A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative
Abstract We study the SEIR epidemic model for the spread of AH1N1 influenza using the Caputo–Fabrizio fractional-order derivative. The reproduction number of system and equilibrium points are calculated, and the stability of the disease-free equilibrium point is investigated. We prove the existence...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02945-x |
| _version_ | 1819290126980743168 |
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| author | Shahram Rezapour Hakimeh Mohammadi |
| author_facet | Shahram Rezapour Hakimeh Mohammadi |
| author_sort | Shahram Rezapour |
| collection | DOAJ |
| description | Abstract We study the SEIR epidemic model for the spread of AH1N1 influenza using the Caputo–Fabrizio fractional-order derivative. The reproduction number of system and equilibrium points are calculated, and the stability of the disease-free equilibrium point is investigated. We prove the existence of solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. In the numerical section, we present a simulation to examine the system, in which we calculate equilibrium points of the system and examine the behavior of the resulting functions at the equilibrium points. By calculating the results of the model for different fractional order, we examine the effect of the derivative order on the behavior of the resulting functions and obtained numerical values. We also calculate the results of the integer-order model and examine their differences with the results of the fractional-order model. |
| first_indexed | 2024-12-24T03:17:48Z |
| format | Article |
| id | doaj.art-06617d5f90e74782a9278308547a6c9a |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-24T03:17:48Z |
| publishDate | 2020-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-06617d5f90e74782a9278308547a6c9a2022-12-21T17:17:34ZengSpringerOpenAdvances in Difference Equations1687-18472020-09-012020111510.1186/s13662-020-02945-xA study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivativeShahram Rezapour0Hakimeh Mohammadi1Institute of Research and Development, Duy Tan UniversityDepartment of Mathematics, Miandoab Branch, Islamic Azad UniversityAbstract We study the SEIR epidemic model for the spread of AH1N1 influenza using the Caputo–Fabrizio fractional-order derivative. The reproduction number of system and equilibrium points are calculated, and the stability of the disease-free equilibrium point is investigated. We prove the existence of solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. In the numerical section, we present a simulation to examine the system, in which we calculate equilibrium points of the system and examine the behavior of the resulting functions at the equilibrium points. By calculating the results of the model for different fractional order, we examine the effect of the derivative order on the behavior of the resulting functions and obtained numerical values. We also calculate the results of the integer-order model and examine their differences with the results of the fractional-order model.http://link.springer.com/article/10.1186/s13662-020-02945-xAH1N1 influenzaEquilibrium pointNumerical simulationSEIR model |
| spellingShingle | Shahram Rezapour Hakimeh Mohammadi A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative Advances in Difference Equations AH1N1 influenza Equilibrium point Numerical simulation SEIR model |
| title | A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative |
| title_full | A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative |
| title_fullStr | A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative |
| title_full_unstemmed | A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative |
| title_short | A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative |
| title_sort | study on the ah1n1 09 influenza transmission model with the fractional caputo fabrizio derivative |
| topic | AH1N1 influenza Equilibrium point Numerical simulation SEIR model |
| url | http://link.springer.com/article/10.1186/s13662-020-02945-x |
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