The current epidemic of Ebola Virus Disease (EVD) in West Africa is the largest ever recorded, a fundamental shift in the epidemiology of Ebola with unprecedented spatiotemporal complexity. In this study, we used a spatial transmission model to understand spatiotemporal dynamics of EVD in West Africa, and to compare effectiveness of local interventions (e.g. case isolation, hospitalization) and long-range interventions (e.g. border closures). A compartmental spatial model was fitted to case and death incidence in each country. We evaluated the balance between local (within-country) and long-range (between-country) transmission, dependent on population sizes and distance between regions, using a gravity model. We also examined transmission dynamics between countries and the relative benefits of different interventions. We demonstrate that spatial spread patterns provide an explanation for dynamic patterns observed in early data from the epidemic, at both country and regional levels. In particular, the gravity model successfully captures the multiple waves of epidemic growth in Guinea by incorporating spatial interactions. The model simulations suggest that local transmission reductions were most effective in Liberia, while long-range transmission was dominant in Sierra Leone. The model is successfully able to simultaneously forecast cases and deaths one month ahead in all three countries. To conclude, the gravity model approach accurately captures and forecasts the patterns of spatial spread of EVD between countries in West Africa. The model structure and intervention analysis presented here provide information that can be used by policymakers and public health officials to help guide planning and response efforts for this and future epidemics.