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Mathematical insights and integrated strategies for the control of Aedes aegypti mosquito

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  • Zhang, Hong
  • Georgescu, Paul
  • Hassan, Adamu Shitu

Abstract

This paper proposes and investigates a delayed model for the dynamics and control of a mosquito population which is subject to an integrated strategy that includes pesticide release, the use of mechanical controls and the use of the sterile insect technique (SIT). The existence of positive equilibria is characterized in terms of two threshold quantities, being observed that the “richer” equilibrium (with more mosquitoes in the aquatic phase) has better chances to be stable, while a longer duration of the aquatic phase has the potential to destabilize both equilibria. It is also found that the stability of the trivial equilibrium appears to be mostly determined by the value of the maturation rate from the aquatic phase to the adult phase.

Suggested Citation

  • Zhang, Hong & Georgescu, Paul & Hassan, Adamu Shitu, 2016. "Mathematical insights and integrated strategies for the control of Aedes aegypti mosquito," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1059-1089.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:1059-1089
    DOI: 10.1016/j.amc.2015.10.066
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    References listed on IDEAS

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    1. Garba, S.M. & Gumel, A.B. & Hassan, A.S. & Lubuma, J.M.-S., 2015. "Switching from exact scheme to nonstandard finite difference scheme for linear delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 388-403.
    2. Anguelov, Roumen & Lubuma, Jean M.-S., 2003. "Nonstandard finite difference method by nonlocal approximation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(3), pages 465-475.
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