IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v134y2020ics0960077920301193.html
   My bibliography  Save this article

A fractional order model for Ebola Virus with the new Caputo fractional derivative without singular kernel

Author

Listed:
  • Dokuyucu, Mustafa Ali
  • Dutta, Hemen

Abstract

In this study, the model of the Ebola virus, which has been rapidly spreading in certain parts of Africa, was rearranged using the fractional derivative operator without a singular kernel proposed by Caputo and Fabrizio. It is aimed to obtain better results from the model using this approach of the model. In the first stage, the Ebola virus model was extended to the Caputo–Fabrizio fractional derivative operator. After, existence and uniqueness solutions were obtained for the fractional Ebola virus model via fixed-point theorem. Then, numerical solutions were obtained for the extended model by using Atangana and Owolabi new numerical approach via Adam-Basford method for the Caputo–Fabrizio fractional derivative. Finally, some numerical simulations were presented for different values of fractional order.

Suggested Citation

  • Dokuyucu, Mustafa Ali & Dutta, Hemen, 2020. "A fractional order model for Ebola Virus with the new Caputo fractional derivative without singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301193
    DOI: 10.1016/j.chaos.2020.109717
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920301193
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.109717?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. Amira Rachah & Delfim F. M. Torres, 2015. "Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-9, May.
    2. Nancy J. Sullivan & Anthony Sanchez & Pierre E. Rollin & Zhi-yong Yang & Gary J. Nabel, 2000. "Development of a preventive vaccine for Ebola virus infection in primates," Nature, Nature, vol. 408(6812), pages 605-609, November.
    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. Joshi, Divya D. & Bhalekar, Sachin & Gade, Prashant M., 2023. "Controlling fractional difference equations using feedback," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Singh, Harendra, 2020. "Analysis for fractional dynamics of Ebola virus model," Chaos, Solitons & Fractals, Elsevier, vol. 138(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. Yadav, Ram Prasad & Renu Verma,, 2020. "A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Ogunmiloro, Oluwatayo Michael, 2021. "Mathematical analysis and approximate solution of a fractional order caputo fascioliasis disease model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Amiri, Pari & Afshari, Hojjat, 2022. "Common fixed point results for multi-valued mappings in complex-valued double controlled metric spaces and their applications to the existence of solution of fractional integral inclusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    7. Srivastava, H.M. & Saad, Khaled M. & Khader, M.M., 2020. "An efficient spectral collocation method for the dynamic simulation of the fractional epidemiological model of the Ebola virus," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    8. Baleanu, Dumitru & Shekari, Parisa & Torkzadeh, Leila & Ranjbar, Hassan & Jajarmi, Amin & Nouri, Kazem, 2023. "Stability analysis and system properties of Nipah virus transmission: A fractional calculus case study," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    9. Patra, A. & Baliarsingh, P. & Dutta, H., 2022. "Solution to fractional evolution equation using Mohand transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 557-570.
    10. Günerhan, Hatıra & Dutta, Hemen & Dokuyucu, Mustafa Ali & Adel, Waleed, 2020. "Analysis of a fractional HIV model with Caputo and constant proportional Caputo operators," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    11. Bezziou, Mohamed & Jebril, Iqbal & Dahmani, Zoubir, 2021. "A new nonlinear duffing system with sequential fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    12. Ghanbari, Behzad & Djilali, Salih, 2020. "Mathematical analysis of a fractional-order predator-prey model with prey social behavior and infection developed in predator population," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

    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. Mohamed M. Mousa & Fahad Alsharari, 2021. "A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases," Mathematics, MDPI, vol. 9(22), pages 1-12, November.
    2. Ali Khaleel Dhaiban & Baydaa Khalaf Jabbar, 2021. "An optimal control model of COVID-19 pandemic: a comparative study of five countries," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 790-809, December.
    3. Doungmo Goufo, Emile F. & Kumar, Sunil & Mugisha, S.B., 2020. "Similarities in a fifth-order evolution equation with and with no singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Nicholas V. Olijnyk, 2015. "An algorithmic historiography of the Ebola research specialty: mapping the science behind Ebola," Scientometrics, Springer;Akadémiai Kiadó, vol. 105(1), pages 623-643, October.
    5. Ozyapici, Ali & Bilgehan, Bülent, 2018. "Generalized system of trial equation methods and their applications to biological systems," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 722-732.
    6. Srivastava, H.M. & Saad, Khaled M. & Khader, M.M., 2020. "An efficient spectral collocation method for the dynamic simulation of the fractional epidemiological model of the Ebola virus," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Singh, Harendra, 2020. "Analysis for fractional dynamics of Ebola virus model," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    8. Jeffrey E. Harris, 2021. "The Repeated Setbacks of HIV Vaccine Development Laid the Groundwork for SARS-CoV-2 Vaccines," NBER Working Papers 28587, National Bureau of Economic Research, Inc.
    9. Vaishnav, Vaibhav & Vajpai, Jayashri, 2020. "Assessment of impact of relaxation in lockdown and forecast of preparation for combating COVID-19 pandemic in India using Group Method of Data Handling," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Jade Mitchell & Kara Dean & Charles Haas, 2020. "Ebola Virus Dose Response Model for Aerosolized Exposures: Insights from Primate Data," Risk Analysis, John Wiley & Sons, vol. 40(11), pages 2390-2398, November.
    11. Boukhobza, Meriem & Debbouche, Amar & Shangerganesh, Lingeshwaran & Torres, Delfim F.M., 2024. "Modeling the dynamics of the Hepatitis B virus via a variable-order discrete system," Chaos, Solitons & Fractals, Elsevier, vol. 184(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:134:y:2020:i:c:s0960077920301193. 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.