ALBANY - The total number of deaths in New York due to the coronavirus reached 13,869 on Saturday, and the number of positive cases exceeded 242,000.

New York has the most confirmed cases in the nation, in part due to its aggressive testing.

Initially, Westchester County had the most cases in New York because of a hot spot that developed in New Rochelle, about 30 miles north of New York City.

But since then, the city has by far the most cases due its size of 8.5 million people and its close density of residents.

Gov. Andrew Cuomo has stressed that the more people that are tested, which is the goal, the more positive results the state will find.

Indeed, the confirmed cases have soared as the number of tested exceeded 617,000 statewide. The aim of the tests to isolate sick patients and look for trends on where the virus is spreading.

"The more tests you take, the more positives you find, and I give this caution because I think people misinterpret the number of new cases," Cuomo said.

"They take that number of new cases as if it is reflective of the number of new cases, the spread. It is not."

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New York has commissioned more than two dozen private labs to conduct testing, and a series of state-run, drive-up testing sites have been set up in the New York City metropolitan area.

So New York has tested more people than any state in the nation, and, Cuomo said, more per capita than China or South Korea.

While testing rates and confirmed cases are important, state officials said the critical number to watch is the rate of hospitalizations.

The concern is that as the number of cases rise, so too will hospitalization rates, which may very well overwhelm the health-care system.

That's why New York is scouring the state and the globe for more medical supplies, especially masks and ventilators.

The hospital rate in New York has run between 14% to 23% each day.

Cuomo said estimates worldwide show that 40% to 80% of the population is going to be infected.

The effort, he said, is to slow the rate so the hospital system can handle the increase in patients.

To slow the rate and to limit those who are infected, the state ordered a shutdown March 19 of non-essential businesses and urged people to stay in their homes to the extent possible.

If the estimates hold, that would be between 7.8 million and 15 million New Yorkers would be affected before the virus runs its course — which will likely be months.