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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| 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/10.1155/2014/219173 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |