During the 14th century Black Death , there was a huge increase in demand for saffron-based medicine . Much saffron had to be imported by Venetian and Genoan ships from southern and Mediterranean lands such as Rhodes . During the 14th century Black Death , demand for saffron-based medicine skyrocketed , and much saffron had to be imported via Venetian and Genoan ships from southern and Mediterranean lands such as Rhodes .