There is increasing evidence that New York City and New York state are turning a corner in their efforts to fight back COVID-19, and the timing suggests that the shifts may be a result of social distancing measures.

Whether the state and city have merely flattened the curve to a plateau or actually begin to turn it around is somewhat ambiguous. In his daily press conferences, New York Gov. Andrew Cuomo has described recent data on hospitalizations as good news and emphasized that the curve has become quite flat. On Tuesday, for the first time, New York reported a net decline in hospitalizations, although it remains to be seen whether the trend can be sustained.. The number of people reported as dying from COVID-19 has also been at a plateau in recent days.

But data on the share of New Yorkers who are testing positive for COVID-19 suggests that the curve has not merely flattened but probably begun to turn down. Among tests conducted Monday, April 13 (and reported on Tuesday afternoon), 34.5 percent were positive, down from a peak of 50.4 percent on Tuesday, March 31. The decline in the share of positive tests has been fairly robust across most parts of New York state, including in all five New York City’s five boroughs, although some more clearly so than others.

Still, if the decline has been steady, it has so far been slow. That may imply that while current social distancing measures are enough to gradually decrease the number of new cases in New York, the number of new cases may continue to simmer at relatively high levels for several weeks or longer — and that they could increase again if these measures are relaxed.

All the numbers in this article come from publicly available data from the New York State Department of Health. (There’s also a downloadable version.) The state has been releasing detailed reports on the number of positive and negative tests conducted each day in each county in the state, including in the boroughs of New York City (which are each their own counties).

Information on the overall number of tests — both positive and negative — is critical, because without it, apparent changes in the number of cases can reflect changes in testing volume rather than the actual incidence of disease in the population. In tests conducted on Sunday and disclosed on the state’s website on Monday, for example, 6,337 New Yorkers were found to have COVID-19, the lowest number of new cases since March 24 and a seemingly huge decline from the 10,575 new cases found on Thursday. (The number ticked up again a bit in tests conducted on Monday, to 7,177.) However, perhaps because of Easter, only 16,756 tests were conducted on Sunday, the lowest number since March 31. (By comparison, 26,336 tests were done on Thursday.) There are many such fluctuations in the data:

Evaluating the share of tests that turned up positive can paint a clearer picture. The rate of positive tests was climbing statewide through March 31 but has been falling slowly since then.

It turns out that this Sunday was a pretty good day for New York. The share of tests returning positive results on Sunday was relatively low (37.8 percent) — in fact, the lowest in almost three weeks up to that point (since March 25), although Monday’s figure was lower still. It just wasn’t quite as good a day as the raw numbers imply because of the relative lack of testing.

Adjusting for testing volume doesn’t answer every question. It could be that New York’s criteria for getting tests are becoming more liberal, or more conservative, which could affect positive test rates. These tests are hardly coming from a random sample of the population, in other words.

The still-high rate of positive tests among those who are being tested suggests that there are probably a very large number of undiagnosed cases in New York (as there are in other places). It may even be that literally millions of people in New York City have or had COVID-19. Testing of pregnant women at one NYC hospital late last month and early this month, as reported in a letter to the New England Journal of Medicine, found that around 14 percent of asymptomatic women had COVID-19, and that was at an earlier point in the epidemic than the one we find ourselves in now.

Still, across most of the scenarios that I described in my earlier article on testing, the share of people who tested positive was a more accurate reflection of the shape of the epidemic curve than the raw number of positive tests was without adjusting for testing volume. (Feel free to download our Excel sheet and explore your own assumptions.)

Furthermore, changes in the share of positive tests in New York state are not merely a reflection of where in New York those tests are being conducted. Since upstate New York has a lower rate of positive tests than New York City, for example, doing more tests upstate but fewer in New York City could artificially depress the statewide positive test rate. That is not what’s happening here, however. Instead, if we break New York into three parts, we find a decline in the rate of positive tests in each one.

In New York City — applying a trend line to smooth out slight fluctuations from day to day — the share of positive tests has declined from a peak of around 57 percent on March 30 to around 42 percent now. In five suburban counties that are part of the New York City metro area — Suffolk and Nassau Counties on Long Island, and Westchester, Rockland and Putnam Counties in the Hudson Valley — positives have fallen from a peak of around 50 percent on April 1 to 38 percent now. And in the rest of the state — which I’m referring to as upstate New York, though the definition of “upstate” is controversial — positives peaked at around 22 percent on April 2 and have now fallen to about 17 percent.

These communities haven’t followed exactly the same curves. The suburbs were home to some initial, very bad outbreaks. However, the city then had steeper, sharper growth and a higher but slightly earlier peak than the suburbs.

In upstate New York, the rate of positive tests was never as high as it was in the city or the suburbs, but it also hasn’t declined as much.

The five New York City boroughs have also had different trajectories. Queens had the highest peak, but has since seen the steepest decline. Manhattan had a lower rate of positive tests than the other boroughs, although that could reflect the fact that residents of Manhattan are wealthier and could find ways to get tested even with limited symptoms.

Staten Island has followed a slightly worrying path, with the rate of positive tests having declined somewhat from their peak, but then leveling off rather than continuing to decline as sharply as in the other four boroughs and in the suburbs. Staten Island is home to many essential service workers such as police and firefighters who are testing positive for COVID-19 at high rates.

But overall, the news is positive in New York. It’s also a sign of the importance of social distancing — which means that the rates of new cases could increase again if measures are relaxed.

If the peak in the rate of positive tests came on or around March 31, it’s likely that the peak in actual infections came sooner than that — probably two or perhaps even three weeks sooner, given the lag between when people get infected and when they become symptomatic, and how long it takes for symptomatic people to get tested and for their tests to show up in the data. That would mean it came in mid-March, a time when New York City was — belatedly, according to some public health officials — closing schools, along with bars, restaurants and other businesses.

The governor’s statewide stay-at-home order, meanwhile, didn’t formally begin until the evening of March 22, which could be reflected in the slightly later peaks outside of New York City.

The decline in the rate of positive tests has not been especially steep, however — at least not until the past two days, when it was sharper. If taken at face value, it would imply that the effective reproduction number (sometimes called R), or how many additional infections are produced by each infected person, is below 1, but perhaps only slightly below 1. When that number is above 1, the number of new infections will continue to increase, while if it’s below 1, the number of new infections will decrease. But if the reproduction number is close to 1 — say, 1.1 or 0.9 — the increases or decreases will be gradual, with a long, relatively flat plateau rather than a sharp peak.

We don’t know for sure yet whether New York is going to follow that course. In Italy, the decline in the rate of positive tests was initially fairly modest, producing a plateau for a week or two, before later picking up steam.

Warmer weather could also help, although the evidence for this is mixed. There is also a lot of uncertainty about how many people in New York ultimately have or had the coronavirus. If many people had it — as implied by the New England Journal of Medicine letter — then herd immunity could potentially play some role in lowering R, though likely not enough to reduce it below 1 on its own until a large share of the population has become immune.

It’s perhaps more likely, though, that New York has been beating COVID-19 by a relatively thin margin so far, and therefore it doesn’t have a lot of margin for error. That’s a lot better than the alternative case where the city and state were losing the fight and the number of hospitalized patients continued to rise at their earlier rates. But it also means that city, state and regional leaders will have to be smart about reopening the economy and relaxing social distancing measures.