Modeling diffusive movement of sterile insects released along aerial flight lines

ABSTRACT

The redistribution of insects that are released from an airplane is described using a diffusion equation to derive optimal spacing of flight lines and time interval between flights to achieve a reasonably uniform spatial distribution of released insects and to minimize costs. This optimization is done based on relative costs of sterile males and of flying time. An example is presented using data on the Mediterranean fruit fly, Ceratitis capitata (Weidmann), from the Moscamed program in Guatemala. For the parameter values used, the cost (sterile males plus flights) is minimized when insects are released at intervals of approximately every 2 days (for daily mortality μ = 0.24) to 10 days (for μ = 0.04) and flights are spaced at 300 m (for μ = 0.24) to 600 m (for μ = 0.04) apart, depending on daily medfly mortality estimates, which vary widely in the literature. A simpler approximate method of optimization is then presented based on a relationship observed in the optimization results between flight-line separations and the standard deviation of the distribution.

KEYWORDS:

• Diffusion
• sterile release
• aerial release
• optimization
• cost
• Moscamed

Acknowledgments

H. J. Barclay would like to thank John Hargrove for comments that rendered this investigation necessary. The research of PvdD is partly supported by an NSERC Discovery grant. The authors are greatful to the Moscamed Program Staff for sharing basic operational program data that was used in this study. We also thank two anonymous referees for constructive comments on a previous draft of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of PvdD is partly supported by an NSERC Discovery grant.