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Fractional Growth Model Applied to COVID-19 Data

Author

Listed:
  • Fernando Alcántara-López

    (Department of Mathematics, Faculty of Science, National Autonomous University of Mexico, Av. Universidad 3000, Circuito Exterior S/N, Delegación Coyoacán 04510, Ciudad de Mexico, Mexico)

  • Carlos Fuentes

    (Mexican Institute of Water Technology, Paseo Cuauhnáhuac Núm. 8532, Jiutepec 62550, Mexico)

  • Carlos Chávez

    (Water Research Center, Department of Irrigation and Drainage Engineering, Autonomous University of Querétaro, Cerro de las Campanas S/N, Col. Las Campanas, Querétaro 76010, Mexico)

  • Fernando Brambila-Paz

    (Department of Mathematics, Faculty of Science, National Autonomous University of Mexico, Av. Universidad 3000, Circuito Exterior S/N, Delegación Coyoacán 04510, Ciudad de Mexico, Mexico)

  • Antonio Quevedo

    (Mexican Institute of Water Technology, Paseo Cuauhnáhuac Núm. 8532, Jiutepec 62550, Mexico)

Abstract

Growth models have been widely used to describe behavior in different areas of knowledge; among them the Logistics and Gompertz models, classified as models with a fixed inflection point, have been widely studied and applied. In the present work, a model is proposed that contains these growth models as extreme cases; this model is generalized by including the Caputo-type fractional derivative of order 0 < β ≤ 1 , resulting in a Fractional Growth Model which could be classified as a growth model with non-fixed inflection point. Moreover, the proposed model is generalized to include multiple sigmoidal behaviors and thereby multiple inflection points. The models developed are applied to describe cumulative confirmed cases of COVID-19 in Mexico, US and Russia, obtaining an excellent adjustment corroborated by a coefficient of determination R 2 > 0.999 .

Suggested Citation

  • Fernando Alcántara-López & Carlos Fuentes & Carlos Chávez & Fernando Brambila-Paz & Antonio Quevedo, 2021. "Fractional Growth Model Applied to COVID-19 Data," Mathematics, MDPI, vol. 9(16), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1915-:d:612758
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    References listed on IDEAS

    as
    1. Torrealba-Rodriguez, O. & Conde-Gutiérrez, R.A. & Hernández-Javier, A.L., 2020. "Modeling and prediction of COVID-19 in Mexico applying mathematical and computational models," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Alkahtani, Badr Saad T. & Alzaid, Sara Salem, 2020. "A novel mathematics model of covid-19 with fractional derivative. Stability and numerical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. 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).
    4. Abdeljawad, Thabet & Al-Mdallal, Qasem M. & Jarad, Fahd, 2019. "Fractional logistic models in the frame of fractional operators generated by conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 94-101.
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