Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 Data

Fernando Alcántara-López, Carlos Fuentes, Carlos Chávez, Jesús López-Estrada and Fernando Brambila-Paz
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Fernando Alcántara-López: Department of Mathematics, Faculty of Science, National Autonomous University of Mexico, Av. Universidad 3000, Circuito Exterior S/N, Delegación Coyoacán, Ciudad de Mexico 04510, 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 SN, Col. Las Campanas, Querétaro 76010, Mexico
Jesús López-Estrada: Department of Mathematics, Faculty of Science, National Autonomous University of Mexico, Av. Universidad 3000, Circuito Exterior S/N, Delegación Coyoacán, Ciudad de Mexico 04510, Mexico
Fernando Brambila-Paz: Department of Mathematics, Faculty of Science, National Autonomous University of Mexico, Av. Universidad 3000, Circuito Exterior S/N, Delegación Coyoacán, Ciudad de Mexico 04510, Mexico

Mathematics, 2022, vol. 10, issue 5, 1-18

Abstract: There are a great many epidemiological models that have been implemented to describe COVID-19 data; however, few attempted to reproduce the entire phenomenon due to the complexity of modeling recurrent outbreaks. In this work a fractional growth model with delay is developed that implements the Caputo fractional derivative with 0 < β ≤ 1 . Furthermore, in order to preserve the nature of the phenomenon and ensure continuity in the derivatives of the function, a method is proposed to construct an initial condition function to implement in the model with delay. This model is analyzed and generalized to model recurrent outbreaks. The model is applied to fit data of cumulative confirmed cases from Mexico, the United States, and Russia, obtaining excellent fitting corroborated by the coefficient of determination, where R 2 > 0.9995 in all cases. Lastly, as a result of the implementation of the delay effect, the global phenomenon was decomposed into its local parts, allowing for directly comparing each outbreak and its different characteristics.

Keywords: multiple outbreaks; time delay; Caputo fractional derivative; Gompertz model; logistic model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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