Dynamics of interactive wild and sterile mosquitoes with time delay
We develop a delay differential equation model for the interactive wild and sterile mosquitoes. Different from the existing modelling studies, we assume that only those sexually active sterile mosquitoes play a role for the interactive dynamics. We consider the cases where the release amount is eith...
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Online Access: | http://dx.doi.org/10.1080/17513758.2019.1682201 |
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doaj-2fd96b0933f34985a0404142dcaff7832020-11-25T03:02:07ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662019-01-0113160662010.1080/17513758.2019.16822011682201Dynamics of interactive wild and sterile mosquitoes with time delayJianshe Yu0Jia Li1Guangzhou UniversityThe University of Alabama in HuntsvilleWe develop a delay differential equation model for the interactive wild and sterile mosquitoes. Different from the existing modelling studies, we assume that only those sexually active sterile mosquitoes play a role for the interactive dynamics. We consider the cases where the release amount is either constant or described by a given function of time. For the constant releases, we establish a threshold of releases to determine whether the wild mosquito suppression succeeds or fails. We study the existence and stability of the model equilibria. When the releases are described by given functions, the trivial equilibrium is no longer globally but locally uniformly asymptotically stable if the amount of releases is below the threshold whereas it is still globally uniformly asymptotically stable if the release amount is above the threshold. Numerical examples demonstrating the model dynamical features and brief discussions of our findings are also provided.http://dx.doi.org/10.1080/17513758.2019.1682201sterile mosquitoesmosquito population suppressiondelay differential equationglobal stabilitybi-stabilitysemi-stability |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Jianshe Yu Jia Li |
spellingShingle |
Jianshe Yu Jia Li Dynamics of interactive wild and sterile mosquitoes with time delay Journal of Biological Dynamics sterile mosquitoes mosquito population suppression delay differential equation global stability bi-stability semi-stability |
author_facet |
Jianshe Yu Jia Li |
author_sort |
Jianshe Yu |
title |
Dynamics of interactive wild and sterile mosquitoes with time delay |
title_short |
Dynamics of interactive wild and sterile mosquitoes with time delay |
title_full |
Dynamics of interactive wild and sterile mosquitoes with time delay |
title_fullStr |
Dynamics of interactive wild and sterile mosquitoes with time delay |
title_full_unstemmed |
Dynamics of interactive wild and sterile mosquitoes with time delay |
title_sort |
dynamics of interactive wild and sterile mosquitoes with time delay |
publisher |
Taylor & Francis Group |
series |
Journal of Biological Dynamics |
issn |
1751-3758 1751-3766 |
publishDate |
2019-01-01 |
description |
We develop a delay differential equation model for the interactive wild and sterile mosquitoes. Different from the existing modelling studies, we assume that only those sexually active sterile mosquitoes play a role for the interactive dynamics. We consider the cases where the release amount is either constant or described by a given function of time. For the constant releases, we establish a threshold of releases to determine whether the wild mosquito suppression succeeds or fails. We study the existence and stability of the model equilibria. When the releases are described by given functions, the trivial equilibrium is no longer globally but locally uniformly asymptotically stable if the amount of releases is below the threshold whereas it is still globally uniformly asymptotically stable if the release amount is above the threshold. Numerical examples demonstrating the model dynamical features and brief discussions of our findings are also provided. |
topic |
sterile mosquitoes mosquito population suppression delay differential equation global stability bi-stability semi-stability |
url |
http://dx.doi.org/10.1080/17513758.2019.1682201 |
work_keys_str_mv |
AT jiansheyu dynamicsofinteractivewildandsterilemosquitoeswithtimedelay AT jiali dynamicsofinteractivewildandsterilemosquitoeswithtimedelay |
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1724691336710324224 |