I believe it has a longer incubation period than other childhood diseases, and that is why they thought all the toys and clothing of a child had to be destroyed: they thought the germs were living longer than other germs.
The long incubation is part of the problem, so I’m curious about why the article didn’t mention that.
Measles for example has a fixed incubation period (onset of the rash) of approximately two weeks (other studies give a range of 10 to 12 days w/wo the rash). In my mathematical modeling class I used 14 days for the incubation period. My research project was a modified SEIR model that did a good job of mimicking empirical data. My model will not work for scarlet fever, because of the random nature of the incubation period.
In all honesty we really don't know the real incubation period for measles, scarlet fever, or many other childhood diseases.