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2014 Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate
Kwang Sung Lee, Abid Ali Lashari
Abstr. Appl. Anal. 2014: 1-11 (2014). DOI: 10.1155/2014/219173

Abstract

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 R01, 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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Kwang Sung Lee. Abid Ali Lashari. "Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate." Abstr. Appl. Anal. 2014 1 - 11, 2014. https://doi.org/10.1155/2014/219173

Information

Published: 2014
First available in Project Euclid: 26 March 2014

zbMATH: 07021953
MathSciNet: MR3166580
Digital Object Identifier: 10.1155/2014/219173

Rights: Copyright © 2014 Hindawi

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