A severe outbreak of whooping cough is hitting the Bay Area, raising concerns among local health officials that the preventable disease is spreading in communities where parents are reluctant to vaccinate their children.

The jump in cases across the state prompted health officials on Wednesday to declare the outbreak an epidemic. In the Bay Area, cases of whooping cough—otherwise known as pertussis—are up nearly sixfold to 173 through May this year compared with the same period in 2009. Statewide,...