Measles

Measles is a highly contagious illness.  In an era before modern medicine it was hard to deal with fevers and high temperatures.  Patients were isolated and sometimes siblings sent elsewhere.  There is still no cure for measles, but as more of the population is immunized, cases should become increasingly scarce. 

Measles is a significant infectious disease because, while the rate of complications is not high, the disease itself is so infectious that the sheer number of people who would suffer complications in an outbreak amongst non-immune people would quickly overwhelm available hospital resources.
http://en.wikipedia.org/wiki/Measles