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Stability Analysis and Optimal Control Strategy for Prevention of Pine Wilt Disease

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  • Kwang Sung Lee

Abstract

We propose a mathematical model of pine wilt disease (PWD) which is caused by pine sawyer beetles carrying the pinewood nematode (PWN). We calculate the basic reproduction number R0 and investigate the stability of a disease‐free and endemic equilibrium in a given mathematical model. We show that the stability of the equilibrium in the proposed model can be controlled through the basic reproduction number R0. We then discuss effective optimal control strategies for the proposed PWD mathematical model. We demonstrate the existence of a control problem, and then we apply both analytical and numerical techniques to demonstrate effective control methods to prevent the transmission of the PWD. In order to do this, we apply two control strategies: tree‐injection of nematicide and the eradication of adult beetles through aerial pesticide spraying. Optimal prevention strategies can be determined by solving the corresponding optimality system. Numerical simulations of the optimal control problem using a set of reasonable parameter values suggest that reducing the number of pine sawyer beetles is more effective than the tree‐injection strategy for controlling the spread of PWD.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:182680
    DOI: 10.1155/2014/182680
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    References listed on IDEAS

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    1. 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.
    2. 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).
    3. 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).
    4. 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, Hindawi, vol. 2014, pages 1-11, January.
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    Cited by:

    1. Ali Raza & Mohammed Mahyoub Ali Al-Shamiri & Wafa F. Alfwzan & Muhammad Rafiq & Emad Fadhal & Nauman Ahmed, 2025. "Stochastic Analysis of Pine Wilt Epidemic Model With Dynamically Consistent Approximation," Complexity, John Wiley & Sons, vol. 2025(1).
    2. Khaled Aldwoah & Shahid Ahmed & Shah Jahan & Amel Touati & Nidal EIjaneid & Tariq AIjaaidi, 2025. "Fractal-fractional modeling and stability analysis of pine wilt disease dynamics," PLOS ONE, Public Library of Science, vol. 20(2), pages 1-23, February.

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