Is the New York Times Offering A Misleadingly Bleak Depiction of Status of “Herd Immunity” in New York City?

Today's New York Times front page featuring a petri dish chart for its home city of New York, saying that those with antibodies in the city are scarce, while it describes the potential of herd immunity as a "distant objective" and cautions that there is no safety from the spread.  But,the presentation of its NYC statistic is suspiciously inaccurate.

[NOTE: This article was updated July 2, 2020 to refer to the estimated lag times it takes for Coronavisrus antibodies to develop thus making it important to look back and consider April's random testing of New York City residents as being a snap shot of the status of the infection's spread earlier in the month of April.] 

Front page, above the fold, upper right there is a big prominent chart in the physical copy of today’s New York Times to go along with the headline: “In battling Outbreak, Herd Immunity,  Remains Distant Objective,” by Nadja Popovich and Margot Sanger-Katz May 28, 2020.  (The Times internet version of its headline is currently “The World Is Still Far From Herd Immunity for Coronavirus”)

That chart has a dramatic petri dish-looking dot diagram labeled to say that it shows that in New York City 19.9% of the population have covid antibodies and in the smaller print adding “May 2nd.”  The chart has its own bold headline label: "Still not Safe From The Spread."

The print version of this article provides this text:

In New York City, which has had the largest coronavirus outbreak in the United States, around 20 percent of the city’s residents have been infected by the virus as of early May, according to a survey of people in grocery stores and community centers released by the governor’s office.

But, in actuality, the study results just described by the New York Times as fixing this percentage in “early May,” were reported in the New York Times April 23rd: "1 in 5 New Yorkers May Have Had Covid-19, Antibody Tests Suggest" By J. David Goodman and Michael Rothfeld, April 23, 2020-

In New York City, about 21 percent tested positive for coronavirus antibodies during the state survey.

That article also stated:

State officials said the test had been calibrated to err on the side of producing false negatives — to miss some who may have antibodies —

That April Times article didn’t say then when in April the study had been conducted, perhaps an unusual skip, saying only that the study had involved tests conducted “over two days, including about 1,300 in New York City, at grocery and big-box stores” that had then been “sent to the state’s Wadsworth facility in Albany” and generated an announcement about its results on Wednesday, April 22, 2020 (publicly discussed by NYS Governor Cuomo the next day).  All of this would push back somewhat the unknown date that the random study was actually conducted.-- 

-- Pushing things back further in assessing things is that antibodies for Covid are not said to develop for one-to-three, or even more weeks after becoming infected.  That means that the random sample snap-shot involves a lag.  If you push things back two weeks plus a few days to compensate for all this, that means that the snap shot may best reflect a date of about Friday, April 3rd.  The "confirmed case" for New York City count the New York Times gave on April 2nd was 52,000.  May 29th the New York Times gives a "confirmed case" count figure of "205,854."

While the results of that mid-April random study were intriguing, there seems to be no hint of another updating random study since.

Reporting on rates of coronavirus infection is a moving target.  The virus is capably of spreading at an exponential rate, which is clearly what it did in the beginning in many locations including New York City.  At about the time of the NYC random study it had been reported (April 15, 2020 on Democracy Now) that the milestone of 10,000 deaths from the virus in New York City had just been reached.  The death toll in New York City is now more than double that number at about 21,000.  Increases in and accelerations of the infection rate precede the reported death rate.

So, if random testing were done, now, at the tail end of May, probably about six or more weeks since the last random tests were conducted, where would the current antibody detection rate in New York City be?  That would have to take into consideration that April, followed by the first half of May was the month during which the virus was spreading most rapidly in New York City to create new infections.  Would it be more than double the April random test figure the Times splashed on its front page incorrectly saying the figures were from May as it based it article on that?  The charts below, from the New York Times itself, are elucidating in considering this:

Remember, when looking at these charts, that although the numbers are consistent for what they are, the "confirmed case" figure is always just a tiny fraction of the number of the people who have actually contracted the virus.  That's something that is widely acknowledged.  So, for instance, the April 2nd date when there were a reported about 52,000 confirmed cases is the approximate date when random testing indicates that probably about 21% of New Yorkers had had the virus.  By the May 29th date that the New York Times gives a "confirmed case" count figure of "205,854" for one can expect, following at least somewhat proportionally, a fairly major increase in the actual cases.
 
So the question I ask is: Is the New York Times offering a misleadingly bleak depiction respecting the possibilities of when the protections of herd immunity may be kick in for those who live in New York City, the Times' home base?  Still a "distant objective" that new Yorkers are "far from"?