Mathematical assessment of the role of non-linear birth and maturation delay in the population dynamics of the malaria vector

Gideon A. Ngwa, Ashrafi M. Niger, Abba B. Gumel

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

A delay ordinary deterministic differential equation model for the population dynamics of the malaria vector is rigorously analysed subject to two forms of the vector birth rate function: the Verhulst-Pearl logistic growth function and the Maynard-Smith-Slatkin function. It is shown that, for any birth rate function satisfying some assumptions, the trivial equilibrium of the model is globally-asymptotically stable if the associated vectorial reproduction number is less than unity. Further, the model has a non-trivial equilibrium which is locally-asymptotically stable under a certain condition. The non-trivial equilibrium bifurcates into a limit cycle via a Hopf bifurcation. It is shown, by numerical simulations, that the amplitude of oscillating solutions increases with increasing maturation delay. Numerical simulations suggest that the Maynard-Smith-Slatkin function is more suitable for modelling the vector population dynamics than the Verhulst-Pearl logistic growth model, since the former is associated with increased sustained oscillations, which (in our view) is a desirable ecological feature, since it guarantees the persistence of the vector in the ecosystem.

Original languageEnglish (US)
Pages (from-to)3286-3313
Number of pages28
JournalApplied Mathematics and Computation
Volume217
Issue number7
DOIs
StatePublished - Dec 1 2010
Externally publishedYes

Keywords

  • Birth rate function
  • Hopf bifurcation
  • Maturation delay
  • Vector population dynamics

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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