So what was reducing the case-fatality rate? I don't know, but it might have been nutrition. There's evidence at least that Vitamin A makes measles less severe/deadly.
Sanitation, antibiotics, oral rehydration therapy, machine ventilation, nutrition, and so on.
It's not the measles itself that was the cause of most fatalities, it was the pneumonia, diahrrea, and other opportunistic infections that come with it.