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Mathematical Modelling, Analysis and Simulations to Improve the Control of Miridae, a Cocoa Pest

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Mathematical Modelling, Analysis and Simulations to Improve the Control of Miridae, a Cocoa Pest REPUBLIQUE DU CAMEROUN REPUBLIC OF CAMEROON Paix - Travail - Patrie Peace - Work - Fatherland ----------------- ----------------- UNIVERSITE DE DOUALA THE UNIVERSITY OF DOUALA ----------------- ----------------- ECOLE DOCTORALE DES SCIENCES POSTGRADUATE SCHOOL FOR FONDAMENTALES ET APPLIQUEES PURE AND APPLIED SCIENCE ----------------- ----------------- Unité de Formation Doctorale Postgraduate Training Unit for de Mathématiques, Informatique Mathematics, Applied Computer Appliquée et Physique Fondamentale Science and Pure Physics ----------------- ----------------- Laboratoire de Mathématiques Laboratory of Mathematics BP 24157 Douala PO Box 24157 Douala Email: [email protected] Email: [email protected] MATHEMATICAL MODELLING, ANALYSIS AND SIMULATIONS TO IMPROVE THE CONTROL OF MIRIDAE, A COCOA PEST THESIS defended publicly on June 19, 2020 in fulfillment of the requirements for the award of DOCTORAT / Ph.D in Applied Mathematics Specialty MATHEMATICAL MODELLING By DJOUKWE TAPI Myriam Sonia DEA in Applied Mathematics Registration number: 08S02819 Jury: President: OWONO ONANA Charles Professor The University of Douala Reporters: SALLET Gauthier Professor Université de Lorraine NGWA Gidéon Associate Professor University of Buea FONO Louis Aimé Associate Professor The University of Douala Advisors: BOWONG Samuel Professor The University of Douala DUMONT Yves Director of Research CIRAD BAGNY BEILHE Leila Researcher CIRAD Academic Year: 2018-2019 MATHEMATICAL MODELLING, ANALYSIS AND SIMULATIONS TO IMPROVE THE CONTROL OF MIRIDAE, A COCOA PEST DJOUKWE TAPI Myriam Sonia Academic Year: 2018/2019 Dedication To My late father TAPI Jean Pierre, Dad, you left early and you did not have the grace to see your daughter shine. Father, I miss you so much and you will always be in my heart. My mother MANGWA Rosalie, Mom, Thanks for all your love, all your sacrifices and efforts made during all these years for me. Doctorate Thesis i Remerciements La préparation de cette thèse a nécessité l’intervention de plusieurs personnes sans lesquelles ce travail n’aurait pas abouti. C’est pourquoi, je tiens à remercier tous ceux qui ont contribué à la préparation de ce travail. Je remercie Dieu le père tout puissant pour le don de la vie et pour son infinie assistance. L’immense rôle joué par mes encadrants Pr Samuel Bowong (Chef de Département de Math- ématiques et Informatique, Université de Douala, Cameroun), Pr Yves Dumont (Professeur ex- traordinaire, Université de Pretoria, CIRAD/AMAP) and Dr Leila Bagny-Beilhe (Chargé de la recherche, CIRAD), ne sera en aucun cas quantifié pour façonner mon potentiel de recherche et réaliser mon rêve de devenir Docteur en Mathématiques et œuvrer au développement de la com- munauté scientifique. Je vous remercie très sincèrement pour votre patience, vos conseils et votre enthousiasme tout au long de ma période d’étude. L’énorme soutien (financier) et vos contributions (nouvelles idées mathématiques et différents séminaires) ont conduit à la concrétisation de ce projet de recherche. Monsieur le Professeur Samuel Bowong, vous avez accepté de me faire partager vos activités de recherche en me proposant de réaliser mon mémoire de Master 2, puis ma thèse de doc- torat sous votre direction. Vous m’avez toujours honoré de votre confiance durant tout ce temps en me conseillant et en me tenant par la main. Vous m’avez laissé prendre des initiatives, et vous avez constamment été présent pour orienter et corriger mon travail. Nos discussions ainsi que votre vision toute particulière pour aborder les questions scientifiques m’ont beaucoup influencé et ont grande- ment contribué à développer mon jeune esprit d’apprenti chercheur. Je ne vous remercierai jamais assez pour tout ce que vous m’avez appris. De plus, je remercie tout particulièrement le Professeur Yves Dumont. Par votre amour du travail bien fait et par votre rigueur, vous avez développé en moi un intérêt particulier pour la recherche en biologie mathématique. J’ai réellement apprécié travaillé avec vous, nos différents échanges par mails, vos différents séjours ici au Cameroun durant ma thèse et surtout le séjour que j’ai effectué au centre de recherche AMAP, Montpellier n’ont fait qu’apprécier le travail à vos côtés. Vous m’avez fourni durant ces différentes séances de travail de précieux conseils et surtout de la critique en vue de l’amélioration de mon travail. Docteur Leila Bagny-Beilhe, vous avez toujours ménagé de votre temps chaque fois que je rencontrais des difficultés. J’apprécie Doctorate Thesis ii tous les encouragements à mon égard et toutes les critiques apportées durant ces années de travail. N’étant pas mathématicienne de formation, j’ai sincèrement apprécié tous les efforts consentis pour comprendre toutes les grosses formules mathématiques: ce n’était pas toujours facile de passer d’un langage à l’autre; mais avec nos différentes séances de travail on a toujours réussi à se comprendre. Merci chers encadrants pour le chercheur que je suis devenu. Mes remerciements vont à l’endroit de tout le staff académique et administratif de l’Université de Douala pour les différentes opportunités et facilités pour la réalisation de ce travail. Un merci particulier à tous les rapporteurs de cette thèse. Vous avez sacrifié de votre temps pour apporter votre part de contribution à l’amélioration de ce travail à travers vos idées et vos recommandations. Merci à l’équipe projet EPITAG à travers le laboratoire LIRIMA; à l’équipe projet GRIMCAPAE et UMMISCO, au DP/PCP Agroforesterie Cameroun, au CIRAD, l’IRD et l’INRIA/LIRIMA pour le support logsistique et financier durant la préparation et la finalisation de cette thèse. Je remercie tous les membres de l’UMR AMAP et de l’équipe projet BIOCORE pour leur esprit d’équipe durant mon séjour à leurs côtés. J’ai vraiment appris de vous. Je remercie tous les enseignants du département de Mathématiques et Informatique de l’Université de Douala et tous les enseignants du département de Mathématiques de l’Université de Yaoundé I pour toute votre aide et vos enseignements. Que cette soutenance soit pour vous l’accomplissement d’un dur labeur. Plus particulièrement Pr Jean Jules Tewa, Pr Louis Aimé Fono, Dr Anatole Temgoua, Dr Ferdinand Ngakeu, Dr Armand Tsimi, Dr Bertrand Mbama, merci pour tous vos conseils et pour la patience que vous avez toujours eu à mon égard. Dr Roger Tagne Wafo, merci pour votre assistance et votre support inconditionnel. Durant toutes ces années, vous avez été et vous êtes un père pour moi; vous m’avez toujours encouragé à me surpasser et à aller de l’avant. Merci pour tous ces sacrifices consentis à ma juste personne. Je remercie mes camarades de promotion et mes ainés: Dr Plaire Tchinda, Dr Alexis Tchuinte, Dr Valaire Yatat, Dr Gabriel Kolaye, Dr Yannick Malong, Dr Vidal Kamdem, Dr Janvier Ntahomvukiye, Justin Dzuche, Luther Mann, Yves Fotso. Merci pour votre support et votre collaboration, vous m’avez toujours prêté une oreille attentive. Je remercie tous les membres du laboratoire de Mathématiques de l’Université de Douala spéciale- ment tous les membres de l’équipe "Team Mathematical Modelling" pour tous vos encouragements et pour votre esprit d’équipe. J’ai vraiment aimé travaillé avec vous. Je pense spécialement à Camelle Kabiwa, Yssel Hyonta, Cédric Hameni et Clotilde Djuikem. Merci à mes amis, mon autre famille. Je pense particulièrement à Giresse Noubissie, Hermann Doctorate Thesis iii Tafo, Boris Njike, Eddy Kowa, Sophie Menkui, Armel Foko, Floriane Fondop, Giresse Essouan, Franc Djapa, Ismael Ngounou, Carole Djokam et Félicité Barth Nkamen. Merci pour votre disponibilité et votre attention à mon égard durant toutes ces années. Merci à vous tous qui avez toujours été là pour moi et qui m’avez toujours soutenu. Je pense particulièrement aux prêtres: les abbés René Ngon, Michel Tchoumbou, Henri-Joel Ndjeyep, Meinrad Hebga, Dimitri Chokouago, le couple Mbolda et mes amis Ulrich Nguemdjo, Yannick Foadjo, Sandra Mbialeu, Corneille Megaptche, Nathalie Matsinkou, Alphonsine Massu, Cabrelle Ndjodo. Merci pour toutes vos prières. Il n’y a pas un jour qui passe sans que je ne pense avec amour à mes parents précisement à ma maman Mangwa Rosalie. Les valeurs que tu m’as enseigné ne cessent de guider mes pas. Que cette thèse soit le témoignage que tout ceci n’ait pas été vain. Sachez que je t’aime de tout mon coeur. Merci à ma grand mère Nguenang Elise, à vous mes frères et soeurs: Dimitri, Flavien, William, Michelle et Claude; mes oncles Joseph Ledoux Teponou, Calvin Njayong, Etienne Yankou et mon cousin Mohoue Jacques pour votre amour, votre patience, votre support et tous les sacrifices consentis dans la réalisation de projet. Enfin, nous disons merci à tous ceux qui de près ou de loin ont contribué à la réalisation de ce travail. Recevez l’expression de ma profonde gratitude et de ma sympathie. Doctorate Thesis iv Contents Dedication i Remerciements ii Abstract xii Résumé xiii General Introduction1 1 Literature review and Mathematical tools4 1.1 The cacao tree: Theobroma cacao ..............................4 1.1.1 Origin and importance................................4 1.1.2 Characteristics of agroforests in Cameroon....................6 1.1.3 Phenology and physioloygy of cacao tree Theobroma cacao ............9 1.1.4 Diseases and bugs of T. cacao ............................ 12 1.2 Cacao mirids......................................... 12 1.2.1 The cacao mirid: Sahlbergella singularis ...................... 13 1.2.1.1 Presentation of Sahlbergella singularis .................. 13 1.2.2 Life cycle of S.singularis
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