They are the sort of parties — drawing throngs of maskless strangers to rave until sunrise — that local health officials say have been a notable contributing factor to the soaring number of coronavirus cases in Florida, one of the most troubling infection spots in the country.

On Belle Meade Island, neighbors fear the large numbers of people going in and out of the house parties are precisely what public health officials have warned them about.

The city of Miami and the Miami-Dade Police Department shut down a party at the house just before midnight on Wednesday, a spokesman for the department said.

But the quest to end parties and other social gatherings has gained new urgency because of the exploding coronavirus in Florida, which reported more than 10,000 new cases on Sunday.

The state’s contact tracers, already overwhelmed by the surging number of new cases, have found it especially difficult to track how the virus jumped from one party guest to the next because some infected people refused to divulge whom they went out with or had over to their house.

Glenn Morris Jr., director of the Emerging Pathogens Institute at the University of Florida in Gainesville, a college town where local officials have begged students to stop partying.

In Miami, the city attorney plans to sue the owner of the Belle Meade Island party house this week, citing repeated “illegal activity.” Local officials have not publicly disclosed any case of the virus traced to the house, whose owner could not be reached for comment.

The contact tracing effort was intended to be comprehensive.

Human nature, however, has made it frustratingly narrow, its limitations amplified in Florida by the state’s failure to hire sufficient contact tracers, test everyone who has shared close quarters with infected people and isolate all of those who test positive, experts say.

The Florida Department of Health has about 1,600 students, epidemiologists and other staff doing contact tracing, and it has hired a contractor to bring on 600 more people, for a total of 2,200.

That is about a third of the roughly 6,400 tracers that will be needed to meet the target of 30 tracers per 100,000 people recommended by the National Association of County and City Health Officials.

With so much community spread, trying to trace the contacts of every positive case becomes unrealistic, several public health officials said.

“We may have to change the priorities on tracing as the numbers continue to increase, because at some point it is like drinking out of a fire hose,” said Dr.

He has traced some contacts himself and found that many of the cases emerged from people going out to dinner and parties.

Dalton Price, a recent college graduate who has been hired to do contact tracing in Daytona Beach, said he and the other tracers used to have a handful of new cases to call each day.

Officials in Miami-Dade, which recorded more than 1,600 cases on Thursday, wanted to pay for additional contact tracers to work locally.

But because they must be hired by the state, the county has been unable to grow the contact tracing force on its own.