At first I thought lesbianism was the disease but then read further, and there was the plague. (Why doesn't ague, a symptom, rhyme with plague? I only found out it didn't in grad school. But that is an aside.)

Ring around the rosy is *not* about the plague.

I remembered where the lady in the alligator purse was from, a hand-clappy thing, Miss Lucy had a baby, she named it Tiny Tim.

George Collins rode out one wintry night, was taken sick, and died.

Two little chil'n layin' in bed, one was sick and the other 'most dead
Sent for the doctor, the doctor said
Feed them chil'en some shortnin' bread!

Then there are LOTS about depression, and other *mental* illnesses...