Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 Data
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 Capu...
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MDPI AG
2022-03-01
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| Online Access: | https://www.mdpi.com/2227-7390/10/5/825 |
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| author | Fernando Alcántara-López Carlos Fuentes Carlos Chávez Jesús López-Estrada Fernando Brambila-Paz |
| author_facet | Fernando Alcántara-López Carlos Fuentes Carlos Chávez Jesús López-Estrada Fernando Brambila-Paz |
| author_sort | Fernando Alcántara-López |
| collection | DOAJ |
| description | 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 <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>. 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 <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>0.9995</mn></mrow></semantics></math></inline-formula> 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. |
| first_indexed | 2024-03-09T20:29:55Z |
| format | Article |
| id | doaj.art-375c57d26f0e41a9bd3623c00a337ade |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T20:29:55Z |
| publishDate | 2022-03-01 |
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| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-375c57d26f0e41a9bd3623c00a337ade2023-11-23T23:24:13ZengMDPI AGMathematics2227-73902022-03-0110582510.3390/math10050825Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 DataFernando Alcántara-López0Carlos Fuentes1Carlos Chávez2Jesús López-Estrada3Fernando Brambila-Paz4Department of Mathematics, Faculty of Science, National Autonomous University of Mexico, Av. Universidad 3000, Circuito Exterior S/N, Delegación Coyoacán, Ciudad de Mexico 04510, 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 SN, 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, Ciudad de Mexico 04510, MexicoDepartment of Mathematics, Faculty of Science, National Autonomous University of Mexico, Av. Universidad 3000, Circuito Exterior S/N, Delegación Coyoacán, Ciudad de Mexico 04510, MexicoThere 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 <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>. 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 <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>0.9995</mn></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2227-7390/10/5/825multiple outbreakstime delayCaputo fractional derivativeGompertz modellogistic model |
| spellingShingle | Fernando Alcántara-López Carlos Fuentes Carlos Chávez Jesús López-Estrada Fernando Brambila-Paz Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 Data Mathematics multiple outbreaks time delay Caputo fractional derivative Gompertz model logistic model |
| title | Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 Data |
| title_full | Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 Data |
| title_fullStr | Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 Data |
| title_full_unstemmed | Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 Data |
| title_short | Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 Data |
| title_sort | fractional growth model with delay for recurrent outbreaks applied to covid 19 data |
| topic | multiple outbreaks time delay Caputo fractional derivative Gompertz model logistic model |
| url | https://www.mdpi.com/2227-7390/10/5/825 |
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