Étude d’un modèle mathématique pour lutter contre les insectes nuisibles

Abstract

This thesis is mainly a synthesis of the article of R. Anguelov, C. Dufourd and Y. Dumont, entitled : Mathematical model for pest-insect control using mating disruption and trapping and published in the journal : Applied Mathematical Modeling in 2017. The objective is to develop a mathematical model governed by a piecewise dynamic system of ODE to control the pest population using female artificial pheromones to confuse males and harm their mating possibilities. As a result, the reproductive rate decreases, resulting in a decrease in the size of the pest population. In order to make control more efficient, we use trapping which consists of capturing the males attracted by the artificial pheromone. In a first part, a theoretical analysis of the model without control is carried out to evaluate the properties of the endemic equilibrium. Then, the control is added to determine the threshold value above which the pest population disappears. Finally, numerical simulations were made to illustrate the theoretical results