The dynamics of Zika virus with Caputo fractional derivative
In the present paper, we investigate a fractional model in Caputo sense to explore the dynamics of the Zika virus. The basic results of the fractional Zika model are presented. The local and global stability analysis of the proposed model is obtained when the basic reproduction reproduction number i...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2019-02-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/Math.2019.1.134/fulltext.html |
| _version_ | 1818068113163288576 |
|---|---|
| author | Muhammad Altaf Khan Saif Ullah Muhammad Farhan |
| author_facet | Muhammad Altaf Khan Saif Ullah Muhammad Farhan |
| author_sort | Muhammad Altaf Khan |
| collection | DOAJ |
| description | In the present paper, we investigate a fractional model in Caputo sense to explore the dynamics of the Zika virus. The basic results of the fractional Zika model are presented. The local and global stability analysis of the proposed model is obtained when the basic reproduction reproduction number is less or greater than 1. To show the global stability of the fractional Zika model, we use the Lyapunov function theory in fractional environment. Further, we simulate the fractional Zika model to present the graphical results for different values of fractional order and model parameters. |
| first_indexed | 2024-12-10T15:34:24Z |
| format | Article |
| id | doaj.art-757e7a5f306f47d58a8de4e1695ee80f |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-10T15:34:24Z |
| publishDate | 2019-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-757e7a5f306f47d58a8de4e1695ee80f2022-12-22T01:43:17ZengAIMS PressAIMS Mathematics2473-69882019-02-014113414610.3934/Math.2019.1.134The dynamics of Zika virus with Caputo fractional derivativeMuhammad Altaf Khan0Saif Ullah1Muhammad Farhan21 Department of mathematics, City university of Science and Information Technology, Peshawar, KP, Pakistan2 Department of mathematics, University of Peshawar, KP, Pakistan3 Department of mathematics, Abdul wali khan university, Mardan, KP, PakistanIn the present paper, we investigate a fractional model in Caputo sense to explore the dynamics of the Zika virus. The basic results of the fractional Zika model are presented. The local and global stability analysis of the proposed model is obtained when the basic reproduction reproduction number is less or greater than 1. To show the global stability of the fractional Zika model, we use the Lyapunov function theory in fractional environment. Further, we simulate the fractional Zika model to present the graphical results for different values of fractional order and model parameters.https://www.aimspress.com/article/10.3934/Math.2019.1.134/fulltext.htmlZika virus modelstability analysisgeneralized mean value theoremLyapunov functionCaputo derivativenumerical results |
| spellingShingle | Muhammad Altaf Khan Saif Ullah Muhammad Farhan The dynamics of Zika virus with Caputo fractional derivative AIMS Mathematics Zika virus model stability analysis generalized mean value theorem Lyapunov function Caputo derivative numerical results |
| title | The dynamics of Zika virus with Caputo fractional derivative |
| title_full | The dynamics of Zika virus with Caputo fractional derivative |
| title_fullStr | The dynamics of Zika virus with Caputo fractional derivative |
| title_full_unstemmed | The dynamics of Zika virus with Caputo fractional derivative |
| title_short | The dynamics of Zika virus with Caputo fractional derivative |
| title_sort | dynamics of zika virus with caputo fractional derivative |
| topic | Zika virus model stability analysis generalized mean value theorem Lyapunov function Caputo derivative numerical results |
| url | https://www.aimspress.com/article/10.3934/Math.2019.1.134/fulltext.html |
| work_keys_str_mv | AT muhammadaltafkhan thedynamicsofzikaviruswithcaputofractionalderivative AT saifullah thedynamicsofzikaviruswithcaputofractionalderivative AT muhammadfarhan thedynamicsofzikaviruswithcaputofractionalderivative AT muhammadaltafkhan dynamicsofzikaviruswithcaputofractionalderivative AT saifullah dynamicsofzikaviruswithcaputofractionalderivative AT muhammadfarhan dynamicsofzikaviruswithcaputofractionalderivative |