The elimination of infectious diseases requires reducing transmission below a certain threshold. The Visceral Leishmaniasis (VL) Elimination Initiative in Southeast Asia aims to reduce the annual VL incidence rate below 1 case per 10,000 inhabitants in endemic areas by 2015 via a combination of case management and vector control. Using a previously developed VL transmission model, we investigated transmission thresholds dependent on measures reducing the sand fly density either by killing sand flies (e.g., indoor residual spraying and long-lasting insecticidal nets) or by destroying breeding sites (e.g., environmental management). Model simulations suggest that elimination of VL is possible if the sand fly density can be reduced by 67% through killing sand flies, or if the number of breeding sites can be reduced by more than 79% through measures of environmental management. These results were compared to data from two recent cluster randomised controlled trials conducted in India, Nepal and Bangladesh showing a 72% reduction in sand fly density after indoor residual spraying, a 44% and 25% reduction through the use of long-lasting insecticidal nets and a 42% reduction after environmental management. Based on model predictions, we identified the parameters within the transmission cycle of VL that predominantly determine the prospects of intervention success. We suggest further research to refine model-based predictions into the elimination of VL.