(3-day measles perhaps?). In Letter #53, JA writes:

There has been a cold and sore-throat prevailing very much in this house lately; the children have almost all been ill with it, and we were afraid Lizzy** was going to be very ill one day. She had specks and a great deal of fever. It went off, however, and they are all pretty well now.

This was written a week after JA wrote about Cassandra's "violent breaking-out," so whatever the disease, it seems to have passed quickly.