IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i19p3081-d1490384.html
   My bibliography  Save this article

Influence of Fractional Order on the Behavior of a Normalized Time-Fractional SIR Model

Author

Listed:
  • Junseok Kim

    (Department of Mathematics, Korea University, Seoul 02841, Republic of Korea)

Abstract

In this paper, we propose a novel normalized time-fractional susceptible–infected–removed (SIR) model that incorporates memory effects into epidemiological dynamics. The proposed model is based on a newly developed normalized time-fractional derivative, which is similar to the well-known Caputo fractional derivative but is characterized by the property that the sum of its weight function equals one. This unity property is crucial because it helps with evaluating how the fractional order influences the behavior of time-fractional differential equations over time. The normalized time-fractional derivative, with its unity property, provides an intuitive understanding of how fractional orders influence the SIR model’s dynamics and enables systematic exploration of how changes in the fractional order affect the model’s behavior. We numerically investigate how these variations impact the epidemiological dynamics of our normalized time-fractional SIR model and highlight the role of fractional order in improving the accuracy of infectious disease predictions. The appendix provides the program code for the model.

Suggested Citation

  • Junseok Kim, 2024. "Influence of Fractional Order on the Behavior of a Normalized Time-Fractional SIR Model," Mathematics, MDPI, vol. 12(19), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3081-:d:1490384
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/19/3081/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/19/3081/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "A SIR model assumption for the spread of COVID-19 in different communities," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Zhang, Yong & Yu, Xiangnan & Sun, HongGuang & Tick, Geoffrey R. & Wei, Wei & Jin, Bin, 2020. "Applicability of time fractional derivative models for simulating the dynamics and mitigation scenarios of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Sene, Ndolane, 2020. "SIR epidemic model with Mittag–Leffler fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    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. 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. Talal Daghriri & Michael Proctor & Sarah Matthews, 2022. "Evolution of Select Epidemiological Modeling and the Rise of Population Sentiment Analysis: A Literature Review and COVID-19 Sentiment Illustration," IJERPH, MDPI, vol. 19(6), pages 1-20, March.
    3. Asamoah, Joshua Kiddy K. & Owusu, Mark A. & Jin, Zhen & Oduro, F. T. & Abidemi, Afeez & Gyasi, Esther Opoku, 2020. "Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "Dynamic tracking with model-based forecasting for the spread of the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Lin William Cong & Ke Tang & Bing Wang & Jingyuan Wang, 2021. "An AI-assisted Economic Model of Endogenous Mobility and Infectious Diseases: The Case of COVID-19 in the United States," Papers 2109.10009, arXiv.org.
    6. Nie, Shiqian & Lei, Xiaochun, 2023. "A time-dependent model of the transmission of COVID-19 variants dynamics using Hausdorff fractal derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).
    7. Ghanbari, Behzad, 2021. "On detecting chaos in a prey-predator model with prey’s counter-attack on juvenile predators," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    8. Wan, Jinming & Ichinose, Genki & Small, Michael & Sayama, Hiroki & Moreno, Yamir & Cheng, Changqing, 2022. "Multilayer networks with higher-order interaction reveal the impact of collective behavior on epidemic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    9. Zhou, Jiaying & Ye, Yong & Arenas, Alex & Gómez, Sergio & Zhao, Yi, 2023. "Pattern formation and bifurcation analysis of delay induced fractional-order epidemic spreading on networks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    10. Miguel Casares & Hashmat Khan, 2020. "The Timing and Intensity of Social Distancing to Flatten the COVID-19 Curve: The Case of Spain," IJERPH, MDPI, vol. 17(19), pages 1-14, October.
    11. Pablo Valdes-Donoso & Lovell S Jarvis, 2022. "Combining epidemiology and economics to assess control of a viral endemic animal disease: Porcine Reproductive and Respiratory Syndrome (PRRS)," PLOS ONE, Public Library of Science, vol. 17(9), pages 1-20, September.
    12. Aditya Goenka & Lin Liu & Manh-Hung Nguyen, 2021. "Modeling optimal quarantines with waning immunity," Discussion Papers 21-10, Department of Economics, University of Birmingham.
    13. Wu, Yue & Li, Linjiao & Yu, Qiannan & Gan, Jiaxin & Zhang, Yi, 2023. "Strategies for reducing polarization in social networks," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    14. Samuel O. M. Manda & Timotheus Darikwa & Tshifhiwa Nkwenika & Robert Bergquist, 2021. "A Spatial Analysis of COVID-19 in African Countries: Evaluating the Effects of Socio-Economic Vulnerabilities and Neighbouring," IJERPH, MDPI, vol. 18(20), pages 1-15, October.
    15. Guihua Wang, 2022. "Stay at home to stay safe: Effectiveness of stay‐at‐home orders in containing the COVID‐19 pandemic," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2289-2305, May.
    16. Qu, Hongbo & Song, Yu-Rong & Li, Ruqi & Li, Min, 2023. "GNR: A universal and efficient node ranking model for various tasks based on graph neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P2).
    17. Lee, Chaeyoung & Kwak, Soobin & Kim, Sangkwon & Hwang, Youngjin & Choi, Yongho & Kim, Junseok, 2021. "Robust optimal parameter estimation for the susceptible-unidentified infected-confirmed model," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    18. Rabih Ghostine & Mohamad Gharamti & Sally Hassrouny & Ibrahim Hoteit, 2021. "An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter," Mathematics, MDPI, vol. 9(6), pages 1-16, March.
    19. Martínez-Guerra, Rafael & Flores-Flores, Juan Pablo, 2021. "An algorithm for the robust estimation of the COVID-19 pandemic’s population by considering undetected individuals," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    20. Alberto Olivares & Ernesto Staffetti, 2021. "Optimal Control Applied to Vaccination and Testing Policies for COVID-19," Mathematics, MDPI, vol. 9(23), pages 1-22, December.

    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:19:p:3081-:d:1490384. 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.