At the heart of the matter is a concept known as herd immunity. It means that the overall national rate of vaccination is not the only significant gauge. The rate in each community must also be kept high to ensure that pretty much everyone will be protected against sudden disease, including those who have not been immunized. A solid display of herd immunity reduces the likelihood in a given city or town that an infected person will even brush up against, let alone endanger, someone who could be vulnerable, like a 9-year-old whose parents rejected inoculations, or a baby too young for the M.M.R. shot. Health professionals say that a vaccination rate of about 95 percent is needed to effectively protect a community. Fall much below that level and trouble can begin.

Mass vaccinations have been described by the C.D.C. as among the “10 great public health achievements” of the 20th century, one that had prevented tens of thousands of deaths in the United States. Yet diseases once presumed to have been kept reasonably in check are bouncing back. Whooping cough is one example. Measles draws especially close attention because it is highly infectious. Someone who has it can sneeze in a room, and the virus will linger in the air for two hours. Any unvaccinated person who enters that room risks becoming infected and, of course, can then spread it further. Disneyland proved a case in point. The measles outbreak there showed that it is indeed a small world, after all.

What motivates vaccine-averse parents? One factor may be the very success of the vaccines. Several generations of Americans lack their parents’ and grandparents’ visceral fear of polio, for example. For those people, “you might as well be protecting against aliens — these are things they’ve never seen,” said Seth Mnookin, who teaches science writing at the Massachusetts Institute of Technology and is the author of “The Panic Virus,” a 2011 book on vaccinations and their opponents.

Mr. Mnookin, interviewed by Retro Report, said skepticism about inoculations is “one of those issues that seem to grab people across the political spectrum.” It goes arm in arm with a pervasive mistrust of many national institutions: the government that says vaccinations are essential, news organizations that echo the point, pharmaceutical companies that make money on vaccines, scientists who have hardly been shown to be error-free.

Then, too, Mr. Mnookin said, scientists don’t always do themselves favors in their choice of language. They tend to shun absolutes, and lean more toward constructions on the order of: There is no vaccine-autism link “to the best of our knowledge” or “as far as we know.” Those sorts of qualifiers leave room for doubters to question how much the lab guys do, in fact, know.

Thus far, the Disneyland measles outbreak has failed to deter the more fervent anti-vaccine skeptics. “Hype.” That is how the flurry of concern in California and elsewhere was described by Barbara Loe Fisher, president of the National Vaccine Information Center, an organization that takes a dim view of vaccinations. The hype, Ms. Fisher said in a Jan. 28 post on her group’s website, “has more to do with covering up vaccine failures and propping up the dissolving myth of vaccine acquired herd immunity than it does about protecting the public health.” Clearly, she remained untroubled that most health professionals regard her views as belonging somewhere in Fantasyland.