Measles doesn't scare these people, for the most part, as they're confident they can fight the disease off.
The way vaccines are going, we can find a common cold vaccine, and any "outbreak" of the common cold will result in the same hysteria. The survival rate for measles is actually quite high. Schools are responding appropriately. People who know they're at risk are responding appropriately. This isn't going to turn into mass deaths.
I support the unpopular opinion that the growth of anti-vaxers is primarily caused by improvements in technology and a failure of modern medicine.
YouTube is filled with examples of "vaccine injuries" - ASPCA-style image slide shows of kids before and after receiving a vaccine. The effects are scary, and not proven uncorrelated to the vaccine itself. Antivax communities are more comfortable exposing their families to risk of measles than risk of the vaccine injury, despite the risk being much, much lower. This is irrational, but also understandable human behavior, since the prognosis is perceived to be worse in a vaccine injury case than in a measles case.
The recordkeeping of vaccine injuries are also horrible, so trying to make any rational, numbers-based argument is impossible.
Ultimately, the spread of vax-injury videos is no different than the spread of the Eric Garner video on facebook. That's something we never would have heard about 10 years ago, and would never have caused such a national uproar. People are acting irrationally despite the very low chance of being affected.
Bottom line - if you want to stop anti-vaxers, you need better prevention (pretty much elimination) of vaccine injuries. The anecdotal evidence against vaccines can't be on Youtube or people will continue to avoid them. Science is working on it, but we're not there yet. For now, I think we need to be realistic that measles and other "eradicated" diseases will have a growth in occurrences. Chances are we'll see very few deaths or long-term effects, though.