Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission
The deterministic pine wilt model with vital dynamics to determine the equilibria and their stability by considering nonlinear incidence rates with horizontal transmission is analyzed. The complete global analysis for the equilibria of the model is discussed. The explicit formula for the reproductiv...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/204241 |
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| _version_ | 1832545962495574016 |
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| author | Muhammad Ozair |
| author_facet | Muhammad Ozair |
| author_sort | Muhammad Ozair |
| collection | DOAJ |
| description | The deterministic pine wilt model with vital dynamics to determine the equilibria and their stability by considering nonlinear incidence rates with horizontal transmission is analyzed. The complete global analysis for the equilibria of the model is discussed. The explicit formula for the reproductive number is obtained and it is shown that the “disease-free” equilibrium always exists and is globally asymptotically stable whenever R0≤1. Furthermore, the disease persists at an “endemic” level when the reproductive number exceeds unity. |
| format | Article |
| id | doaj-art-f5a89798a539462094a149406aa7ecb5 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-f5a89798a539462094a149406aa7ecb52025-02-03T07:24:22ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/204241204241Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal TransmissionMuhammad Ozair0School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad, PakistanThe deterministic pine wilt model with vital dynamics to determine the equilibria and their stability by considering nonlinear incidence rates with horizontal transmission is analyzed. The complete global analysis for the equilibria of the model is discussed. The explicit formula for the reproductive number is obtained and it is shown that the “disease-free” equilibrium always exists and is globally asymptotically stable whenever R0≤1. Furthermore, the disease persists at an “endemic” level when the reproductive number exceeds unity.http://dx.doi.org/10.1155/2014/204241 |
| spellingShingle | Muhammad Ozair Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission Journal of Applied Mathematics |
| title | Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission |
| title_full | Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission |
| title_fullStr | Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission |
| title_full_unstemmed | Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission |
| title_short | Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission |
| title_sort | analysis of pine wilt disease model with nonlinear incidence and horizontal transmission |
| url | http://dx.doi.org/10.1155/2014/204241 |
| work_keys_str_mv | AT muhammadozair analysisofpinewiltdiseasemodelwithnonlinearincidenceandhorizontaltransmission |