## Abstract and Applied Analysis

### Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate

#### 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 ${R}_{0}$. 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 ${R}_{0}\le 1$, the disease free equilibrium is globally asymptotically stable, and the disease will be eliminated. If ${R}_{0}>1$, 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 219173, 11 pages.

Dates
First available in Project Euclid: 26 March 2014

https://projecteuclid.org/euclid.aaa/1395858512

Digital Object Identifier
doi:10.1155/2014/219173

Mathematical Reviews number (MathSciNet)
MR3166580

Zentralblatt MATH identifier
07021953

#### Citation

Lee, Kwang Sung; Lashari, Abid Ali. Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate. Abstr. Appl. Anal. 2014 (2014), Article ID 219173, 11 pages. doi:10.1155/2014/219173. https://projecteuclid.org/euclid.aaa/1395858512

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