Abstract
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 (R0) 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 < R0 < RC 0 (this equilibrium bifurcates into a limit cycle, via a Hopf bifurcation at R0 = RC 0 ). 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]0C, [98 ? 121] mm; [24 ? 27]0C, [113 ? 255] mm and [20.5 ? 21.5]0C, [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).
| Original language | English (US) |
|---|---|
| Pages (from-to) | 57-93 |
| Number of pages | 37 |
| Journal | Mathematical Biosciences and Engineering |
| Volume | 15 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 1 2018 |
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Keywords
- Autonomous
- Bézout matrix
- Climate change
- Mosquitoes
- Non-autonomous model
- Reproduction number
- Stability
- Stage-structure
ASJC Scopus subject areas
- Modeling and Simulation
- Agricultural and Biological Sciences(all)
- Computational Mathematics
- Applied Mathematics
Cite this
Mathematical analysis of a weather-driven model for the population ecology of mosquitoes. / Okuneye, Kamaldeen; Abdelrazec, Ahmed; Gumel, Abba.
In: Mathematical Biosciences and Engineering, Vol. 15, No. 1, 01.02.2018, p. 57-93.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Mathematical analysis of a weather-driven model for the population ecology of mosquitoes
AU - Okuneye, Kamaldeen
AU - Abdelrazec, Ahmed
AU - Gumel, Abba
PY - 2018/2/1
Y1 - 2018/2/1
N2 - 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 (R0) 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 < R0 < RC 0 (this equilibrium bifurcates into a limit cycle, via a Hopf bifurcation at R0 = RC 0 ). 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]0C, [98 ? 121] mm; [24 ? 27]0C, [113 ? 255] mm and [20.5 ? 21.5]0C, [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).
AB - 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 (R0) 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 < R0 < RC 0 (this equilibrium bifurcates into a limit cycle, via a Hopf bifurcation at R0 = RC 0 ). 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]0C, [98 ? 121] mm; [24 ? 27]0C, [113 ? 255] mm and [20.5 ? 21.5]0C, [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).
KW - Autonomous
KW - Bézout matrix
KW - Climate change
KW - Mosquitoes
KW - Non-autonomous model
KW - Reproduction number
KW - Stability
KW - Stage-structure
UR - http://www.scopus.com/inward/record.url?scp=85039433082&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85039433082&partnerID=8YFLogxK
U2 - 10.3934/mbe.2018003
DO - 10.3934/mbe.2018003
M3 - Article
C2 - 29161827
AN - SCOPUS:85039433082
VL - 15
SP - 57
EP - 93
JO - Mathematical Biosciences and Engineering
JF - Mathematical Biosciences and Engineering
SN - 1547-1063
IS - 1
ER -