IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2022y2022i1n2009910.html

A Fractional Model for the Dynamics of Smoking Tobacco Using Caputo–Fabrizio Derivative

Author

Listed:
  • Belaynesh Melkamu
  • Benyam Mebrate

Abstract

In this paper, we propose a Caputo–Fabrizio fractional derivative mathematical model consisting of smoker, people exposed to secondhand smoker, people exposed to thirdhand smoker, and quitters. Secondhand smoke exposure consists of an unintentional inhalation of smoke that occurs close to people smoking and/or in indoor environments where tobacco was recently used, and thirdhand smoke consists of pollutants that remain on surfaces and in dust after tobacco has been smoked, are reemitted into the gas phase, or react with other compounds in the environment to form secondary pollutants. The solution of the proposed model, which is carried out using a fixed‐point theorem and an iterative method, exists and is unique. Furthermore, the model is biologically meaningful, that is, positive and bounded. The reproduction number R0 is determined from the model. If R0 1, the smoking‐free equilibrium point is unstable. The results confirm that the smoking‐free equilibrium point becomes increasingly stable as the fractional order is increased. Numerical simulations are performed using a three‐step Adams‐Moulton predictor‐corrector method for a range of fractional orders to show the effects of varying the fractional order and to support the theoretical results.

Suggested Citation

  • Belaynesh Melkamu & Benyam Mebrate, 2022. "A Fractional Model for the Dynamics of Smoking Tobacco Using Caputo–Fabrizio Derivative," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnljam:v:2022:y:2022:i:1:n:2009910
    DOI: 10.1155/2022/2009910
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2022/2009910
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/2009910?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
    ---><---

    References listed on IDEAS

    as
    1. Anwar Zeb & Sunil Kumar & Tareq Saeed, 2022. "A Robust Computational Dynamics Of Fractional-Order Smoking Model With Relapse Habit," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-11, February.
    2. Salih Djilali & Soufiane Bentout & Anwar Zeb & Tareq Saeed, 2022. "Global Stability Of Hybrid Smoking Model With Nonlocal Diffusion," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(08), pages 1-13, December.
    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. Abdul-Aziz Hussein & Benyam Mebrate, 2025. "A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).

    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. Ye, Yong & Zhao, Yi & Zhou, Jiaying, 2022. "Promotion of cooperation mechanism on the stability of delay-induced host-generalist parasitoid model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Nisar, Kottakkaran Sooppy & Farman, Muhammad & Hincal, Evren & Shehzad, Aamir, 2023. "Modelling and analysis of bad impact of smoking in society with Constant Proportional-Caputo Fabrizio operator," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnljam:v:2022:y:2022:i:1:n:2009910. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.