IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v164y2022ics0960077922008840.html
   My bibliography  Save this article

Dynamical analysis of fractional plant disease model with curative and preventive treatments

Author

Listed:
  • Shaw, Pawan Kumar
  • Kumar, Sunil
  • Momani, Shaher
  • Hadid, Samir

Abstract

Food security has become a major concern as the human population grows. Agriculture is crucial in this environment. The majority of staple meals are derived from plants. Plant diseases, on the other hand, can lower food production and quality. In this paper, two stage plant disease (TSPD) dynamics can be studied using a fractional order model. Here we used two fractional operator: Caputo fractional derivative (CFD) and Caputo–Fabrizio fractional derivative (CFFD) each of arbitrary order ϖ∈(0,1]. We evaluate the effects of curative and preventive treatments on plant disease transmission dynamics in the concerned model. We demonstrate that this model has non-negative solutions, which is desirable in population dynamics. For the suggested model, we discuss the stability of a disease-free and endemic equilibrium. For numerical simulation, we used generalized fractional RK2 scheme, Adams–Bashforth Moulton (ABM) scheme, and three step fractional Adam–Bashforth scheme (ABS) to visualize the outcomes of the concerned model. We discovered that combining curative and preventive treatment can help to reduce the number of diseased plants.

Suggested Citation

  • Shaw, Pawan Kumar & Kumar, Sunil & Momani, Shaher & Hadid, Samir, 2022. "Dynamical analysis of fractional plant disease model with curative and preventive treatments," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
  • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008840
    DOI: 10.1016/j.chaos.2022.112705
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922008840
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2022.112705?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. El-Sayed, A.M.A. & Rida, S.Z. & Gaber, Y.A., 2020. "Dynamical of curative and preventive treatments in a two-stage plant disease model of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    2. Agarwal, Praveen & Singh, Ram, 2020. "Modelling of transmission dynamics of Nipah virus (Niv): A fractional order Approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    3. Muhammad Sarmad Arshad & Dumitru Baleanu & Muhammad Bilal Riaz & Muhammad Abbas & Qasem M. Al-Mdallal, 2020. "A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-8, June.
    4. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2019. "A fractional mathematical model of breast cancer competition model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 38-54.
    5. I. Ameen & M. Hidan & Z. Mostefaoui & H.M. Ali, 2020. "Fractional Optimal Control with Fish Consumption to Prevent the Risk of Coronary Heart Disease," Complexity, Hindawi, vol. 2020, pages 1-13, February.
    6. 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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stefania Tomasiello & Jorge E. Macías-Díaz, 2023. "A Mini-Review on Recent Fractional Models for Agri-Food Problems," Mathematics, MDPI, vol. 11(10), pages 1-12, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ali, Hegagi Mohamed & Ameen, Ismail Gad, 2021. "Optimal control strategies of a fractional order model for Zika virus infection involving various transmissions," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Ameen, Ismail Gad & Baleanu, Dumitru & Ali, Hegagi Mohamed, 2022. "Different strategies to confront maize streak disease based on fractional optimal control formulation," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Ameen, I. & Baleanu, Dumitru & Ali, Hegagi Mohamed, 2020. "An efficient algorithm for solving the fractional optimal control of SIRV epidemic model with a combination of vaccination and treatment," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    4. El-Sayed, A.M.A. & Rida, S.Z. & Gaber, Y.A., 2020. "Dynamical of curative and preventive treatments in a two-stage plant disease model of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    5. Ebrahem A. Algehyne & Musaad S. Aldhabani & Mounirah Areshi & Essam R. El-Zahar & Abdelhalim Ebaid & Hind K. Al-Jeaid, 2023. "A Proposed Application of Fractional Calculus on Time Dilation in Special Theory of Relativity," Mathematics, MDPI, vol. 11(15), pages 1-11, July.
    6. Laila F. Seddek & Abdelhalim Ebaid & Essam R. El-Zahar & Mona D. Aljoufi, 2023. "Exact Solution of Non-Homogeneous Fractional Differential System Containing 2 n Periodic Terms under Physical Conditions," Mathematics, MDPI, vol. 11(15), pages 1-12, July.
    7. Rika Amelia & Nursanti Anggriani & Asep K. Supriatna & Noor Istifadah, 2022. "Mathematical Model for Analyzing the Dynamics of Tungro Virus Disease in Rice: A Systematic Literature Review," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    8. Zehba Raizah & Rahat Zarin, 2023. "Advancing COVID-19 Understanding: Simulating Omicron Variant Spread Using Fractional-Order Models and Haar Wavelet Collocation," Mathematics, MDPI, vol. 11(8), pages 1-30, April.
    9. Ragwa S. E. Alatwi & Abdulrahman F. Aljohani & Abdelhalim Ebaid & Hind K. Al-Jeaid, 2022. "Two Analytical Techniques for Fractional Differential Equations with Harmonic Terms via the Riemann–Liouville Definition," Mathematics, MDPI, vol. 10(23), pages 1-11, December.
    10. Rehman, Attiq ul & Singh, Ram & Agarwal, Praveen, 2021. "Modeling, analysis and prediction of new variants of covid-19 and dengue co-infection on complex network," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    11. Rehman, Attiq ul & Singh, Ram & Singh, Jagdev, 2022. "Mathematical analysis of multi-compartmental malaria transmission model with reinfection," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    12. Ahmed, Najma & Shah, Nehad Ali & Taherifar, Somaye & Zaman, F.D., 2021. "Memory effects and of the killing rate on the tumor cells concentration for a one-dimensional cancer model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    13. Akinlar, M.A. & Inc, Mustafa & Gómez-Aguilar, J.F. & Boutarfa, B., 2020. "Solutions of a disease model with fractional white noise," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    14. Agarwal, Praveen & Singh, Ram & Rehman, Attiq ul, 2021. "Numerical solution of hybrid mathematical model of dengue transmission with relapse and memory via Adam–Bashforth–Moulton predictor-corrector scheme," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    15. Ali, Hegagi Mohamed & Ameen, Ismail Gad & Gaber, Yasmeen Ahmed, 2024. "The effect of curative and preventive optimal control measures on a fractional order plant disease model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 496-515.
    16. 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).
    17. Gao, Wei & Baskonus, Haci Mehmet, 2022. "Deeper investigation of modified epidemiological computer virus model containing the Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    18. Baba, Bashir Abdullahi & Bilgehan, Bulent, 2021. "Optimal control of a fractional order model for the COVID – 19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008840. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.