There is one documented case where prostitution was completely eliminated from a society, this happened during the Mao era of  China.  After 2000 year of it flourishing, it was strictly forbidden and eliminated by rounding up all the prostitutes and holding them in “re-education” camps.  Only the elite of the government had access to selected girls.   This happened from 1950 to approximately 1970, however by the mid 1970’s prostitution was again wide spread and integral to Chinese culture.