Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

A model for the biocontrol of mosquitoes using predatory fish

Pages: 3283 - 3298, Volume 19, Issue 10, December 2014      doi:10.3934/dcdsb.2014.19.3283

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Rongsong Liu - Department of Mathematics and Department of Zoology and Physiology, University of Wyoming, Laramie, WY, 82071, United States (email)
Stephen A. Gourley - Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom (email)

Abstract: We present a mathematical model for the localised control of mosquitoes using larvivorous fish. It is supposed that the adult mosquitoes choose among a finite number of isolated ponds for oviposition and that these ponds differ in various respects including physical size, survival prospects and maturation times for mosquito larvae. We model a mosquito control effort that involves stocking some or all of these ponds with larvivorous fish such as the mosquitofish Gambusia affinis. The effect of doing so may vary from pond to pond, and the ponds are coupled via the adult mosquitoes in the air. Also, adult mosquitoes may avoid ovipositing in ponds containing the larvivorous fish. Our model enables us to predict how the larvivorous fish should be allocated between ponds, and shows in particular that only certain ponds should be stocked if there is a limited supply of the fish. We also consider oviposition pond selection by mosquitoes, and show that in some situations mosquitoes might do better to simply choose a pond at random.

Keywords:  Biocontrol, mosquito, mosquitofish, delay, stability.
Mathematics Subject Classification:  Primary: 34K12, 34K20, 34K25, 92D40.

Received: June 2013;      Revised: March 2014;      Available Online: October 2014.