18 Iyar (Lag Be'omer)

The Rema seems to hold that we celebrate Lag Be'omer because that is when R' Akiva's students stopped dying. How does that make sense? They stopping dying for the obvious reason that every last one of them died (see Yevamos 62b -"world was desolate until R' Akiva got the 5 new talmidim"). How can we celebrate that they were all finished off?