IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i7p985-d1364134.html
   My bibliography  Save this article

Optimal Control Applied to Piecewise-Fractional Ebola Model

Author

Listed:
  • Silvério Rosa

    (Instituto de Telecomunicações and Department of Mathematics, University of Beira Interior, 6201-001 Covilhã, Portugal)

  • Faïçal Ndaïrou

    (Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal)

Abstract

A recently proposed fractional-order mathematical model with Caputo derivatives was developed for Ebola disease. Here, we extend and generalize this model, beginning with its correction. A fractional optimal control (FOC) problem is then formulated and numerically solved with the rate of vaccination as the control measure. The research presented in this work addresses the problem of fitting real data from Guinea, Liberia, and Sierra Leone, available at the World Health Organization (WHO). A cost-effectiveness analysis is performed to assess the cost and effectiveness of the control measure during the intervention. We come to the conclusion that the fractional control is more efficient than the classical one only for a part of the time interval. Hence, we suggest a system where the derivative order changes over time, becoming fractional or classical when it makes more sense. This type of variable-order fractional model, known as piecewise derivative with fractional Caputo derivatives, is the most successful in managing the illness.

Suggested Citation

  • Silvério Rosa & Faïçal Ndaïrou, 2024. "Optimal Control Applied to Piecewise-Fractional Ebola Model," Mathematics, MDPI, vol. 12(7), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:985-:d:1364134
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/7/985/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/7/985/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Atangana, Abdon & İğret Araz, Seda, 2021. "New concept in calculus: Piecewise differential and integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Rosa, Silvério & Torres, Delfim F.M., 2018. "Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 142-149.
    Full references (including those not matched with items on IDEAS)

    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. Xu, Changjin & Liu, Zixin & Pang, Yicheng & Akgül, Ali & Baleanu, Dumitru, 2022. "Dynamics of HIV-TB coinfection model using classical and Caputo piecewise operator: A dynamic approach with real data from South-East Asia, European and American regions," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Shoaib, Muhammad & Kiani, Adiqa Kausar, 2022. "Fractional order Lorenz based physics informed SARFIMA-NARX model to monitor and mitigate megacities air pollution," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Mehmood, Ammara & Raja, Muhammad Asif Zahoor, 2022. "Fuzzy-weighted differential evolution computing paradigm for fractional order nonlinear wiener systems," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    4. 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).
    5. Muhammad, Yasir & Khan, Nusrat & Awan, Saeed Ehsan & Raja, Muhammad Asif Zahoor & Chaudhary, Naveed Ishtiaq & Kiani, Adiqa Kausar & Ullah, Farman & Shu, Chi-Min, 2022. "Fractional memetic computing paradigm for reactive power management involving wind-load chaos and uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    6. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Heydari, M.H. & Razzaghi, M., 2021. "A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Sharbayta, Sileshi Sintayehu & Buonomo, Bruno & d'Onofrio, Alberto & Abdi, Tadesse, 2022. "‘Period doubling’ induced by optimal control in a behavioral SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    9. Silvério Rosa & Delfim F. M. Torres, 2023. "Numerical Fractional Optimal Control of Respiratory Syncytial Virus Infection in Octave/MATLAB," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    10. Chaudhary, Naveed Ishtiaq & Raja, Muhammad Asif Zahoor & Khan, Zeshan Aslam & Mehmood, Ammara & Shah, Syed Muslim, 2022. "Design of fractional hierarchical gradient descent algorithm for parameter estimation of nonlinear control autoregressive systems," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    11. Silva, Cristiana J. & Torres, Delfim F.M., 2019. "Stability of a fractional HIV/AIDS model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 180-190.
    12. Shah, Kamal & Abdeljawad, Thabet & Ali, Arshad, 2022. "Mathematical analysis of the Cauchy type dynamical system under piecewise equations with Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    13. He, Sha & Tang, Sanyi & Zhang, Qimin & Rong, Libin & Cheke, Robert A., 2023. "Modelling optimal control of air pollution to reduce respiratory diseases," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    14. Baleanu, Dumitru & Hasanabadi, Manijeh & Mahmoudzadeh Vaziri, Asadollah & Jajarmi, Amin, 2023. "A new intervention strategy for an HIV/AIDS transmission by a general fractional modeling and an optimal control approach," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    15. Li, Xiao-Ping & Din, Anwarud & Zeb, Anwar & Kumar, Sunil & Saeed, Tareq, 2022. "The impact of Lévy noise on a stochastic and fractal-fractional Atangana–Baleanu order hepatitis B model under real statistical data," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    16. 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).
    17. Berhe, Hailay Weldegiorgis, 2020. "Optimal Control Strategies and Cost-effectiveness Analysis Applied to Real Data of Cholera Outbreak in Ethiopia’s Oromia Region," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    18. Xu, Changjin & Liu, Zixin & Pang, Yicheng & Saifullah, Sayed & Inc, Mustafa, 2022. "Oscillatory, crossover behavior and chaos analysis of HIV-1 infection model using piece-wise Atangana–Baleanu fractional operator: Real data approach," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    19. Sabbar, Yassine & Din, Anwarud & Kiouach, Driss, 2023. "Influence of fractal–fractional differentiation and independent quadratic Lévy jumps on the dynamics of a general epidemic model with vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    20. Saad, Khaled M., 2021. "Fractal-fractional Brusselator chemical reaction," Chaos, Solitons & Fractals, Elsevier, vol. 150(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:gam:jmathe:v:12:y:2024:i:7:p:985-:d:1364134. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.