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A mathematical analysis of Pine Wilt disease with variable population size and optimal control strategies

Author

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  • Khan, Muhammad Altaf
  • Khan, Rizwan
  • Khan, Yasir
  • Islam, Saeed

Abstract

The present paper describes the dynamics of the Pine Wilt disease with variable population size. The basic mathematical results for the model are presented. The stability analysis of both the disease-free and endemic cases are presented whenever R0 lesser or greater than one, respectively. Further, an optimal control problem is formulated and the necessarily involved results are presented. Moreover, the numerical simulation of the optimal control problem with suggested control strategies for the possible eliminations of the infection in the pine trees population is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:108:y:2018:i:c:p:205-217
    DOI: 10.1016/j.chaos.2018.02.002
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    References listed on IDEAS

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    1. Muhammad Altaf Khan & Saeed Islam & Sher Afzal Khan & Ilyas Khan & Sharidan Shafie & Taza Gul, 2014. "Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, November.
    2. 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.
    3. Kwang Sung Lee, 2014. "Stability Analysis and Optimal Control Strategy for Prevention of Pine Wilt Disease," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-15, June.
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    Citations

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    Cited by:

    1. Gao, Shujing & Yu, Dan & Meng, Xinzhu & Zhang, Fumin, 2018. "Global dynamics of a stage-structured Huanglongbing model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 60-67.
    2. Ali, Hegagi Mohamed & Ameen, Ismail Gad, 2020. "Save the pine forests of wilt disease using a fractional optimal control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Yusuf, Abdullahi & Acay, Bahar & Mustapha, Umar Tasiu & Inc, Mustafa & Baleanu, Dumitru, 2021. "Mathematical modeling of pine wilt disease with Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Alzahrani, E.O. & Khan, M.A., 2018. "Modeling the dynamics of Hepatitis E with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 287-301.
    5. L., Diego F. Aranda & González-Parra, Gilberto & Benincasa, Tommaso, 2019. "Mathematical modeling and numerical simulations of Zika in Colombia considering mutation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 1-18.
    6. 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).

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