Résumé
Food security is an important issue throughout the World. While it is important to maintain food production in a changing environment, it is also important to improve crop yield and crop protection against pest attacks and diseases. To this aim, many programs have been launched, since decades, to select crops and/or to develop (biological) tools against pest and diseases, etc. However, these field experiments are long, tedious and costly. That is why, Modeling is more than useful. Some people, in Europe and North-America, decided to use computers and developed simulations tools to realize in-silico or virtual experiments of crop growth and pest/disease control. However, these digital developments leaded to very complex models with hundreds of parameters, relying on thousands of (long time) simulations. In general these models have been or are developed by thematicians, like crop experts, using computer modeling tools that are now available and are supposed to easier the development of models. Thus, the (natural) tendency is to replicate exactly what is supposed to occur in the crop, and not to model, only, the important processes. Last but not least, the use of such models require a long and tedious learning, such that only very few people are able to use them. In mathematical modeling, the objective is to capture the essential processes in such a way that a theoretical analysis of the model is still possible in order to derive useful (new) outputs to the field experts, according to the initial questioning. I will present an overview of biological issues we studied in Cameroon (Mirid-Cacao), Indonesia (Pollinator-Oil palm), South Africa (pest/vector control), and, now studying in La Réunion (fruit flies-sterile insect), leading to a wide variety of mathematical models and, thus, to "nice" mathematical issues: see for instance [1, 2, 3, 4, 5, 6, 7]. I will also discuss about ongoing projects and upcoming mathematical challenges.References[1] Anguelov R, Dumont Y, Djeumen VY. Sustainable vector/pest control us- ing the permanent Sterile Insect Technique. Mathematical Methods in the Applied Sciences, 43(18), 10391-10412 (2020)[2] Aronna MS, Dumont Y, On Nonlinear Pest/Vector Control via the Sterile Insect Technique: Impact of Residual Fertility. Bulletin of Mathematical Biology, 82, 110 (2020)[3] Chapwanya M, Dumont, Y. On crop vector-borne diseases. Impact of virus lifespan and contact rate on the traveling-wave speed of infective fronts. Ecological Complexity, 34, 119-133 (2018)[4] Chapwanya M, Dumont Y. Application of Mathematical Epidemiology to crop vector-borne diseases. The cassava mosaic virus disease case. Editors: Miranda I. Teboh-Ewungkem; Gideon Akumah Ngwa. Infectious Diseases and our Planet, 7, Springer, 2021, Mathematics of Planet Earth, 57-95 (2021)[5] Chapwanya M, Matusse A, Dumont Y. On synergistic co-infection in crop diseases. The case of the Maize Lethal Necrosis Disease. Applied Mathe- matical Modelling, 90, 912-942 (2021)[6] Dumont Y, Soulie J-C, Michel F. Modeling oil palm pollinator dynamics using deterministic and agent-based approaches. Applications on fruit set estimates. Some preliminary results. Mathematical Methods in the Applied Sciences, 41 (18), 8545-8564 (2018)[7] Tapi MD, Bagny-Beilhe L, Dumont Y. Miridae control using sex-pheromone traps. Modeling, analysis and simulations. Nonlinear Analysis: Real World Applications, 54, 1-22 (2020)