Health officials in Westchester County, N.Y., reported on Friday a whooping cough outbreak involving 19 people, many of them children who had been vaccinated against the illness. The county health department said that the patients range in age from three months to 14 years, with many of them being playmates or classmates. Health Commissioner Joshua Lipsman noted that while the whooping cough vaccine does not make someone completely immune to infection, it does cause the illness to be less severe if someone contracts it.