Modelling and analysis of impulsive releases of sterile mosquitoes
To study the impact of releasing sterile mosquitoes on mosquito-borne disease transmissions, we propose two mathematical models with impulsive releases of sterile mosquitoes. We consider periodic impulsive releases in the first model and obtain the existence, uniqueness, and globally stability of a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2017-01-01
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| Series: | Journal of Biological Dynamics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/17513758.2016.1254286 |
| _version_ | 1818479702747119616 |
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| author | Mingzhan Huang Xinyu Song Jia Li |
| author_facet | Mingzhan Huang Xinyu Song Jia Li |
| author_sort | Mingzhan Huang |
| collection | DOAJ |
| description | To study the impact of releasing sterile mosquitoes on mosquito-borne disease transmissions, we propose two mathematical models with impulsive releases of sterile mosquitoes. We consider periodic impulsive releases in the first model and obtain the existence, uniqueness, and globally stability of a wild-mosquito-eradication periodic solution. We also establish thresholds for the control of the wild mosquito population by selecting the release rate and the release period. In the second model, the impulsive releases are determined by the closely monitored wild mosquito density, or the state feedback. We prove the existence of an order one periodic solution and find a relatively small attraction region, which ensures the wild mosquito population is under control. We provide numerical analysis which shows that a smaller release rate and more frequent releases are more efficient in controlling the wild mosquito population for the periodic releases, but an early release of sterile mosquitoes is more effective for the state feedback releases. |
| first_indexed | 2024-12-10T11:14:15Z |
| format | Article |
| id | doaj.art-dc9baa284a524df8bebd38bd80475d69 |
| institution | Directory Open Access Journal |
| issn | 1751-3758 1751-3766 |
| language | English |
| last_indexed | 2024-12-10T11:14:15Z |
| publishDate | 2017-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Biological Dynamics |
| spelling | doaj.art-dc9baa284a524df8bebd38bd80475d692022-12-22T01:51:17ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662017-01-0111114717110.1080/17513758.2016.12542861254286Modelling and analysis of impulsive releases of sterile mosquitoesMingzhan Huang0Xinyu Song1Jia Li2Xinyang Normal UniversityXinyang Normal UniversityUniversity of Alabama in HuntsvilleTo study the impact of releasing sterile mosquitoes on mosquito-borne disease transmissions, we propose two mathematical models with impulsive releases of sterile mosquitoes. We consider periodic impulsive releases in the first model and obtain the existence, uniqueness, and globally stability of a wild-mosquito-eradication periodic solution. We also establish thresholds for the control of the wild mosquito population by selecting the release rate and the release period. In the second model, the impulsive releases are determined by the closely monitored wild mosquito density, or the state feedback. We prove the existence of an order one periodic solution and find a relatively small attraction region, which ensures the wild mosquito population is under control. We provide numerical analysis which shows that a smaller release rate and more frequent releases are more efficient in controlling the wild mosquito population for the periodic releases, but an early release of sterile mosquitoes is more effective for the state feedback releases.http://dx.doi.org/10.1080/17513758.2016.1254286Sterile mosquitoesimpulsive releasesemi-continuous dynamical systemperiodic solution |
| spellingShingle | Mingzhan Huang Xinyu Song Jia Li Modelling and analysis of impulsive releases of sterile mosquitoes Journal of Biological Dynamics Sterile mosquitoes impulsive release semi-continuous dynamical system periodic solution |
| title | Modelling and analysis of impulsive releases of sterile mosquitoes |
| title_full | Modelling and analysis of impulsive releases of sterile mosquitoes |
| title_fullStr | Modelling and analysis of impulsive releases of sterile mosquitoes |
| title_full_unstemmed | Modelling and analysis of impulsive releases of sterile mosquitoes |
| title_short | Modelling and analysis of impulsive releases of sterile mosquitoes |
| title_sort | modelling and analysis of impulsive releases of sterile mosquitoes |
| topic | Sterile mosquitoes impulsive release semi-continuous dynamical system periodic solution |
| url | http://dx.doi.org/10.1080/17513758.2016.1254286 |
| work_keys_str_mv | AT mingzhanhuang modellingandanalysisofimpulsivereleasesofsterilemosquitoes AT xinyusong modellingandanalysisofimpulsivereleasesofsterilemosquitoes AT jiali modellingandanalysisofimpulsivereleasesofsterilemosquitoes |