Crops are often subject to intense attacks by pests and diseases. Among them, Maize Lethal Necrosis (MLN) is a serious disease that impact maize crops in many Southern countries. It results from the synergistic interaction of two plant viruses, transmitted by two vectors. In this paper, we develop a general deterministic epidemic model of crop-vector-borne disease for synergistic co-infection, with a particular focus on MLN disease. A theoretical analysis shows that different thresholds exists that drive the dynamics of the system: the well known basic reproduction numbers and also invasion reproduction numbers. The latter are essential for the emergence or not of the MLN disease. After a global sensitivity analysis, we illustrate our results through numerical simulations and discuss potential control methods such as vector control and roguing.