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

Kamaldeen Okuneye, Ahmed Abdelrazec, Abba Gumel

Research output: Contribution to journalArticle

4 Citations (Scopus)

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

Fingerprint

population ecology
Weather
Rainfall
Ecology
Culicidae
Mathematical Analysis
weather
Globally Asymptotically Stable
Rain
Temperature
Population
Mosquito Control
Reproduction number
Density Dependence
Mosquito control
South Africa
Africa South of the Sahara
Kenya
Deterministic Model
Nigeria

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 journalArticle

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