Models of a banana bunchy top virus disease epidemic were developed to incorporate the two key features of an epidemic in a plantation in the Philippines: an exponential increase in disease incidence over 10 years, and a declining gradient of incidence from the outside edge of the plantation to the centre. A non-spatial model consisted of three difference equations to describe the numbers of latently infected and of infectious plants in the plantation and the size of the inoculum source outside the plantation. In a spatial model the outside portion of the plantation was divided into eight blocks running parallel to the outside edge. The dispersal gradient of the inoculum was assumed to be negative exponential. Analysis of the two models showed that for disease incidence to increase exponentially over time, the rate of disease progress could be dependent either on internal spread and roguing rate (proportion of diseased plants removed and replaced per unit time) or on the rate of increase of external inoculum pressure. The observed incidence gradient from the edge to the centre of the plot could be explained only if external inoculum dominated the parameters in the spatial model. This model was also used to explore a variable roguing rate across blocks. Simulations indicated that this may produce small gains over the adoption of a constant roguing rate over all blocks, but was risky because a shift of roguing emphasis only slightly too far towards the outside blocks can result in a dramatic increase in disease.