As the article dances around, the problem is not typically random individuals falling for social media misinformation about vaccines, but communities where the importance of getting vaccinated doesn't spread. It's hard for officials to message straightforwardly, because you're not going to get a community to listen to you if you're simultaneously running around telling the rest of the country that the outbreak is their fault.
I don't really understand the question. They eliminated measles in the first place by convincing more of those communities to have higher vaccination rates than they have today.