Ms. Carlson said she understood what was at stake. “I cannot deny that my child can put someone else at risk,” she said.

In 1991, less than 1 percent of children in the states with personal-belief exemptions went without vaccines based on the exemption; by 2004, the most recent year for which data are available, the percentage had increased to 2.54 percent, said Saad B. Omer, an assistant scientist at the Johns Hopkins Bloomberg School of Public Health.

While nationwide over 90 percent of children old enough to receive vaccines get them, the number of exemptions worries many health officials and experts. They say that vaccines have saved countless lives, and that personal-belief exemptions are potentially dangerous and bad public policy because they are not based on sound science.

“If you have clusters of exemptions, you increase the risk of exposing everyone in the community,” said Dr. Omer, who has extensively studied disease outbreaks and vaccines.

It is the absence, or close to it, of some illnesses in the United States that keep some parents from opting for the shots. Worldwide, 242,000 children a year die from measles, but it used to be near one million. The deaths have dropped because of vaccination, a 68 percent decrease from 2000 to 2006.

“The very success of immunizations has turned out to be an Achilles’ heel,” said Dr. Mark Sawyer, a pediatrician and infectious disease specialist at Rady Children’s Hospital in San Diego. “Most of these parents have never seen measles, and don’t realize it could be a bad disease so they turn their concerns to unfounded risks. They do not perceive risk of the disease but perceive risk of the vaccine.”

Dr. Sawyer and the vast majority of pediatricians believe strongly that vaccinations are the cornerstone of sound public health. Many doctors view the so-called exempters as parasites, of a sort, benefiting from the otherwise inoculated majority.