More U.S. hospitals are requiring masks and limiting visitors as health officials face an expected but still nasty post-holiday spike in flu, COVID-19 and other illnesses.

While many experts say this season likely won’t prove to be as deadly as some other recent winters, it still could mean hundreds of thousands of hospitalizations and many thousands of deaths across the country.

New York City last week instituted a mask mandate for the city’s 11 public hospitals. Similar measures were ordered last week at some hospitals in Los Angeles and Massachusetts. Some hospitals reinstated masking rules for employees months ago, in anticipation of a seasonal rush of sick people.