogen density. The basic reproduction
number R0 is defined and the formula for minimal wave speed c* is given. It
is proved by shooting method that there exists a traveling wave solution with
speed c for cholera model if and only if c≥c*. |
| format | Article |
| id | doaj-art-b3019b448a1b4e44a4aff842768a18b0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b3019b448a1b4e44a4aff842768a18b02025-02-03T01:24:08ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/201094201094Existence of Traveling Wave Solutions for Cholera ModelTianran Zhang0Qingming Gou1Xiaoli Wang2School of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaCollege of Mathematics & Computer Science, Yangtze Normal University, Chongqing 408100, ChinaSchool of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaTo investigate the spreading speed of cholera, Codeço’s cholera model (2001) is developed by a reaction-diffusion model that incorporates both indirect environment-to-human and direct human-to-human transmissions and the pathogen diffusion. The two transmission incidences are supposed to be saturated with infective density and pathogen density. The basic reproduction number R0 is defined and the formula for minimal wave speed c* is given. It is proved by shooting method that there exists a traveling wave solution with speed c for cholera model if and only if c≥c*.http://dx.doi.org/10.1155/2014/201094 |
| spellingShingle | Tianran Zhang Qingming Gou Xiaoli Wang Existence of Traveling Wave Solutions for Cholera Model Abstract and Applied Analysis |
| title | Existence of Traveling Wave Solutions for Cholera Model |
| title_full | Existence of Traveling Wave Solutions for Cholera Model |
| title_fullStr | Existence of Traveling Wave Solutions for Cholera Model |
| title_full_unstemmed | Existence of Traveling Wave Solutions for Cholera Model |
| title_short | Existence of Traveling Wave Solutions for Cholera Model |
| title_sort | existence of traveling wave solutions for cholera model |
| url | http://dx.doi.org/10.1155/2014/201094 |
| work_keys_str_mv | AT tianranzhang existenceoftravelingwavesolutionsforcholeramodel AT qingminggou existenceoftravelingwavesolutionsforcholeramodel AT xiaoliwang existenceoftravelingwavesolutionsforcholeramodel |