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Table of contents
I Introduction
II Mathematical Preliminaries
1 Mathematical preliminaries
1.1 Semi-discrete modelling and overview on impulsive differential equations
1.1.1 Floquet theory
1.1.2 Comparison principle
1.2 Singular perturbation theory for slow-fast dynamics
1.3 Random search algorithms
1.3.1 General random search and convergence
1.3.2 Adaptive Random Search on the simplex
III Literature Review
2 Biological background
2.1 Biology and cultivation of banana and plantain
2.2 Biology of Radopholus similis
3 Existing soilborne pest, plant epidemic and crop rotation mathematical models
3.1 Soilborne pest and plant epidemics mathematical models
3.1.1 The model of Gilligan and Kleczkowski [40]
3.1.2 The model of Madden and Van den Bosch [65]
3.1.3 The model of Mailleret et al. [66]
3.1.4 A cohort model adapted to Radopholus similis : the model of Tixier et al.[133]
3.2 Some crop rotation mathematical models
3.2.1 Taylor and Rodrìguez-Kábana’s model of rotation of peanuts and cotton to manage soilborne organisms [127]
3.2.2 The model of Van Den Berg and Rossing [139]
3.2.3 The model of Nilusmas et al. [83]
IV Results and discussion
4 Modelling and analysis of the dynamics of the banana burrowing nematode Radopholus similis in a multi-seasonal framework
4.1 Modelling
4.1.1 Core model
4.1.2 Chemical control model
4.1.3 Fallow deployment model
4.1.4 Well-posedness of the problem
4.2 Analysis and results
4.2.1 Chemical control
4.2.2 Sufficient fallow deployment
4.3 Discussion
4.4 Conclusion
5 Optimal fallow deployment for the sustainable management of Radopholus similis
5.0.1 Yield and profit
5.0.2 Parameter values
5.1 Optimization
5.1.1 Location of the optimal solutions
5.1.2 Optimization algorithm
5.2 Numerical results
5.2.1 Small dimensions
5.2.2 High dimensions
5.2.3 Regulation of high dimension solutions
5.2.4 Comparisons
5.3 Discussion and future work
6 Toward a mixed control strategy
6.1 Optimization problem
6.2 Optimization with fixed-size chains and constant fallow
6.2.1 Resolution
6.2.2 A case study
6.3 Optimization with fixed-size chains and varying fallows
6.3.1 Resolution
6.3.2 A case study
6.4 Conclusion
V Conclusion
VI Bibliography
