Approximating Optimal Release in a Deterministic Model for the Sterile Insect Technique

Sergio Ramirez,Luis F Gordillo

doi:10.1155/2016/8492107

Abstract

Cost/benefit analyses are essential to support management planning and decisions before launching any pest control program. In particular, applications of the sterile insect technique (SIT) are often prevented by the projected economic burden associated with rearing processes. This has had a deep impact on the technique development and its use on insects with long larval periods, as often seen in beetles. Under the assumptions of long adult timespan and multiple mating, we show how to find approximate optimal sterile release policies that minimize costs. The theoretical framework proposed considers the release of insects by pulses and finds approximate optimal release sizes through stochastic searching. The scheme is then used to compare simulated release strategies obtained for different pulse schedules and release bounds, providing a platform for evaluating the convenience of increasing sterile male release intensity or extending the period of control.

Highlights

The use of ionizing radiation, genetic modification, or exposure to chemicals to induce sterility in male insects, which are later released in the wild, is considered an ideal pest control method because of its harmless impact on the environment and absence of detrimental consequences for human health [1]
Minimum effective sterile production is sometimes approximated if the theoretical model used is simple enough [4]; the model complexity might increase dramatically when specific biological details are to be incorporated or when production constraints are to be taken into account
It is natural for these methods to be modeled through impulsive differential equations due to their relatively large and instantaneous effects; see, for instance, [19,20,21,22]

Summary

Introduction

The use of ionizing radiation, genetic modification, or exposure to chemicals to induce sterility in male insects, which are later released in the wild, is considered an ideal pest control method because of its harmless impact on the environment and absence of detrimental consequences for human health [1]. One of the main decisionmaking challenges is to determine economically feasible levels of mass-rearing that may drive pest populations to extinction This search often uses deterministic, stochastic, or computational models that have been successfully developed during the last decades to predict or explain the behavior of insect populations in presence of sterile males [4,5,6,7]. The motivation comes from promising results that have been obtained in pilot control programs tested against cockchafers (Melolontha vulgaris) [8], the boll weevil (Anthonomus grandis) [9,10,11], and sweet potato weevils (Cylas formicarius) [12] In the latter case, carried out at Kumo Island, Okinawa Prefecture in Japan, the eradication with SIT was complete. By comparing the results from the computations it might be possible to determine suitable release strategies for control program planning

Model Framework

Optimization by Simulated Annealing

Example

Conclusions