NEW YORK (NYTIMES) - One woman in Harlem who wanted to be tested was told by healthcare workers not to worry about her coronavirus-like symptoms. In Brooklyn, a woman had to wait to get tested until her mother tested positive for the virus. One doctor at a statewide hospital network has turned away patients who probably had the coronavirus because they did not meet the current testing criteria.

President Donald Trump has proclaimed that anyone who wants to get a coronavirus test can. Governor Andrew Cuomo has declared that the state should be testing 1,000 people a day.

In New York, at least, the reality seems far more complicated.

Numerous interviews with doctors, hospital administrators and health officials this week revealed a confused and often troubled testing system in New York that has left many people who believe that they have been exposed to the coronavirus deeply frustrated.

The accounts suggest that the state and local governments have at times struggled to roll out one of the most effective means for responding to the epidemic: widespread testing.

Fewer than 2,000 people in total have been tested since New York was approved to test in state in late February, even with an escalation in testing in the last several days, according to officials.

For now it appears that a large majority of New Yorkers who end up having the coronavirus are likely to not know it during the duration of their illness because testing is so limited.

And without much ability to detect cases or track their spread, it is difficult to know what mitigation strategies are working or when it is time to try more aggressive measures.

On Wednesday, Mr Cuomo acknowledged that the testing shortage was having a significant effect on the state's effort to curb the outbreak.

He said he had asked 28 private labs in the state to "get up, get running and start moving forward with testing" in order to "greatly increase our testing capacity".

Those private labs would still need federal approval in order to begin testing, Mr Cuomo said.

"We can't just wait anymore," Mr Cuomo said. "It's compounding the problem."

Mr Cuomo had said last week that he wanted to test 1,000 people per day within a week.

Other states have experienced difficulties getting people tested quickly, but the issue appears to be especially pronounced in New York, which now has one of the largest clusters of coronavirus cases in the country.

The frustration is compounded by a confusing morass of local, state and federal guidelines about when testing is appropriate - meant to help ration the available tests - and by differing interpretations of those rules on the part of hospitals, clinics, medical practices and individual doctors.

Not everyone who wants to be tested needs to be tested if they aren't exhibiting symptoms related to the illness. But for many, it's an ordeal just finding out what the actual symptoms or guidelines are.

As a result, people with symptoms or who fear they have been exposed report spending hours on the phone trying to figure out whether they should get tested and which facilities might be able to do the tests.

Some just give up.

"People with fever are tested, but not those with only respiratory symptoms," one emergency room doctor in Brooklyn said. But people with no fever "aren't being tested", he added.

"There are just not enough testing supplies, so we're basically rationing testing supplies," the doctor said.

The message from City Hall has compounded the confusion. Mayor Bill de Blasio has been urging people with symptoms to rush to their healthcare providers and seek testing.

"So, we want to keep telling parents, keep telling school personnel: Get tested immediately," Mr De Blasio has said.

"That is the ballgame. So, we're continuing to pump out that message."

But New Yorkers are often finding that when they seek testing, they are rebuffed. Early on, some didn't fit the Centres for Disease Control and Prevention's guidelines, which started out being exceedingly narrow, then expanded.

But at other times, the bottleneck has been the city's own Department of Health, which runs most of the testing in New York City.

When doctors have called there to inquire about testing a patient, they have often been instructed not to send a sample to the Health Department lab for testing, according to interviews with doctors and other hospital employees.

In New York City, testing is still largely being done manually, by lab workers, limiting the number of tests that a laboratory can perform.

The city's public health laboratory is only able right now to test "samples for 60 people" a day, the health commissioner, Dr Oxiris Barbot, said on Tuesday (March 10), adding that she hoped to ramp up to roughly 100 people a day soon.

On Long Island, the laboratory division of Northwell Health, which runs 23 hospitals in the state and on Sunday was given approval from the Food and Drug Administration to start testing, said it would soon begin an automated process, using manufactured cartridge kits, that would expand capacity from the 60 or 70 tests it was doing manually each day at the start of the week.

But those changes aren't coming fast enough for people who want to be tested now.

Ms Ludmila Janda, a 34-year-old data scientist who lives in Manhattan, said that last week she had developed coronavirus-like symptoms - a cough and 38.8-degree Celsius fever.

But at Community Healthcare Network in Harlem, she was told to monitor her symptoms and to visit urgent care if she felt worse.

Ms Janda said she asked the nurse if she should get tested for the coronavirus and was told no. Even as her symptoms began to alleviate, Ms Janda said she was worried about being contagious and called the health centre again over the weekend to see if she could get tested.

"Every time I tried to reach a medical doctor, I was told not to worry about it," she said.

"It seems, as a country, that we are being misinformed about how many people are being tested and how many may have the disease."

Northwell said they will only test the very sick and the people most vulnerable to complications. The rest they will send home. Patients who want to be tested are turned down every day.

When turning people away, Dr John D'Angelo, who oversees Northwell's emergency departments and urgent care centres, said that doctors try to explain the reasons to patients who are upset.

"Some folks are more persistent than others, but you just try to be able to have people understand that in the big picture - and to be providing the right care to the sickest and most vulnerable patients - it's a necessity right now," he said.

He said that some of the patients turned away probably had the new coronavirus.

"The reality is, it's out there in the community," Dr D'Angelo said.

Last week, a husband and wife who live in Brooklyn, and spoke on the condition of anonymity, had to jump through complicated hoops and complex hurdles - from heated phone calls to multiple hospital visits - to be tested for the coronavirus after the wife's mother tested positive.

The mother had been on a cruise ship in Egypt in February when she fell ill, showing most of the coronavirus' symptoms, those similar to pneumonia.

Initially, the mother was refused testing because she had not travelled to one of the countries with an outbreak.

But after another passenger tested positive, and following a long and highly charged call with a city health official, the daughter said she persuaded the city to have her mother tested March 4.

Two days later, they received a call informing them she had tested positive.

"On TV basically everybody is saying, 'We have the kits. Come on down. Everyone who wants a test can get a test,'" the husband said. "Even down to the President saying it."

But the reality is different, he said.

The following day, the couple made arrangements with the city to be tested at Mount Sinai Queens. The husband's test came back negative. The wife is still awaiting results.

With so little testing, doctors said, patients suspected of having mild cases of the coronavirus were sent home - as they would have been if they had the flu - and told to isolate themselves.

"From a medical standpoint, the testing in the lower-acuity, moderate patient is not going to make much of a difference in our medical management," Dr D'Angelo said.

But the lack of testing, even if it might not matter much for the treatment of an individual case, has hampered the broader public health campaign.

Without a vaccine or proven treatments against the coronavirus, diagnostic testing was to be a key component of the public health response.

Now some city officials are beginning to conclude that it's time to take more dramatic action.

"Given that we have now crossed into community spread, it's not a good use of scarce testing resources to test thousands of people who are asymptomatic just because they were in the same room of someone who tested positive," Mr Mark Levine, a city councilman who heads the City Council's Committee on Health, said in an interview.