Optimization of Insecticide Treatments in Rivers: an Application of Graph Theory for Planning a Black Fly Larvae Control Program

Abstract

Combining a model of susceptibility of black fly larvae to commercial formulations of Bacillus thuringiensis var. israelensis and a one-dimensional transport equation in a river, the quantity of larvicide that should be applied at a given site in order to achieve a given mortality downstream can be calculated. The obtained relation, a function of biological and hydrological parameters, allowed us to calculate the costs related to the treatment of a section of river. It is then possible to determine an optimal strategy of treatment which minimizes the quantity of an insecticide applied and the logistic movement between injection sites. Optimal solution is found with the aid of a well known algorithm developed in operations research theory to solve this combinatorial problem. An experimental treatment conducted in the Onchocerciasis Control Program in West Africa is analyzed as an example of the model's application to illustrate the savings of insecticide, time, and money using this approach.