# Mathematical modelling, analysis and simulations to improve the control of Miridae, a cocoa pest

Abstract : Cocoa is an important cash crop in Central and West Africa, especially in Cameroon. In this part of the world, cacao production is impacted by several diseases, like the Cocoa Swollen Shoot Virus (CSSV) and the black pod disease, and several pests, like Miridae, Distantiella theobroma and Sahlbergella singularis, causing significant damage to pods and vegetative parts of the cocoa tree, and thus impacting the cocoa production. However, the damage and losses associated with this pest remain difficult to estimate due in particular to the bio/ecology of this species (camouflage, low Statistical models have shown to be ineffective in describing these dynamics. That is why we have developed several Mathematical models to describe the time evolution dynamics of mirids, including the effect of different control methods. After an introductory chapter where we recall the biology and ecology of mirids, we develop, analyze and study a compartmental cooperative periodic and nonperiodic model in chapter 2. Then, considering time developments and sexual maturation duration for females, we develop and study a delayed cooperative model (with and without periodic parameters). In this latter model, we consider different control methods, including chemical control (insecticides) and semi-chemical control (sexual confusion and trapping). Through our numerical simulations, we recover recommendation given by mirid control organizations for the use of insecticides and show that chemical treatment can be replaced efficiently by mating disrupting and trapping. We also derive a global sensitivity analysis highlighting the importance of some key parameters. Then, based on the previous results, we develop, in chapter 3, a more complex delay model, modeling mating disrupting and trapping, using the piecewise-smooth system approach. Our analysis shows the existence of two thresholds based on mirid’s biological parameters: one under which the control has no effect on established populations, and the second above which control on established populations is feasible. We illustrate our results with various numerical simulations and discuss the results. We conclude our thesis with possible extension of our models and also applications in the field.
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• HAL Id : tel-03122705, version 1

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Myriam Sonia Djoukwe Tapi. Mathematical modelling, analysis and simulations to improve the control of Miridae, a cocoa pest. Mathematics [math]. Université de Douala, 2020. English. ⟨tel-03122705⟩

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