A terrible epidemic, probably the Bubonic Plague, in the 14th century before Christ prompted one of the exodus-like events–or so I have speculated on the basis of Manetho’s claim that lepers or diseased quarry workers were quarenteened. Here is the quotation from Josephus’s commentary on Manetho in Against Apion. A certain oracle told the Pharaoh
he would be able to see the gods if he cleansed the whole land of lepers and other polluted persons. The king was delighted, and assembled all those in Egypt whose bodies were wasted by disease: they numbered 80,000 persons. (source here)
I just ran across an article, which puts together the original Egyptian and Hittite texts that refer to the plague. The site is by Edward Pegler and is called Armchair Prehistory.
He covers several plagues over several centuries. You have to scroll down to the 14th century.
From the Hittite records, Pegler concludes:
This is clearly an extensive fatal epidemic. The evidence suggests that epidemic is recurring, no longer spreading uniformly but attacking individual towns at different times. The first wave of the epidemic is suggested to be around 1322 BC (short chronology) but could be earlier, perhaps dating to before 1344 BC.