“Our efforts to flatten the curve are starting — I say starting — to pay off even with the lag time in getting test results back from the lab,” Murphy said at his daily press briefing before quickly adding, “I use that word cautiously.”

The best case scenario is still quite grim.

New Jersey officials expect to see infections and hospitalizations peak between April 19 and May 11, according to models Murphy presented during the briefing. The state could see anywhere between 86,000 and 509,000 patients test positive, with hospitalizations ranging between 9,000 and 36,000.

“If we keep our current practice, we can get through our peak with the hospital beds we are preparing, the new wings, the reinstated buildings, the field medical stations,” Murphy said. “It will be tough, it will be stressful, but our health system can get through this intact.”

But any relaxation of the state’s social distancing order could quadruple the size of the surge, Murphy said, which would represent “a nightmare scenario on a good day.”

The more patients infected, the greater the strain on the state’s already meager stockpile of medical supplies.

One slide included in Murphy’s presentation put the state’s projected need for ventilators anywhere between 1,987 — well within its current capacity — and 7,811, or roughly double what New Jersey’s hospitals and emergency management team has on hand.

The number of intensive care beds needed to treat 9,000 patients hospitalized with Covid-19 is close to 2,300, the governor said. If that number swelled to 36,000, the demand for critical care beds would climb above 9,000.

As of Monday, New Jersey hospitals were treating 6,390 patients who have tested positive for Covid-19 or were awaiting test results, Health Commissioner Judith Persichilli said during the briefing. Almost a quarter of those patients — 1,505 in all — are being treated in intensive care units, she said.

The number of Covid-19 hospitalizations has climbed steadily over the last several days, underscoring the need for the state’s medical centers to expand their critical care capacity in anticipation of the peak.

Murphy said he spoke with President Donald Trump and Vice President Mike Pence shortly before Monday’s briefing and received an assurance that some New Jersey patients would be treated on the USNS Comfort, a 1,000-bed hospital ship docked at Pier 90 on New York City’s West Side.

“That news is literally hot off the press and I thank the president and vice president who were on the call together,” Murphy said, later adding that the state’s receipt of 500 additional ventilators — announced Sunday evening — also followed conversations with Pence.

The number of people in New Jersey who have died from Covid-19 complications rose by 86 on Monday, to 1003, while new positive cases increased by 3,663, bringing the statewide total to 41,090.

New Jersey’s mortality rate of known cases is quite high, around 2.4 percent, Persichilli said. Over time, she said, she expects that figure to fall to around 1 percent or 1.5 percent, but it’s likely state officials will never know the true statistic because of supply deficiencies across the testing regime.

New Jersey has wrestled with how to track the pandemic’s spread with only a small supply of tests since early last month, encouraging those who are “worried well” or exhibiting mild symptoms to seek care from their physicians before getting tested.

“What we don’t have is [data on] everyone at home with mild or moderate symptoms who are positive Covid-19,” Persichilli said. “We will probably never get tests on [those individuals].”

The data on who’s been tested is also somewhat incomplete, largely because of backlogs on swabs submitted to labs capable of performing the tests. The length of the delay varies, but Murphy and Persichilli have said it can sometimes take as long as two weeks for the state to receive data.

Quest Diagnostics, one of the largest commercial labs fielding swabs from New Jersey, announced Monday it had slashed its backlog by 50 percent since March 25. There are now 80,000 swabs in the queue across all 12 of its labs and wait times for patients in the New York City metro area and New Jersey are three days “or more,” according to a press release.

Even so, data collected by the state Health Department and analyzed by the Office of Innovation show that the growth rate for positive cases has started to decline, Noveck said.

The state’s also developed tools to determine where they expect to see more cases in the coming days and weeks. On Monday, Murphy said the state had been using location data from the state’s Covid-19 symptom self-assessment tool to identify potential hot spots in Passaic and Middlesex counties, with the latter suggesting the surge is starting to drift south from the New York City suburbs to an area many refer to as Central Jersey.

“We are seeing, particularly in Middlesex and Somerset [counties], which I consider central — it’s up to you — we see them as being stressed,” Persichilli said, adding that hospitals in Hudson County, which is directly across the Hudson River from New York City, will likely continue to be strained “for a couple weeks.”

“The curve is flattening. But this is no time to spike any footballs or take our foot off the gas,” Murphy said. “We still have a week and a half to go, at least, before we hit the peak. This is not over. And not by a long shot.”

As if to emphasize that point, shortly before the end of the two-hour briefing, Col. Patrick Callahan, superintendent of the New Jersey State Police, said he had requested 20 refrigerated trucks from the federal government.

New Jersey morgues may not be able hold the number of dead once the pandemic reaches its peak, particularly with funerals on hold in accordance with Murphy’s stay-at-home directive.

The trucks can store 1,680 bodies.