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 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 < R^C ₀ (this equilibrium bifurcates into a limit cycle, via a Hopf bifurcation at R₀ = R^C 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).