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

Pest insects represent a major threat to public health, to food security as well as to the economy. Constant effort is being made to develop or improve control strategies in the framework of Integrated Pest Management (IPM). IPM aims to maintain pests at low levels that do not represent risks for health or economy, while satisfying environmentally respectful toxicological and ecological requirements. Planning of efficient control strategies requires in-depth knowledge of the pest's biology and ecology. In particular, it is essential to have accurate estimates of parameters of biological and ecological relevance like population size and distribution, dispersal capacity, as well as good understanding of the underlying processes governing the dynamics of the population in time and space. The aim of this thesis is to provide a mathematical framework for the development of efficient IPM control strategies. 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 objective of this the- sis is to develop mathematical methods and practical protocols to estimate a pest population size and distribution. The second objective is to predict the impact of a specific control strategy on a pest population and identify how full control of the population can be achieved. Typically, the only data available on the field is trapping data. Further, to increase the capture of insects, those traps are often combined with a chemical attractant. The first objective of this thesis is addressed by constructing a generic 2-dimensional spatio-temporal Trap-Insect-Model (TIM) based on biological and ecological knowledge of the pest. This model is formulated by Advection-Diffusion-Reaction (ADR) equations which account for the dispersal capacity of the insects, their attractive- ness towards the traps and their demography and trapping. The unknown insect population size and distribution is the initial condition of the model. Usually, the dispersal capacity as well as the parameters related to the traps are also unknown and may vary in time. A major outcome of this thesis is a protocol to identify a set of parameters using trap data collected over a short period of time during which the parameters can be assumed constant. To address the second objective, we consider a model for the control of crop- pest insects via mating disruption, using a female pheromone, and trapping. Here, males are diverted from females compromising their insemination. The model uses compartmental structure taking into account the specific behaviour of the different groups in the population. It is formulated as a system of ODEs. 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. (Résumé d'auteur