The measles outbreak which started at Disneyland appears to be continuing to spread across the United States, alarming even parents of children vaccinated against the disease.

Officials in Michigan confirmed on Friday that an adult in Oakland County had been diagnosed with measles, suggesting the outbreak is zigzagging east from the theme park in California.

Six other states – Utah, Washington, Colorado, Oregon, Nebraska and Arizona, plus Mexico – have recorded cases since a young woman, dubbed patient zero, fell sick at Disneyland just before Christmas.

There are now an estimated 100 cases in the US, most in California.

Hospitals and doctors’ offices in the state expect a continued spike in requests for vaccinations and advice.

The outbreak has shone a light on parents who delay inoculating, or refuse to inoculate, their children over concerns about vaccine safety. They dispute assurances from the medical establishment that vaccines are safe and effective.

Most of those infected have not been vaccinated. However, a small number has fallen ill despite inoculation – worrying some who fear their inoculated children may succumb.

“People who have had the shot can get the virus. That to me is terrifying,” Cassandra Politzer Wiseman, a mother in Malibu with three inoculated children, said on Monday. Her 17-year-old son played soccer across southern California, increasing his chances of exposure, she said.

A freshman baseball coach at nearby Santa Monica high school was diagnosed with measles last week.

Politzer Wiseman faulted parents who did not inoculate their children for spreading the virus. “We’ve stopped believing in science. That makes me furious.”

She also faulted ABC for giving Jenny McCarthy, a celebrity noted for anti-vaccine views, a talkshow. “They shouldn’t be promoting people who peddle ghost stories and urban myths.”

At least five of California’s 70 reported cases were vaccinated. Federal guidelines have recommended two shots since 1989. Before that it was just one shot. Many of those immunised in the 60s, 70s and 80s lack the second, booster shot.

An immunised 22-year-old woman infected four other immunised people in an outbreak in New York City in 2011. Doctors, however, strongly urge vaccination as the best way to stay safe, calling it 99% effective. Studies have debunked the vaccine’s alleged link to autism.

The Centers for Disease Control and Prevention (CDC) calls measles, a virus that lives in the nose and throat, the “most deadly of all childhood rash/fever illnesses”. About 90% of those who are not immune will become infected if they come close to an infected person, according to the CDC.

An estimated 20 million people worldwide contract measles each year. In the US, the CDC typically expects only 220 cases. Last year there were 644, a nearly two-decade high which looks set to be exceeded this year.

Anti-vaccine sentiment is growing in the US, especially in wealthy areas such as coastal Orange County, which sits alongside Disneyland.

Much media coverage has focused on the anti-vaccination movement’s threat to “herd immunity”, a level of inoculation high enough to protect even the most vulnerable, including newborns, the elderly and those with auto-immune conditions.

California is a lightning rod for such debate because it has unusually lax rules permitting parents to opt out of vaccination for non-specific personal beliefs. It also has a relatively high population of affluent, protective parents which has tapped into an online community of doubters, critics and conspiracy theorists.