ABSTRACT – The aim of this thesis is to propose, on the one hand, a framework for mathematical analysis and simulation of the burrowing nematode Radopholus similis dynamic interaction with banana or plantain roots, and the other hand to identify the best control mean in order to optimize the economical yield of banana and plantain crops.
In the first step, we study the infestation dynamics of banana or plantain plants by R. similis. Two control strategies are analyzed: pesticides, which are widely used, and fallow deployment, which is more environmentally friendly. To represent the host-parasite dynamics, two semi-discrete models are proposed. In these models, during each cropping season, free nematodes enter the plant roots, on which they feed and reproduce. At the end of the cropping season, fruits are harvested. In the first model, the parent plant is cut down to be replaced by one of its suckers and pesticides are applied. In the second model, the parent plant is uprooted and a fallow period is introduced, inducing the decay of the free pest populations; at the beginning of the next cropping season, a pest-free vitro-plant is planted. For both models, we find a condition of global stability of the pest-free equilibrium. Then, the effective reproduction number of the pest is computed, assuming that the infestation dynamics is fast compared to the other processes, which leads to the model order reduction. Conditions on the pesticide load or the fallow duration are then derived to ensure the stability of the pest-free equilibrium. Finally, numerical simulations illustrated these theoretical results.
In a second step, we propose an eco-friendly optimization of banana or plantain yield by the control of the burrowing nematode. This control relies on fallow deployment. The optimization is based on the multi-seasonal model in which fallow periods follow cropping seasons. The aim is to find the best way, in terms of profit, to allocate the durations of fallow periods between the cropping seasons, over a fixed time horizon spanning several seasons. The existence of an optimal allocation is proven and an adaptive random search algorithm is proposed to solve the optimization problem. For a relatively long time horizon, deploying one season less than the maximum possible number of cropping seasons allows us to increase the fallow period durations and result in a better multi-seasonal profit. For regular fallow durations, the profit is lower than the optimal solution, but the final soil infestation is also lower.
In the last step, we propose a strategy of mixed control where cropping seasons can succeed each other by vegetative growth of the plant or by planting a healthy vitro-plant, after eventually a fallow. We derive an optimization problem in order to know when to implement one or the other reproductive strategy and to know how long to make the fallow period last in case of fallow deployment. We obtain initial results and present perspectives.