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“The incidents tend to oscillate,” said Herbert Hethcote, a professor emeritus from the University of Iowa who is a specialist in mathematical modeling of the spread of infectious diseases,

He said the growth of pertussis in Washington state has followed a pattern: As the population ages, the immunity level goes down because the vaccine is wearing off. The disease spreads and the cases grow until more people get the vaccine and the numbers go down again.

Hethcote said his daughter had whooping cough as an adult during the last spike of cases in Washington, four or five years ago. She coughed so hard she broke a rib and was sick for more than a month, he recalls. She never found out how she caught it but the experience raised awareness in his family that pertussis is not just a children’s disease.