نبذة مختصرة : Fungal diseases cause serious damages in crops, which threatens food security worldwide. In response, chemical fungicides are commonly used, yet they are harmful to the environment and human health and they may induce fungus resistance. There is a definite need for more sustainable control methods. To tackle this issue, our approach consisted in developing mathematical models representing crop-fungus interactions, in order to design alternative control methods. We obtained generic qualitative results, which we applied to coffee leaf rust caused by Hemileia vastatrix, a major coffee disease. Coffee being an important cash crop which provides a living for numerous small producers and their family, controlling coffee leaf rust is hence a major socio-economic issue.First, we developed a crop-fungus interaction model using ordinary differential equations. As in classical epidemiological models, the host population was subdivided by health status, considering the crop leaf as an individual. The infection being mediated by fungus spores released in the plantation, their dynamics were also included. Moreover, this model differentiated between young and mature leaves, to take into account variations in fungus aggressiveness according to host development. We computed the basic reproduction number R0, which classically determines the stability of the disease free equilibrium. This model exhibited complex asymptotic properties, that differed from classical epidemiological models: R0< 1 was not sufficient to obtain the stability of the disease free equilibrium, as a stable endemic equilibrium could exist; R0>1 did not guarantee the existence and stability of an endemic equilibrium, because high R0 values could lead to the destruction of the plantation.Then, based on the knowledge that spores of fungi such as H. vastatrix are dispersed by wind, we considered a spatio-temporal model describing the disease propagation in a plantation during the rainy and dry seasons, using partial differential equations. We computed two ...
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