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

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  • 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
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    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)

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