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

Kamaldeen Okuneye, Ahmed Abdelrazec, Abba Gumel

Research output: Contribution to journalArticle

7 Scopus citations

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 languageEnglish (US)
Pages (from-to)57-93
Number of pages37
JournalMathematical Biosciences and Engineering
Volume15
Issue number1
DOIs
StatePublished - Feb 1 2018

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

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