Both nursing home residents and staff need flu shots to prevent potentially deadly flu outbreaks, a new study finds.

If more than 55% of the staff and more than 89% of the residents were vaccinated, outbreaks of influenza-like-illness were reduced by 60%, according to a study by the nonprofit Rand Corp.

Vaccinating elderly residents or staff alone did not decrease the number of flu outbreaks, the study found. Only about 67% of the elderly people who should get flu vaccines every year actually get vaccinated, according to the CDC. Fewer than 40% of healthcare and nursing home workers get vaccinated.