Fractional Growth Model Applied to COVID-19 Data

Fernando Alcántara-López, Carlos Fuentes, Carlos Chávez, Fernando Brambila-Paz and Antonio Quevedo
Additional contact information
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

Mathematics, 2021, vol. 9, issue 16, 1-13

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 < ? ? 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 .

Keywords: fractional Caputo derivative; sigmoidal function; Gompertz model; logistic model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/16/1915/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/16/1915/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:16:p:1915-:d:612758

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().