I believe Hippocrates was the first to mention (what we believe to be) Chlorea in his works. He did not regard this as an "epidemic", however, and it wasn't recognized until the early 19th century. It is believed that Cholera originated from the Ganges River and was thought to have widely spread because of the high population density. I'm unaware of whether Babylon was hit with an epidemic of cholera, but 400 years before the date of your story it was estimated to have been the largest city in the world at that time. However, this was during the reign of Hammurabi and the empire collapsed quite a bit after his passing and was dominated by other empires in the region which would have surely impacted population numbers negatively. Babylon wasn't on top again until around the 7th century BC.