Joe Gawronski said concerns about the coronavirus outbreak hit home on March 13.

“Our attitude has changed markedly since Friday,” he said of his family’s reaction to the viral outbreak causing the disease COVID-19.

The president of New York brokerage firm Rosenblatt Securities lives in Summit, N.J., a suburb a little more than 20 miles west of the New York Stock Exchange in lower Manhattan, and his children’s school district announced on March 12 that it would be closing until at least April 6 as more than two dozen confirmed cases of the pandemic virus cropped up in the Garden State.

After a trader and an NYSE worker tested positive for the coronavirus, the exchange said late Wednesday that it was moving to fully electronic trading beginning Monday.

Gawronski recalled that things hadn’t change much immediately after the school closure; he even allowed one of his kids to have a sleepover on Friday, but over the subsequent days things changed starkly.

“There were no play dates, no parks … by yesterday my kids weren’t going out all,” he said.

That may be why, Gawronski, one of the head honchos at the NYSE’s largest floor broker, harbored some ambivalence as the exchange wrestled with the decision of whether to keep its trading floor open during the pandemic that has spread rapidly across the globe, causing New York City to consider drastic measures to contain the deadly pathogen.

“It’s a tough call,” Gawronski said, adding that, before its Wednesday decision the exchange seemed to have “struck the right balance,” emphasizing that the initial measures taken by the NYSE had assured him.

NYSE officials had been adamant about the need for the exchange to remain open and to maintain a staff of flesh-and-blood traders on the floor even as New York City Mayor Bill de Blasio hinted on Tuesday at the possibility of tighter restrictions on the movement of the city’s residents to mitigate the contagion, which has infected about 200,000 people around the world and claimed nearly 8,000 lives, according to data compiled by Johns Hopkins University.

The spread of the disease is in its nascence in the U.S. and in New York, where 13 people have died, and measures are being undertaken to prevent those who do take ill from overrunning public health facilities all at once.

New York Gov. Andrew Cuomo on Tuesday warned that the outbreak could peak over the next 45 days and the roughly 53,000 hospital beds in New York state won’t be sufficient for the tens of thousands who will likely fall ill.

A number of other exchanges have indefinitely closed their trading floors and reverted to electronic dealings as a precaution amid the outbreak, including the CME Group Inc. CME, -0.97% , owner of the Chicago Mercantile Exchange and the Chicago Board of Trade. Cboe Global Markets CBOE, +2.14% also has temporarily closed its trading floor, as has the London Metal Exchange, according to FNLondon.com.

On top of that, a number of major rivals had called out the NYSE for keeping its trading floor open, according to a Wall Street Journal report. “I find it kind of amazing that the NYSE trading floor is still open,” Terrence Duffy, chief executive of Chicago futures-exchange giant CME, said. “I thought we were not supposed to have 50 people or more in one location.”

Most trading at those firms occurs electronically, so having traders on hand isn’t critical to their operations.

Stacey Cunningham, the NYSE Group’s president, has seemingly been locked in a battle on twin fronts, with some advocating for trading-floor closures, while others have floated the notion of a marketwide closure, which she has adamantly resisted. The Wall Street Journal reported that several executives raised the possibility of a shutdown for financial markets during a conference call with Bank of England Gov. Andrew Bailey. However, they concluded such a closure wouldn’t be helpful, the paper reported.

“There’s a very big difference between closing the floor and closing the markets overall,” Cunningham told CNBC during a Monday interview after the Dow Jones Industrial Average DJIA, -0.87% and the S&P 500 index SPX, -1.11% put in their worst daily drops since the 1987 crash.

“We could close the floor and continue with the market open and continue trading,” Cunningham said.

She said, however, that physical traders have a vital role to play in smoothing out the volatility that has reared up on Wall Street, with the Cboe Volatility Index VIX, -2.38% spiking of late to multiyear highs.

“Our model leads to trading with less volatility,” Cunningham told the business channel. “So right now the people on the floor are proud to come in and provide that service of dampening volatility around the edges.”

Prior to its more definitive action on Wednesday, the NYSE had taken a number of measures intended to prevent the spread of the virus, including restrictions on outside visitors, temperature checks of people coming to the floor and on-site testing of personnel for COVID-19, if screening indicates the need to escalate diagnostic efforts.

It wasn’t clear that those measures would suffice to limit the spread of the illness.

“It may be time for the NYSE to revisit the decision,” James Angel, professor at Georgetown University and an expert in market structure, told MarketWatch on Sunday of the trading floor’s remaining open. “I’m not a public health expert; I’m a market-structure expert. But maybe we need to see the exchange take this [illness] more seriously because the NYSE has the capability to run without the floor.”

Cunningham declined to be interviewed for this article but through a spokeswoman said “members of the NYSE trading-floor community choose to come into the exchange because they believe in our mission to serve issuers and investors during all market conditions.”

“To keep the market open and safe,” the statement continued, “the NYSE has worked closely with local, state and federal authorities to develop and implement an extraordinary set of protocols, which include social distancing, deep cleaning, travel screening, mandatory temperature checks and symptom scans, for everyone entering our building.”

Jonathan Corpina, senior managing partner at Meridian Equity Partners and an NYSE member firm, said he was content with the measures the exchange had taken to protect traders, including a deep cleaning of the trading floors and work areas. Those took place over the weekend.

“The measures and precautions are the right steps,” he said. “If I didn’t feel comfortable with that I wouldn’t be there,” said Corpina, who commutes to work from Armonk, N.Y., about 40 miles northeast of the NYSE.

Gawronski, who himself doesn’t work on the floor directly, does commute daily from Summit to Wall St., near the NYSE headquarters building. He said floor traders are a patriotic, duty-bound bunch who feel as if they have a responsibility to stay on the front lines even as markets reel.

The legacy of endurance and patriotism for traders can be traced back to 1792, when what would come to be the NYSE was founded, and 1817, when the New York Stock Exchange Board was formed.

In 1918, America and the world were under siege by another pandemic, the so-called Spanish flu, which infected roughly a third of the world’s population, killing some 50 million to 100 million people, according to reports.

Gawronski pointed out that the NYSE hadn’t closed a century ago amid that worst outbreak of the modern era. “They have to balance the health and safety of not only the people who work there, but broader social responsibility,” he said of the NYSE today.

Gawronski said, however, that the human component of NYSE floor traders is very important. That is particularly the case near the close of marketwide trading. Only NYSE floor traders can use so-called D-orders, or D-qotes, which can help to resolve imbalances during the final minutes of a trading day.

In times of extreme volatility, “market quality benefits from the brokers … but I’m not a doctor or a scientist, so that doesn’t mean that I’m right that the exchange should stay open,” he said.

A recent research note from J.P. Morgan & Chase Co., published on March 16, makes the case that the reversion to all-electronic trade by the Cboe hurt its options trading volume in the S&P 500 and in the volatility index in the near term. However, the researchers, including Kenneth Worthington, Jenny Ni and William Cuddy, forecast that there would be benefits over the longer term.

“Despite near-term challenges and more tepid volumes versus recent weeks, we see the migration longer term to electronic trading of SPX and VIX as positive for Cboe trading and earnings growth,” the analysts wrote.

For its part, the NYSE had been testing its all-electronic contingency plan for weeks, according to the Wall Street Journal. The last time the floor brokers weren’t present at the exchange was during Superstorm Sandy in 2012, when flooding knocked the entire exchange offline for a period.

Gawronski speculated it’s possible that time could come sooner because events are evolving so rapidly.

“I wouldn’t be surprised at some point to see the exchange floor shut,” he said, referring to government orders that could potentially be invoked, but until virtually the final moments he hoped the NYSE would “fight to keep the exchange open.”

“It’s a balance,” he allowed, “and it’s changing constantly.”