“The very large outbreaks we’ve seen around the world often started with a small number of cases,” said Dr. Anne Schuchat, director of the agency’s National Center for Immunization and Respiratory Diseases.

Officials in three counties in the Phoenix area — Maricopa, Gila and Pinal — have already asked residents who have not been vaccinated and who might have been exposed to stay home from school, work or day care for 21 days. Schools in some other states are considering more formal bans on unvaccinated children.

“This is a critical point in this outbreak,” the Arizona state health director, Will Humble, wrote on his blog. Any missed cases, he wrote, could cause “a long and protracted outbreak.”

Each case so far has spawned an exhaustive public health response.