IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v164y2022ics0960077922008785.html
   My bibliography  Save this article

Different strategies to confront maize streak disease based on fractional optimal control formulation

Author

Listed:
  • Ameen, Ismail Gad
  • Baleanu, Dumitru
  • Ali, Hegagi Mohamed

Abstract

In this paper, we propose a general formulation for the transmission dynamics of maize streak virus (MSV) pathogen interaction with a pest invasion in the maize plant. The mathematical formalism for this model is dependent on Caputo fractional operator with modification of its parameters. In the considered model, the total population of maize plants is divided into two classes: susceptible, infected maize and the total population of leafhopper vector contains two compartments: susceptible, infected leafhopper vector, with a compartment for MSV pathogen. In addition, this fractional-order model (FOM) is involving the proportion of three controls u1,u2 and u3 which namely respectively prevention, quarantine and chemical control. We present the positivity and boundedness of the projected solutions to assure the feasibility of solutions of this FOM. The control reproduction number (Rc) is derived by next generation matrix (NGM) method and showed graphically the effect of the controls for each proposed strategy on the behavior of Rc. The local stability analysis for all possible equilibrium points (EPs) has been examined in detail. Moreover, the fractional optimal control problem (FOCP) is characterized and fractional necessary optimality conditions (NOCs) are derived by using Pontryagin’s maximum principle (PMP). These NOCs are solved numerically, where the state and co-state equations based on the left Caputo fractional derivative (CFD). We offer four strategies to illustrate the effects of the proposed controls to investigate the preferable strategy for the elimination of maize streak disease (MSD), as each one of these strategies is able to alleviate this disease at a specific time. Finally, simulations are performed utilizing MATLAB with realistic ecological parameter values to demonstrate the obtained theoretical results. Comparative studies illustrated that infection of maize plants can be reduced through the proposed model, which has a significant impact on plant epidemiology.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008785
    DOI: 10.1016/j.chaos.2022.112699
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922008785
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112699?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. Md Rafiul Islam & Angela Peace & Daniel Medina & Tamer Oraby, 2020. "Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles," IJERPH, MDPI, vol. 17(6), pages 1-19, March.
    2. Darren Martin & Dionne Shepherd, 2009. "The epidemiology, economic impact and control of maize streak disease," Food Security: The Science, Sociology and Economics of Food Production and Access to Food, Springer;The International Society for Plant Pathology, vol. 1(3), pages 305-315, September.
    3. Mylonas, Panagiotis & Yonow, Tania & Kriticos, Darren J., 2014. "Cicadulina mbila (Naudé) (Maize Leafhopper )," Pest Geography Briefs 249747, HarvestChoice.
    4. Sunil Kumar & Ali Ahmadian & Ranbir Kumar & Devendra Kumar & Jagdev Singh & Dumitru Baleanu & Mehdi Salimi, 2020. "An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets," Mathematics, MDPI, vol. 8(4), pages 1-22, April.
    5. 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).
    6. 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.
    7. Vasily E. Tarasov, 2020. "Non-Linear Macroeconomic Models of Growth with Memory," Mathematics, MDPI, vol. 8(11), pages 1-22, November.
    8. Khajji, Bouchaib & Kouidere, Abdelfatah & Elhia, Mohamed & Balatif, Omar & Rachik, Mostafa, 2021. "Fractional optimal control problem for an age-structured model of COVID-19 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    9. 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).
    10. Haileyesus Tessema Alemneh & Oluwole Daniel Makinde & David Mwangi Theuri, 2019. "Ecoepidemiological Model and Analysis of MSV Disease Transmission Dynamics in Maize Plant," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2019, pages 1-14, January.
    11. 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).
    12. 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).
    13. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    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. 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.

    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 & 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.
    2. 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).
    3. 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).
    4. Kumar, Pushpendra & Erturk, Vedat Suat & Vellappandi, M. & Trinh, Hieu & Govindaraj, V., 2022. "A study on the maize streak virus epidemic model by using optimized linearization-based predictor-corrector method in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    5. 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).
    6. 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).
    7. Abdelhamid Mohammed Djaouti & Zareen A. Khan & Muhammad Imran Liaqat & Ashraf Al-Quran, 2024. "A Study of Some Generalized Results of Neutral Stochastic Differential Equations in the Framework of Caputo–Katugampola Fractional Derivatives," Mathematics, MDPI, vol. 12(11), pages 1-20, May.
    8. Prakash, Amit & Kaur, Hardish, 2021. "Analysis and numerical simulation of fractional Biswas–Milovic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 298-315.
    9. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    10. Rahman, Mati ur & Arfan, Muhammad & Shah, Kamal & Gómez-Aguilar, J.F., 2020. "Investigating a nonlinear dynamical model of COVID-19 disease under fuzzy caputo, random and ABC fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    11. Deniz, Sinan, 2021. "Optimal perturbation iteration method for solving fractional FitzHugh-Nagumo equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    12. Aliyu, Aliyu Isa & Inc, Mustafa & Yusuf, Abdullahi & Baleanu, Dumitru, 2018. "A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 268-277.
    13. Bonyah, Ebenezer & Gómez-Aguilar, J.F. & Adu, Augustina, 2018. "Stability analysis and optimal control of a fractional human African trypanosomiasis model," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 150-160.
    14. Djilali, Salih & Ghanbari, Behzad & Bentout, Soufiane & Mezouaghi, Abdelheq, 2020. "Turing-Hopf bifurcation in a diffusive mussel-algae model with time-fractional-order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    15. Marasi, H.R. & Derakhshan, M.H., 2023. "Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 368-389.
    16. Jing Chang & Jin Zhang & Ming Cai, 2021. "Series Solutions of High-Dimensional Fractional Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-21, August.
    17. Hansin Bilgili & Chwen Sheu, 2022. "A Bibliometric Review of the Mathematics Journal," Mathematics, MDPI, vol. 10(15), pages 1-17, July.
    18. Zizhen Zhang & Soumen Kundu & Ruibin Wei, 2019. "A Delayed Epidemic Model for Propagation of Malicious Codes in Wireless Sensor Network," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    19. Singh, Jagdev, 2020. "Analysis of fractional blood alcohol model with composite fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    20. Uçar, Sümeyra & Uçar, Esmehan & Özdemir, Necati & Hammouch, Zakia, 2019. "Mathematical analysis and numerical simulation for a smoking model with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 300-306.

    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:s0960077922008785. 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.