Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate
Based on classical epidemic models, this paper considers a deterministic epidemic model for the spread of the pine wilt disease which has vector mediated transmission. The analysis of the model shows that its dynamics are completely determined by the basic reproduction number R0. Using a Lyapunov f...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/219173 |
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| _version_ | 1832556740383604736 |
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| author | Kwang Sung Lee Abid Ali Lashari |
| author_facet | Kwang Sung Lee Abid Ali Lashari |
| author_sort | Kwang Sung Lee |
| collection | DOAJ |
| description | Based on classical epidemic models, this paper considers a
deterministic epidemic model for the spread of the pine wilt disease
which has vector mediated transmission. The analysis of the model
shows that its dynamics are completely determined by the basic
reproduction number R0. Using a Lyapunov function and a
LaSalle's invariant set theorem, we proved the global asymptotical
stability of the disease-free equilibrium. We find that if
R0≤1, the disease free equilibrium is globally
asymptotically stable, and the disease will be eliminated.
If R0>1, a unique endemic equilibrium exists and is shown to
be globally asymptotically stable, under certain restrictions on the
parameter values, using the geometric approach method for global
stability, due to Li and Muldowney and the disease persists at the
endemic equilibrium state if it initially exists. |
| format | Article |
| id | doaj-art-49ab0d0a457d458ab1980e31e48a1200 |
| 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-49ab0d0a457d458ab1980e31e48a12002025-02-03T05:44:27ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/219173219173Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence RateKwang Sung Lee0Abid Ali Lashari1Department of Mathematics, Pusan National University, 30 Geumjeong-Gu, Busan 609-735, Republic of KoreaSchool of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad 44000, PakistanBased on classical epidemic models, this paper considers a deterministic epidemic model for the spread of the pine wilt disease which has vector mediated transmission. The analysis of the model shows that its dynamics are completely determined by the basic reproduction number R0. Using a Lyapunov function and a LaSalle's invariant set theorem, we proved the global asymptotical stability of the disease-free equilibrium. We find that if R0≤1, the disease free equilibrium is globally asymptotically stable, and the disease will be eliminated. If R0>1, a unique endemic equilibrium exists and is shown to be globally asymptotically stable, under certain restrictions on the parameter values, using the geometric approach method for global stability, due to Li and Muldowney and the disease persists at the endemic equilibrium state if it initially exists.http://dx.doi.org/10.1155/2014/219173 |
| spellingShingle | Kwang Sung Lee Abid Ali Lashari Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate Abstract and Applied Analysis |
| title | Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate |
| title_full | Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate |
| title_fullStr | Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate |
| title_full_unstemmed | Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate |
| title_short | Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate |
| title_sort | global stability of a host vector model for pine wilt disease with nonlinear incidence rate |
| url | http://dx.doi.org/10.1155/2014/219173 |
| work_keys_str_mv | AT kwangsunglee globalstabilityofahostvectormodelforpinewiltdiseasewithnonlinearincidencerate AT abidalilashari globalstabilityofahostvectormodelforpinewiltdiseasewithnonlinearincidencerate |