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Analysis of the Mathematical Model for the Spread of Pine Wilt Disease

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  • Xiangyun Shi
  • Guohua Song

Abstract

This paper formulates and analyzes a pine wilt disease model. Mathematical analyses of the model with regard to invariance of nonnegativity, boundedness of the solutions, existence of nonnegative equilibria, permanence, and global stability are presented. It is proved that the global dynamics are determined by the basic reproduction number and the other value which is larger than . If and are both less than one, the disease-free equilibrium is asymptotically stable and the pine wilt disease always dies out. If one is between the two values, though the pine wilt disease could occur, the outbreak will stop. If the basic reproduction number is greater than one, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region, and the disease persists at the endemic equilibrium state if it initially exists. Numerical simulations are carried out to illustrate the theoretical results, and some disease control measures are especially presented by these theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnljam:184054
    DOI: 10.1155/2013/184054
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    Cited by:

    1. Rahman, Ghaus ur & Shah, Kamal & Haq, Fazal & Ahmad, Naveed, 2018. "Host vector dynamics of pine wilt disease model with convex incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 31-39.
    2. Hussain, Takasar & Ozair, Muhammad & Aslam, Adnan & Jameel, Sajid & Nawaz, Maryum & Abdel-Aty, Abdel-Haleem, 2022. "Mathematical study of nematode transmission in pine trees through bark beetles," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Shah, Kamal & Alqudah, Manar A. & Jarad, Fahd & Abdeljawad, Thabet, 2020. "Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    4. Hussain, Takasar & Aslam, Adnan & Ozair, Muhammad & Tasneem, Fatima & Gómez-Aguilar, J.F., 2021. "Dynamical aspects of pine wilt disease and control measures," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

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