Discrete-time model for malaria transmission with constant releases of sterile mosquitoes
In this study, we first formulate a baseline discrete-time mathematical model for malaria transmission where the survival function of mosquitoes is of Beverton–Holt type. We then introduce sterile mosquitoes to the baseline model to explore the transmission dynamics with sterile mosquitoes. We deriv...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2019-03-01
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| Series: | Journal of Biological Dynamics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/17513758.2018.1551580 |
| _version_ | 1811269006316797952 |
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| author | Yang Li Jia Li |
| author_facet | Yang Li Jia Li |
| author_sort | Yang Li |
| collection | DOAJ |
| description | In this study, we first formulate a baseline discrete-time mathematical model for malaria transmission where the survival function of mosquitoes is of Beverton–Holt type. We then introduce sterile mosquitoes to the baseline model to explore the transmission dynamics with sterile mosquitoes. We derive formulas for the reproductive number $ R_0 $ of infection and determine the existence and uniqueness of endemic fixed points as well, for the models with or without sterile mosquitoes. We then study the impact of the releases of sterile mosquitoes on the disease transmissions by investigating the effects of varying the release rates of the sterile mosquitoes. We use a numerical example to illustrate our results for all cases and finally give brief discussions of our findings. |
| first_indexed | 2024-04-12T21:33:21Z |
| format | Article |
| id | doaj.art-20b1d114877645c3938a1fd8ca78fc5b |
| institution | Directory Open Access Journal |
| issn | 1751-3758 1751-3766 |
| language | English |
| last_indexed | 2024-04-12T21:33:21Z |
| publishDate | 2019-03-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Biological Dynamics |
| spelling | doaj.art-20b1d114877645c3938a1fd8ca78fc5b2022-12-22T03:15:58ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662019-03-0113022524610.1080/17513758.2018.15515801551580Discrete-time model for malaria transmission with constant releases of sterile mosquitoesYang Li0Jia Li1University of LouisianaGuangzhou UniversityIn this study, we first formulate a baseline discrete-time mathematical model for malaria transmission where the survival function of mosquitoes is of Beverton–Holt type. We then introduce sterile mosquitoes to the baseline model to explore the transmission dynamics with sterile mosquitoes. We derive formulas for the reproductive number $ R_0 $ of infection and determine the existence and uniqueness of endemic fixed points as well, for the models with or without sterile mosquitoes. We then study the impact of the releases of sterile mosquitoes on the disease transmissions by investigating the effects of varying the release rates of the sterile mosquitoes. We use a numerical example to illustrate our results for all cases and finally give brief discussions of our findings.http://dx.doi.org/10.1080/17513758.2018.1551580Mathematical modellingvector-borne diseasesmalaria transmissiondiscrete-time modelsBeverton–Holt survivabilitysterile mosquitoes |
| spellingShingle | Yang Li Jia Li Discrete-time model for malaria transmission with constant releases of sterile mosquitoes Journal of Biological Dynamics Mathematical modelling vector-borne diseases malaria transmission discrete-time models Beverton–Holt survivability sterile mosquitoes |
| title | Discrete-time model for malaria transmission with constant releases of sterile mosquitoes |
| title_full | Discrete-time model for malaria transmission with constant releases of sterile mosquitoes |
| title_fullStr | Discrete-time model for malaria transmission with constant releases of sterile mosquitoes |
| title_full_unstemmed | Discrete-time model for malaria transmission with constant releases of sterile mosquitoes |
| title_short | Discrete-time model for malaria transmission with constant releases of sterile mosquitoes |
| title_sort | discrete time model for malaria transmission with constant releases of sterile mosquitoes |
| topic | Mathematical modelling vector-borne diseases malaria transmission discrete-time models Beverton–Holt survivability sterile mosquitoes |
| url | http://dx.doi.org/10.1080/17513758.2018.1551580 |
| work_keys_str_mv | AT yangli discretetimemodelformalariatransmissionwithconstantreleasesofsterilemosquitoes AT jiali discretetimemodelformalariatransmissionwithconstantreleasesofsterilemosquitoes |