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Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission

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  • Muhammad Ozair

Abstract

The deterministic pine wilt model with vital dynamics to determine the equilibria and their stability by considering nonlinear incidence rates with horizontal transmission is analyzed. The complete global analysis for the equilibria of the model is discussed. The explicit formula for the reproductive number is obtained and it is shown that the “disease-free†equilibrium always exists and is globally asymptotically stable whenever . Furthermore, the disease persists at an “endemic†level when the reproductive number exceeds unity.

Suggested Citation

  • Muhammad Ozair, 2014. "Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, June.
    • Handle: RePEc:hin:jnljam:204241
    DOI: 10.1155/2014/204241
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    Cited by:

    1. Ruilin Dong & Haokun Sui & Yuting Ding, 2023. "Mathematical Modeling and Stability Analysis of the Delayed Pine Wilt Disease Model Related to Prevention and Control," Mathematics, MDPI, vol. 11(17), pages 1-21, August.
    2. 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).
    3. Khan, Muhammad Altaf & Khan, Rizwan & Khan, Yasir & Islam, Saeed, 2018. "A mathematical analysis of Pine Wilt disease with variable population size and optimal control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 205-217.

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