I don't know how many really stopped on their own given landscapes in europe are scattered with plague stones, whole towns/villages were quarantined, etc.
All of them stopped that were that type, otherwise we'd
still have the Black Death and the English Sweat and leprosy (WIDEspread in the Middle Ages) and many others, except there wouldn't be many people left. Now, some are not that type, like measles and smallpox (now extinct) and mumps and colds and so on. They go on and on forever, until we make them extinct, if we do. We don't yet know what type the COVID-19 is.
The Sweating Sickness did disappear on its own. No one's sure why, because even today, no one's entirely sure what the Sweating Sickness was, since it had stopped happening by the time medical science advanced enough to be able to identify it.
The descriptions written at the time were very clear. I have a pamphlet reprinted from the early 16th century by a physician that tells all the symptoms and the remedies (all useless ) they tried. I'll tell you what ----- we never saw anything like it and we DEFINITELY don't want it back. Sweat just poured out of the skin and the victims dehydrated and died within a day. Like cholera, except the skin. Henry the VIII was terrified of it. He drank pearls dissolved in vinegar -- he never got it, so maybe that worked.
Probably not.
Actually, the Black Death didn't disappear. It was a bubonic plague epidemic, and the bubonic plague is still out there. It's a lot more rare, as we know now how to deal with it, but there was an outbreak of it in Madagascar as recently as 1995.
Leprosy also still exists, and is rare now (at least, outside of the third world) because we learned what it was and how to deal with it.
The Sweating Sickness, however, simply vanished. The last reported case of it was in 1551, and although the descriptions written about it WERE very clear and detailed, no one has ever known what it was or what caused it. Some medical historians believe it was some sort of unidentified hantavirus. With nothing to go on but descriptions of the symptoms and progress of the disease, they can't do anything but guess.