Fractional Growth Model Applied to COVID-19 Data
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...
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/16/1915 |
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| author | Fernando Alcántara-López Carlos Fuentes Carlos Chávez Fernando Brambila-Paz Antonio Quevedo |
| author_facet | Fernando Alcántara-López Carlos Fuentes Carlos Chávez Fernando Brambila-Paz Antonio Quevedo |
| author_sort | Fernando Alcántara-López |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi>β</mi><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>, 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup><mo>></mo><mn>0.999</mn></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-10T08:37:08Z |
| format | Article |
| id | doaj.art-7aa9cd23083f4b8ea19bc9686de9977b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:37:08Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7aa9cd23083f4b8ea19bc9686de9977b2023-11-22T08:33:50ZengMDPI AGMathematics2227-73902021-08-01916191510.3390/math9161915Fractional Growth Model Applied to COVID-19 DataFernando Alcántara-López0Carlos Fuentes1Carlos Chávez2Fernando Brambila-Paz3Antonio Quevedo4Department of Mathematics, Faculty of Science, National Autonomous University of Mexico, Av. Universidad 3000, Circuito Exterior S/N, Delegación Coyoacán 04510, Ciudad de Mexico, MexicoMexican Institute of Water Technology, Paseo Cuauhnáhuac Núm. 8532, Jiutepec 62550, MexicoWater Research Center, Department of Irrigation and Drainage Engineering, Autonomous University of Querétaro, Cerro de las Campanas S/N, Col. Las Campanas, Querétaro 76010, MexicoDepartment of Mathematics, Faculty of Science, National Autonomous University of Mexico, Av. Universidad 3000, Circuito Exterior S/N, Delegación Coyoacán 04510, Ciudad de Mexico, MexicoMexican Institute of Water Technology, Paseo Cuauhnáhuac Núm. 8532, Jiutepec 62550, MexicoGrowth 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi>β</mi><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>, 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup><mo>></mo><mn>0.999</mn></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2227-7390/9/16/1915fractional Caputo derivativesigmoidal functionGompertz modellogistic model |
| spellingShingle | Fernando Alcántara-López Carlos Fuentes Carlos Chávez Fernando Brambila-Paz Antonio Quevedo Fractional Growth Model Applied to COVID-19 Data Mathematics fractional Caputo derivative sigmoidal function Gompertz model logistic model |
| title | Fractional Growth Model Applied to COVID-19 Data |
| title_full | Fractional Growth Model Applied to COVID-19 Data |
| title_fullStr | Fractional Growth Model Applied to COVID-19 Data |
| title_full_unstemmed | Fractional Growth Model Applied to COVID-19 Data |
| title_short | Fractional Growth Model Applied to COVID-19 Data |
| title_sort | fractional growth model applied to covid 19 data |
| topic | fractional Caputo derivative sigmoidal function Gompertz model logistic model |
| url | https://www.mdpi.com/2227-7390/9/16/1915 |
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