Mathematical analysis of a weather-driven model for the population ecology of mosquitoes
A new deterministic model for the population biology of immature and mature mosquitoes is designed and used to assess the impact of temperature and rainfall on the abundance of mosquitoes in a community. The trivial equilibrium of the model is globally-asymptotically stable when the associated vecto...
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| Language: | English |
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AIMS Press
2018-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018003 |
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| author | Kamaldeen Okuneye Ahmed Abdelrazec Abba B. Gumel |
| author_facet | Kamaldeen Okuneye Ahmed Abdelrazec Abba B. Gumel |
| author_sort | Kamaldeen Okuneye |
| collection | DOAJ |
| description | A new deterministic model for the population biology of immature and mature mosquitoes is designed and used to assess the impact of temperature and rainfall on the abundance of mosquitoes in a community. The trivial equilibrium of the model is globally-asymptotically stable when the associated vectorial reproduction number $({\mathcal R}_0)$ is less than unity. In the absence of density-dependence mortality in the larval stage, the autonomous version of the model has a unique and globally-asymptotically stable non-trivial equilibrium whenever $1 < {\mathcal R}_0 < {\mathcal R}_0^C$ (this equilibrium bifurcates into a limit cycle, via a Hopf bifurcation at ${\mathcal R}_0={\mathcal R}_0^C$). Numerical simulations of the weather-driven model, using temperature and rainfall data from three cities in Sub-Saharan Africa (Kwazulu Natal, South Africa; Lagos, Nigeria; and Nairobi, Kenya), show peak mosquito abundance occurring in the cities when the mean monthly temperature and rainfall values lie in the ranges $[22 -25]^{0}$C, $[98 -121]$ mm; $[24 -27]^{0}$C, $[113 -255]$ mm and $[20.5 -21.5]^{0}$C, $[70 -120]$ mm, respectively (thus, mosquito control efforts should be intensified in these cities during the periods when the respective suitable weather ranges are recorded). |
| format | Article |
| id | doaj-art-86dbe3e7056440159d64604ed1a64dfe |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-86dbe3e7056440159d64604ed1a64dfe2025-01-24T02:40:37ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-01-01151579310.3934/mbe.2018003Mathematical analysis of a weather-driven model for the population ecology of mosquitoesKamaldeen Okuneye0Ahmed Abdelrazec1Abba B. Gumel2. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona, USA. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona, USA. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona, USAA new deterministic model for the population biology of immature and mature mosquitoes is designed and used to assess the impact of temperature and rainfall on the abundance of mosquitoes in a community. The trivial equilibrium of the model is globally-asymptotically stable when the associated vectorial reproduction number $({\mathcal R}_0)$ is less than unity. In the absence of density-dependence mortality in the larval stage, the autonomous version of the model has a unique and globally-asymptotically stable non-trivial equilibrium whenever $1 < {\mathcal R}_0 < {\mathcal R}_0^C$ (this equilibrium bifurcates into a limit cycle, via a Hopf bifurcation at ${\mathcal R}_0={\mathcal R}_0^C$). Numerical simulations of the weather-driven model, using temperature and rainfall data from three cities in Sub-Saharan Africa (Kwazulu Natal, South Africa; Lagos, Nigeria; and Nairobi, Kenya), show peak mosquito abundance occurring in the cities when the mean monthly temperature and rainfall values lie in the ranges $[22 -25]^{0}$C, $[98 -121]$ mm; $[24 -27]^{0}$C, $[113 -255]$ mm and $[20.5 -21.5]^{0}$C, $[70 -120]$ mm, respectively (thus, mosquito control efforts should be intensified in these cities during the periods when the respective suitable weather ranges are recorded).https://www.aimspress.com/article/doi/10.3934/mbe.2018003mosquitoesstage-structureclimate changeautonomous and non-autonomous modelstabilitybézout matrix; reproduction number |
| spellingShingle | Kamaldeen Okuneye Ahmed Abdelrazec Abba B. Gumel Mathematical analysis of a weather-driven model for the population ecology of mosquitoes Mathematical Biosciences and Engineering mosquitoes stage-structure climate change autonomous and non-autonomous model stability bézout matrix; reproduction number |
| title | Mathematical analysis of a weather-driven model for the population ecology of mosquitoes |
| title_full | Mathematical analysis of a weather-driven model for the population ecology of mosquitoes |
| title_fullStr | Mathematical analysis of a weather-driven model for the population ecology of mosquitoes |
| title_full_unstemmed | Mathematical analysis of a weather-driven model for the population ecology of mosquitoes |
| title_short | Mathematical analysis of a weather-driven model for the population ecology of mosquitoes |
| title_sort | mathematical analysis of a weather driven model for the population ecology of mosquitoes |
| topic | mosquitoes stage-structure climate change autonomous and non-autonomous model stability bézout matrix; reproduction number |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018003 |
| work_keys_str_mv | AT kamaldeenokuneye mathematicalanalysisofaweatherdrivenmodelforthepopulationecologyofmosquitoes AT ahmedabdelrazec mathematicalanalysisofaweatherdrivenmodelforthepopulationecologyofmosquitoes AT abbabgumel mathematicalanalysisofaweatherdrivenmodelforthepopulationecologyofmosquitoes |