Pennsylvania’s top health official issued a broader mask mandate Tuesday, a bid to force people to wear face coverings as coronavirus case numbers continue to soar.

Imposing new rules to combat the surge without ordering shutdown-style restrictions, Health Secretary Rachel Levine ordered that people wear masks when with anyone outside their own households and directed that anyone entering from out of state must get tested for the coronavirus within 72 hours before arriving as of Friday.

She also told colleges and universities to implement and enforce testing and quarantine procedures and urged the commonwealth’s hospitals to “prepare now” for the possibility of being strained or even overwhelmed as soon as December.

If the state and public do not follow measures to quash the spread, Levine warned, Pennsylvania could run out of intensive-care beds in December and could reach 12,000 total virus-related deaths by January and 18,000 by March. More than 9,300 deaths in the state have been blamed on the virus.

“How Pennsylvania does in terms of this pandemic and whether we follow the [projections] or whether we don’t is going to come down to the actions of every single Pennsylvanian,” she said, citing the surge estimates based on University of Washington modeling.

By Tuesday, the state’s hospitals had more than 2,700 coronavirus patients — nearly as many as they did at the pandemic’s April peak. Two months ago, fewer than 500 virus patients were hospitalized, according to state data.

Violators of the mask mandate could face warnings or citations from local law enforcement agencies. But the new orders rely on the public’s cooperation, and they don’t go as far as the restrictions Philadelphia and other states have imposed in response to the fall surge.

It is difficult to know whether the United States would have experienced death tolls in the millions, she said, as some very early models predicted would occur if no restrictions were imposed. Those models were based on the information available then about a new and poorly understood virus.

“The models we have now presumably are going to be much better predictors than we had in March,” Sweet said.

Staff writers Laura McCrystal and Juliana Feliciano Reyes contributed to this article.

Correction: A previous version of this story misstated the timetable for mandatory testing for travelers entering Pennsylvania.

Nov. 18, 2020