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Advancing COVID-19 Understanding: Simulating Omicron Variant Spread Using Fractional-Order Models and Haar Wavelet Collocation

Author

Listed:
  • Zehba Raizah

    (Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia)

  • Rahat Zarin

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod Thrung Khru, Bangkok 10140, Thailand)

Abstract

This study presents a novel approach for simulating the spread of the Omicron variant of the SARS-CoV-2 virus using fractional-order COVID-19 models and the Haar wavelet collocation method. The proposed model considers various factors that affect virus transmission, while the Haar wavelet collocation method provides an efficient and accurate solution for the fractional derivatives used in the model. This study analyzes the impact of the Omicron variant and provides valuable insights into its transmission dynamics, which can inform public health policies and strategies that are aimed at controlling its spread. Additionally, this study’s findings represent a significant step forward in understanding the COVID-19 pandemic and its evolving variants. The results of the simulation showcase the effectiveness of the proposed method and demonstrate its potential to advance the field of COVID-19 research. The COVID epidemic model is reformulated by using fractional derivatives in the Caputo sense. The existence and uniqueness of the proposed model are illustrated in the model, taking into account some results of fixed point theory. The stability analysis for the system is established by incorporating the Hyers–Ulam method. For numerical treatment and simulations, we apply the Haar wavelet collocation method. The parameter estimation for the recorded COVID-19 cases in Pakistan from 23 June 2022 to 23 August 2022 is presented.

Suggested Citation

  • Zehba Raizah & Rahat Zarin, 2023. "Advancing COVID-19 Understanding: Simulating Omicron Variant Spread Using Fractional-Order Models and Haar Wavelet Collocation," Mathematics, MDPI, vol. 11(8), pages 1-30, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1925-:d:1127615
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    References listed on IDEAS

    as
    1. Agarwal, Praveen & Singh, Ram, 2020. "Modelling of transmission dynamics of Nipah virus (Niv): A fractional order Approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    2. Zarin, Rahat & Khan, Amir & Inc, Mustafa & Humphries, Usa Wannasingha & Karite, Touria, 2021. "Dynamics of five grade leishmania epidemic model using fractional operator with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    4. Komal Bansal & Sugandha Arora & Kocherlakota Satya Pritam & Trilok Mathur & Shivi Agarwal, 2022. "Dynamics Of Crime Transmission Using Fractional-Order Differential Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-16, February.
    5. Amir Khan & Rahat Zarin & Saddam Khan & Anwar Saeed & Taza Gul & Usa Wannasingha Humphries, 2022. "Fractional dynamics and stability analysis of COVID-19 pandemic model under the harmonic mean type incidence rate," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 25(6), pages 619-640, April.
    6. Gao, Wei & Veeresha, P. & Prakasha, D.G. & Baskonus, Haci Mehmet & Yel, Gulnur, 2020. "New approach for the model describing the deathly disease in pregnant women using Mittag-Leffler function," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    7. Omame, Andrew & Abbas, Mujahid & Abdel-Aty, Abdel-Haleem, 2022. "Assessing the impact of SARS-CoV-2 infection on the dynamics of dengue and HIV via fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
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