(Downloads - 0)
For more info about our services contact : help@bestpfe.com
Table of contents
1 Introduction
1.1 General context
1.2 Some insect species of interest
1.3 Control methods
1.3.1 Chemical control
1.3.2 Environmental management
1.3.3 Physical control
1.3.4 Biological control
1.3.5 The sterile insect technique
1.3.6 Genetic control
1.3.7 Behaviour disruption
1.4 Modelling population dynamics
1.4.1 Structured population models
1.4.2 Spatio-temporal models
1.4.2.1 Characteristics of spatio-temporal models
1.4.2.2 Metapopulation models
1.4.2.3 Cellular-automata models
1.4.2.4 Advection-Diffusion-Reaction
1.5 Estimating insect population size
1.5.1 Sampling
1.5.2 Mark-Release-Recapture
1.5.2.1 Assumptions
1.5.2.2 Some common methods
1.5.3 Trapping model approach
1.6 Modelling trapping
1.6.1 Spatially explicit trapping
1.6.2 Spatially implicit trapping
1.7 Aim and objectives of this thesis
2 Mathematical models and methods
2.1 Introduction
2.2 General setting for the models
2.3 Advection-Diffusion-Reaction models
2.3.1 Preliminaries
2.3.2 Variational formulation
2.3.3 Existence and uniqueness
2.3.4 Regularity of the weak solution
2.3.5 The maximum principle
2.3.6 Properties of the weak solution
2.3.7 Asymptotic behaviour
2.3.7.1 Existence and uniqueness
2.3.7.2 Steady state solutions
2.3.8 Application to single PDE model of Chapter 3
2.3.8.1 Variational formulation
2.3.8.2 Existence and uniqueness
2.3.8.3 Positivity of the solution
2.3.9 Application to the system of PDEs of Chapter 4
2.3.9.1 Variational formulation
2.3.9.2 Study of c: the stationary problem
2.3.9.3 Study of c: the evolution problem
2.3.9.4 Study of uf
2.4 Dynamical systems defined by a system of ODEs
2.4.1 Asymptotic properties
2.4.2 Monotone dynamical systems
2.5 Numerical methods for differential equations
2.5.1 Introduction
2.5.2 The Method of Lines and basic concepts
2.5.3 Finite difference method
2.5.3.1 Approximation of the 1st and 2nd space derivatives .
2.5.3.2 The finite difference scheme
2.5.4 Finite element method
2.5.4.1 The Galerkin method
2.5.4.2 The Finite Elements
2.5.4.3 Application to the problem of Chapter 4
2.6 The time discretization
3 Parameter identification in population models for insects using trap data
3.1 Abstract
3.2 Introduction
3.3 The Insect Trapping Model: The Direct Problem
3.4 The Parameter Identification Problem
3.5 Description of the experiments
3.6 Results and Discussion
3.6.1 Do interfering trap-settings provide better results than noninterfering trap settings?
3.6.2 Interfering trap-setting strategies
3.7 Conclusion
4 Simulations and parameter estimation of a trap-insect model using a finite element approach
4.1 Abstract
4.2 Introduction
4.3 The model
4.3.1 Modelling the spread of the chemical attractant
4.3.2 Modelling the insects’ dynamics
4.3.3 The coupled model
4.4 The variational formulation of the problem
4.5 Some qualitative properties
4.6 The numerical scheme
4.6.1 The semi-discrete approximation
4.6.2 The full discretization
4.7 Numerical simulations
4.7.1 Description of the experiments and mesh generation
4.7.2 Numerical simulation for the attractant
4.7.3 Numerical simulation for the insects
4.7.3.1 Using u0 homogeneous
4.7.3.2 Using a heterogeneous distribution for u0
4.8 Application to parameter identification
4.8.1 The parameter identification protocol
4.8.2 Description of the numerical experiments and simulations
4.8.3 Results and discussion
4.8.3.1 STEP 1: Identification of u
4.8.3.2 STEP 2: Identification of and
4.8.3.3 STEP 3: Identification of U
4.9 Conclusion
5 Mathematical model for pest-insect control using mating disruption and trapping
5.1 Abstract
5.2 Introduction
5.3 The compartmental model for the dynamics of the insect
5.3.1 Theoretical analysis of the model
5.3.1.1 Case 1: Male abundance
5.3.1.2 Case 2: Male scarcity
5.3.1.3 Conclusions for model (5.1)
5.4 Modelling mating disruption and trapping
5.4.1 Mating disruption and trapping
5.4.2 The model
5.4.3 Theoretical analysis of the control model
5.4.3.1 Properties of the equilibria in the male abundance region ( M > Y + YP )
5.4.3.2 Properties of the equilibria in the male scarcity region ( M < Y + YP )
5.4.3.3 Global asymptotic stability of the trivial equilibrium for sufficiently large YP
5.5 Numerical Simulation and Discussion
6 Conclusion and perspectives
6.1 Overview
6.2 Major findings of the thesis
6.2.1 Construction of trap-insect models
6.2.2 Protocol for the estimation of population parameters
6.2.3 Identification of thresholds for mating disruption and trapping control
6.3 Limits and perspectives
