On threshold dynamics for periodic and time-delayed impulsive systems and application to a periodic disease model
The basic reproduction ratio $ \mathcal{R}_{0} $ of more general periodic and time-delayed impulsive model which the period of model coefficients is different from that of fixed impulsive moments, is developed. That $ \mathcal{R}_{0} $ is the threshold parameter for the stability of the zero solutio...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2022038?viewType=HTML |
| _version_ | 1818284367205629952 |
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| author | Hai-Feng Huo Fan Wu Hong Xiang |
| author_facet | Hai-Feng Huo Fan Wu Hong Xiang |
| author_sort | Hai-Feng Huo |
| collection | DOAJ |
| description | The basic reproduction ratio $ \mathcal{R}_{0} $ of more general periodic and time-delayed impulsive model which the period of model coefficients is different from that of fixed impulsive moments, is developed. That $ \mathcal{R}_{0} $ is the threshold parameter for the stability of the zero solution of the associated linear system is also shown. The developed theory is further applied to a swine parasitic disease model with pulse therapy. Threshold results on its global dynamics in terms of $ \mathcal{R}_{0} $ are obtained. Some numerical simulation results are also given to support our main results. |
| first_indexed | 2024-12-13T00:51:40Z |
| format | Article |
| id | doaj.art-b74140919b604d3999997608c8b4d785 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-13T00:51:40Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-b74140919b604d3999997608c8b4d7852022-12-22T00:04:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182022-01-0119183685410.3934/mbe.2022038On threshold dynamics for periodic and time-delayed impulsive systems and application to a periodic disease modelHai-Feng Huo0Fan Wu1Hong Xiang2Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, ChinaThe basic reproduction ratio $ \mathcal{R}_{0} $ of more general periodic and time-delayed impulsive model which the period of model coefficients is different from that of fixed impulsive moments, is developed. That $ \mathcal{R}_{0} $ is the threshold parameter for the stability of the zero solution of the associated linear system is also shown. The developed theory is further applied to a swine parasitic disease model with pulse therapy. Threshold results on its global dynamics in terms of $ \mathcal{R}_{0} $ are obtained. Some numerical simulation results are also given to support our main results.https://www.aimspress.com/article/doi/10.3934/mbe.2022038?viewType=HTMLimpulsive modelstime delaybasic reproduction ratioswine parasitic diseasethreshold dynamics |
| spellingShingle | Hai-Feng Huo Fan Wu Hong Xiang On threshold dynamics for periodic and time-delayed impulsive systems and application to a periodic disease model Mathematical Biosciences and Engineering impulsive models time delay basic reproduction ratio swine parasitic disease threshold dynamics |
| title | On threshold dynamics for periodic and time-delayed impulsive systems and application to a periodic disease model |
| title_full | On threshold dynamics for periodic and time-delayed impulsive systems and application to a periodic disease model |
| title_fullStr | On threshold dynamics for periodic and time-delayed impulsive systems and application to a periodic disease model |
| title_full_unstemmed | On threshold dynamics for periodic and time-delayed impulsive systems and application to a periodic disease model |
| title_short | On threshold dynamics for periodic and time-delayed impulsive systems and application to a periodic disease model |
| title_sort | on threshold dynamics for periodic and time delayed impulsive systems and application to a periodic disease model |
| topic | impulsive models time delay basic reproduction ratio swine parasitic disease threshold dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2022038?viewType=HTML |
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