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

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  • Kwang Sung Lee
  • Abid Ali Lashari

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 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.

Suggested Citation

  • Kwang Sung Lee & Abid Ali Lashari, 2014. "Global Stability of a Host‐Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:219173
    DOI: 10.1155/2014/219173
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    References listed on IDEAS

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    1. Cai, Liming & Guo, Shumin & Li, XueZhi & Ghosh, Mini, 2009. "Global dynamics of a dengue epidemic mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2297-2304.
    2. Xiangyun Shi & Guohua Song, 2013. "Analysis of the Mathematical Model for the Spread of Pine Wilt Disease," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, March.
    3. Xiangyun Shi & Guohua Song, 2013. "Analysis of the Mathematical Model for the Spread of Pine Wilt Disease," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
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    Cited by:

    1. Kwang Sung Lee, 2014. "Stability Analysis and Optimal Control Strategy for Prevention of Pine Wilt Disease," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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