(CNN) Social distancing efforts to stop the spread of coronavirus in New York, the epicenter of the American outbreak, are showing signs of working, Gov. Andrew Cuomo said on Wednesday.

Estimates from Sunday showed coronavirus hospitalizations were doubling every 2 days, he said. But Monday's estimates showed hospitalizations were doubling every 3.4 days, and Tuesday's estimates showed hospitalizations were doubling every 4.7 days.

"That is almost too good to be true. But the theory is given the density that we're dealing with, it spreads very quickly, but if you reduce the density you can reduce the spread very quickly," he said.

In addition, New York had 4,790 new confirmed coronavirus cases on Tuesday, a decrease from the 5,707 positive tests on Monday. Though just one data point, it was the first time in over a week that new cases were lower than the day before, according to the state's count. Cuomo cautioned the outbreak is expected to peak in about two to three weeks.

Overall, more than 30,000 people have tested positive for coronavirus in New York, including 17,856 cases in New York City, the country's largest and most densely populated city. The state tally is more than half of the US total, Cuomo said.