Spatio-temporal mathematical models of insect trapping : analysis, parameter estimation and applications to control

Abstract

This thesis provides a mathematical framework for the development of efficient control strategies that satisfy the charters of Integrated Pest Management (IPM) which aims to maintain pest population at a low impact level. This mathematical framework is based on a dynamical system approach and comprises the construction of mathematical models, their theoretical study, the development of adequate schemes for numerical solutions and reliable procedures for parameter identification. The first output of this thesis is the construction of trap-insect spatio-temporal models formulated via advection-diffusion-reaction processes. These models were used to simulate numerically trapping to compare with field data. As a result, practical protocols were identified to estimate pest-population size and distribution as well as its dispersal capacity and parameter values related to the attractiveness of the traps. The second major output of this thesis is the prediction of the impact of a specific control method: mating disruption using a female pheromone and trapping. A compartmental model, formulated via a system of ordinary differential equations, was built based on biological and mating behaviour knowledge of the pest. The theoretical analysis of the model yields threshold values for the dosage of the pheromone above which extinction of the population is ensured. The practical relevance of the results obtained in this thesis shows that mathematical modelling is an essential supplement to experiments in optimizing control strategies.