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Mathematical analysis of a weather-driven model for the population ecology of mosquitoes

†. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona, USA
‡. Present address: Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Kingdom of Saudi Arabia

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).

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Keywords Mosquitoes; stage-structure; climate change; autonomous and non-autonomous model; stability; Bézout matrix; reproduction number

Citation: Kamaldeen Okuneye, Ahmed Abdelrazec, Abba B. Gumel. Mathematical analysis of a weather-driven model for the population ecology of mosquitoes. Mathematical Biosciences and Engineering, 2018, 15(1): 57-93. doi: 10.3934/mbe.2018003

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