(CNN)More than 100 hospital workers in Boston have tested positive for coronavirus, officials at three facilities in the city told CNN.

That news comes as medical officials around the country express fears that hospitals will run short on staff as workers contract the virus from ill patients, even as the rate of sick people going to hospitals still is increasing.

The 100-plus workers who tested positive are at three Boston hospitals. The numbers were reported Wednesday evening by these facilities:

• Brigham and Women's Hospital -- 45 employees

• Massachusetts General Hospital -- 41 employees

• Boston Medical Center -- 15 employees

"Employees who have tested positive are not working until after they have been cleared by occupational health services," Brigham and Women's Hospital spokeswoman Serena Bronda told CNN. Massachusetts General Hospital believes most of its coronavirus-positive employees contracted the virus somewhere other than the hospital, representative Terri Ogan said.

That belief comes from "hospital data, our broad implementation of CDC-guided infection control procedures throughout the hospital, and the extent of community spread now ongoing in Massachusetts," Ogan said.
Doctors and politicians around the country have warned about staff shortages that could come eventually as hospital staff get sick and temporarily remove themselves from the workforce to convalesce. States such as New York have called on retired medical workers to be ready to serve as backup staff.