The dust outbreak, which was quite strong for July/August, started on 28/29 July.
Large thunderstorms over western Africa lifted large amounts of dust into the air. On 30 July, the elevated dust started to cross the Atlantic Ocean and it arrived in the Lesser Antilles on 2 August.
Note: Despite the recent dust outbreaks over the Atlantic, NOAA forecasts are still calling for an elevated hurricane activity over the Atlantic Ocean in 2013, based on the large-scale conditions (warm sea surface temperatures in the Tropical Atlantic and lack of warm El Niño Southern Oscillation (ENSO)). It is not unusual to have suppressed hurricane activity in July, which is typically less active than even June.
Major transport of desert dust (26 June 2007)
Long-term, 15-min intervals Meteosat-10 dust RGB animation from 28 July 00 UTC to 3 August 00 UTC, which shows the details of the dust pick up over Africa and the transport to the Caribbean Sea
Saharan air layer outbreak over the Atlantic Ocean (CIMSS Satellite Blog)