AICME II abstracts

Mathematical modeling and computer simulations...

A Mathematical Model for the Sterile Insect Technique Jos´e D. Flores1 and Jaime Mena-Lorca2 . The Sterile Insect Technique (SIT) is an insect population control. The technique first conceived by E. F. Knipling [3] has been successfully used to control species such as the New World screwworm, the Mediterranean fruit fly, melon fly, Mexican fruit fly, pink bollworm, codling moth, tsetse flies, the onion fly and against several species of mosquitoes. The method consist of releasing a large number of sterilized insect in the natural population into the environment to ensure that wild insect will mate with sterile individual reducing the probability that members of the same species will successfully reproduce. Subsequent released of the same number of sterile individuals are made to increase the ratio of sterile causing total eradication of a defined wild population in a few number of generations. In this paper we intend to extend the algebraic analysis of the SIT [1],[2] to a more general density-dependent situation that consider the Allee Effect introduced into the growth of the population. A logistic model is presented which describes the effects of introducing the critical depensation curve into the population growth. We study and analyze the steady population equilibria of the proposed model.

Mathematical modeling and computer simulations...

[2] Harrison, G.W., Barclay, H.J., van der Driessche, P., 1982, Analysis od a Sterile Insect Release Model with Predation, J. Math. Biology, 16, 33-48. [3] Knipling, E.F., 1955, Possibilities of Insect Control or Eradication Through the Use of Sexually Sterile Males, J. Econ. Entomol., 48, 459-462. [4] Krafsur, E.S., 1998, Sterile Insect Technique for Suppressing and Eradicating Insect Population: 55 Years and Counting, J. Agric. Entomol., 15, 303-317.

References [1] Barclay, H.J. Mackauer, M., 1980, The Sterile Insect Release Method for Pest Control: a Density-Dependent Model, Envir. Entom., 9, 810817. 1 Department of Mathematical Sciences, The University of South Dakota (e-mail: [email protected].). 2 Instituto de Matem´ aticas, Pontificia Universidad Cat´ olica de Valparaiso, Chile. (e-mail: [email protected]).

12-Flo-a

AICME II abstracts

12-Flo-b