Worries about a link between autism and vaccines are leading many parents to refuse vaccines for their children. But in turn, those children are far more susceptible to illness, at least when it comes to whooping cough, researchers say.

According to a new study published in the journal Pediatrics, children who do not receive vaccines are 23 times more likely than their vaccinated peers to get whooping cough and that spells big problems for public health as the number of cases of the disease rise.

In 2004, there were 26,000 cases of the disease in the United States compared with just 1,000 cases in 1976. The increase in the number of cases correlates with an apparent rise in the number of parents choosing not to vaccinate their children, researchers say.

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Some people believe there is a link between vaccines and the diagnosis of autism, though government agencies and the scientific community agree that no such link exists.

“This study helps dispel one of the commonly held beliefs among vaccine-refusing parents: that their children are not at risk for vaccine preventable diseases,” said Jason Glanz, a senior scientist at Kaiser Permanente’s Institute for Health Research, who led the study. “It also shows that the decision to refuse immunizations could have important ramifications for the health of the entire community. Based on our analysis, we found that one in 10 additional whooping cough infections could have been prevented by immunization.”

Whooping cough, also called pertussis, is a bacterial disease marked by violent coughing. It can be deadly, particularly in young children.

Typically children are vaccinated against pertussis as part of a three-part series of vaccines given in a child’s first 18 months of life.