Crop protection and pest control are now important challenges, especially in a changing environment. After decades of chemical controls, it is mandatory to consider biological and safe alternatives. However, it is still important to understand the dynamics of diseases or pests. Mathematical Modelling can be a powerfull tool to give some insights in complex systems, like vector-borne plant diseases [1].However, plant viruses have more complex behaviors than human viruses, leading to new and original models to study. In addition, and contradictory to human, animal or vectors, plants are not ”moving”. In other words, the main assumption of ”homogeneous distribution” used in most of the epidemiological models, does not hold: plants do not move, while vectors can. In this talk, we mainly focus on a model related to non-circulative and non-persistent viruses. After a brief presentation of the temporal model, we extend it to a spatio-temporal model, leading to a system of ordinary and partial differential equations. We present some theoretical results and illustrate our talk with numerical simulations. Finally, we discuss the results and their implication in terms of control [2]. (Texte intégral)