A spatiotemporal model is developed to analyse epidemics of airborne plant diseases which are spread by spores. The observations consist of measurements of the severity of disease at different times, different locations in the horizontal plane and different heights in the vegetal cover. The model describes the joint distribution of the occurrence and the severity of the disease. The three-dimensional dispersal of spores is modelled by combining a horizontal and a vertical dispersal function. Maximum likelihood combined with a parametric bootstrap is suggested to estimate the model parameters and the uncertainty that is attached to them. The spatiotemporal model is used to analyse a yellow rust epidemic in a wheatfield. In the analysis we pay particular attention to the selection and the estimation of the dispersal functions.