Using the observed submillimetre source counts, from 250-1200 microns (including the most recent 250, 350 and 500 micron counts from BLAST), we present a model capable of reproducing these results, which is used as a basis to make predictions for upcoming surveys with the SPIRE instrument aboard the Herschel Space Observatory. The model successfully fits both the integral and differential source counts of submillimetre galaxies in all wavebands, predicting that while ultra-luminous infrared galaxies dominate at the brightest flux densities, the bulk of the infrared background is due to the less luminous infrared galaxy population. The model also predicts confusion limits and contributions to the cosmic infrared background that are consistent with the BLAST results. Applying this to SPIRE gives predicted source confusion limits of 19.4, 20.5 and 16.1mJy in the 250, 350 and 500 micron bands respectively. This means the SPIRE surveys should achieve sensitivities 1.5 times deeper than BLAST, revealing a fainter population of infrared-luminous galaxies, and detecting approximately 2600, 1300, and 700 sources per square degree in the SPIRE bands (with one in three sources expected to be a high redshift ultra-luminous source at 500 microns). The model number redshift distributions predict a bimodal distribution of local quiescent galaxies and a high redshift peak corresponding to strongly evolving star-forming galaxies. It suggests the very deepest surveys with Herschel-SPIRE ought to sample the source population responsible for the bulk of the infrared background.
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