IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v538y2020ics0378437119315067.html
   My bibliography  Save this article

A fractional order model for Hepatitis B virus with treatment via Atangana–Baleanu derivative

Author

Listed:
  • Shah, Syed Azhar Ali
  • Khan, Muhammad Altaf
  • Farooq, Muhammad
  • Ullah, Saif
  • Alzahrani, Ebraheem O.

Abstract

Hepatitis B infection is a serious public health issue worldwide and can be controlled through proper treatment. Mathematical models can be effectively used to explore the effect of different treatment strategies on hepatitis B patients. In this paper, we illustrate a new epidemic fractional order model of the hepatitis B virus with treatment case via Atangana–Baleanu derivative in Caputo sense. In the beginning, we investigate the non-negativity and uniqueness of the model solution. Then, we evaluate the basic reproduction number and equilibria of the model. Further, an iterative scheme is applied to calculate solution of the proposed model. Finally, to show the influence of fractional order and model parameters, we present a detail numerical simulations for different values of fractional order “γ”. The results show the importance and convincing behavior of the fractional order “γ” and ensure that by including the memory effects in the model seems very appropriate for such an investigation.

Suggested Citation

  • Shah, Syed Azhar Ali & Khan, Muhammad Altaf & Farooq, Muhammad & Ullah, Saif & Alzahrani, Ebraheem O., 2020. "A fractional order model for Hepatitis B virus with treatment via Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    • Handle: RePEc:eee:phsmap:v:538:y:2020:i:c:s0378437119315067
    DOI: 10.1016/j.physa.2019.122636
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119315067
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.122636?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. Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "A new derivative with normal distribution kernel: Theory, methods and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 1-14.
    2. Khan, Muhammad Altaf & Islam, Saeed & Zaman, Gul, 2018. "Media coverage campaign in Hepatitis B transmission model," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 378-393.
    3. Qureshi, Sania & Yusuf, Abdullahi & Shaikh, Asif Ali & Inc, Mustafa, 2019. "Transmission dynamics of varicella zoster virus modeled by classical and novel fractional operators using real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    4. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    5. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
    6. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    7. Tailei Zhang & Kai Wang & Xueliang Zhang, 2015. "Modeling and Analyzing the Transmission Dynamics of HBV Epidemic in Xinjiang, China," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-14, September.
    8. Coronel-Escamilla, A. & Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Guerrero-Ramírez, G.V., 2016. "Triple pendulum model involving fractional derivatives with different kernels," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 248-261.
    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. 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.
    2. Hoang, Manh Tuan, 2023. "Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 291-314.

    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. Singh, C.S. & Singh, Harendra & Singh, Somveer & Kumar, Devendra, 2019. "An efficient computational method for solving system of nonlinear generalized Abel integral equations arising in astrophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1440-1448.
    2. Owolabi, Kolade M., 2019. "Mathematical modelling and analysis of love dynamics: A fractional approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 849-865.
    3. Al-khedhairi, A. & Elsadany, A.A. & Elsonbaty, A., 2019. "Modelling immune systems based on Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 25-39.
    4. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    5. Sekerci, Yadigar & Ozarslan, Ramazan, 2020. "Respiration Effect on Plankton–Oxygen Dynamics in view of non-singular time fractional derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    6. Zuñiga Aguilar, C.J. & Gómez-Aguilar, J.F. & Alvarado-Martínez, V.M. & Romero-Ugalde, H.M., 2020. "Fractional order neural networks for system identification," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    7. Qureshi, Sania & Memon, Zaib-un-Nisa, 2020. "Monotonically decreasing behavior of measles epidemic well captured by Atangana–Baleanu–Caputo fractional operator under real measles data of Pakistan," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    8. Pang, Denghao & Jiang, Wei & Liu, Song & Jun, Du, 2019. "Stability analysis for a single degree of freedom fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 498-506.
    9. dos Santos, Maike A.F., 2020. "Mittag-Leffler functions in superstatistics," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    10. Dubey, Ved Prakash & Dubey, Sarvesh & Kumar, Devendra & Singh, Jagdev, 2021. "A computational study of fractional model of atmospheric dynamics of carbon dioxide gas," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    11. Qureshi, Sania & Aziz, Shaheen, 2020. "Fractional modeling for a chemical kinetic reaction in a batch reactor via nonlocal operator with power law kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    12. Qureshi, Sania, 2020. "Periodic dynamics of rubella epidemic under standard and fractional Caputo operator with real data from Pakistan," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 151-165.
    13. Kumar, Sachin & Pandey, Prashant, 2020. "A Legendre spectral finite difference method for the solution of non-linear space-time fractional Burger’s–Huxley and reaction-diffusion equation with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    14. Alkahtani, Badr Saad T., 2018. "Numerical analysis of dissipative system with noise model with the Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 239-248.
    15. Yusuf, Abdullahi & Qureshi, Sania & Feroz Shah, Syed, 2020. "Mathematical analysis for an autonomous financial dynamical system via classical and modern fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    16. Suwan, Iyad & Abdeljawad, Thabet & Jarad, Fahd, 2018. "Monotonicity analysis for nabla h-discrete fractional Atangana–Baleanu differences," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 50-59.
    17. Yavuz, Mehmet & Bonyah, Ebenezer, 2019. "New approaches to the fractional dynamics of schistosomiasis disease model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 373-393.
    18. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    19. Khennaoui, Amina-Aicha & Ouannas, Adel & Bendoukha, Samir & Grassi, Giuseppe & Lozi, René Pierre & Pham, Viet-Thanh, 2019. "On fractional–order discrete–time systems: Chaos, stabilization and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 150-162.
    20. Tassaddiq, Asifa, 2019. "MHD flow of a fractional second grade fluid over an inclined heated plate," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 341-346.

    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:phsmap:v:538:y:2020:i:c:s0378437119315067. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.