HOUSTON — At Lyndon B. Johnson Hospital on Sunday, the medical staff ran out of both space for new coronavirus patients and a key drug needed to treat them. With no open beds at the public hospital, a dozen COVID-19 patients who were in need of intensive care were stuck in the emergency room, awaiting transfers to other Houston area hospitals, according to a note sent to the staff and shared with reporters.

A day later, the top physician executive at the Houston Methodist hospital system wrote to staff members warning that its coronavirus caseload was surging: “It has become necessary to consider delaying more surgical services to create further capacity for COVID-19 patients,” Dr. Robert Phillips said in the note, an abrupt turn from three days earlier, when the hospital system sent a note to thousands of patients, inviting them to keep their surgical appointments.

And at The University of Texas MD Anderson Cancer Center, staff members were alerted recently that the hospital would soon begin taking in cancer patients with COVID-19 from the city’s overburdened public hospital system, a highly unusual move for the specialty hospital.

These internal messages highlight the growing strain that the coronavirus crisis is putting on hospital systems in the Houston region, where the number of patients hospitalized with COVID-19 has nearly quadrupled since Memorial Day. As of Tuesday, more than 3,000 people were hospitalized for the coronavirus in the region, including nearly 800 in intensive care.

“To tell you the truth, what worries me is not this week, where we’re still kind of handling it,” said Roberta Schwartz, Houston Methodist’s chief innovation officer, who’s been helping lead the system’s efforts to expand beds for COVID-19 patents. “I’m really worried about next week.”

What’s happening in Houston draws eerie parallels to New York City in late March, when every day brought steep increases in the number of patients seeking care at overburdened hospitals — though, so far, with far fewer deaths. But as coronavirus cases surge in Texas, state officials here have not reimplemented the same lockdown measures that experts say helped bring New York’s outbreak under control, raising concern among public health officials that Houston won’t be able to flatten the curve.

“The time to act and time to be alarmed is not when you’ve hit capacity, but it’s much earlier when you start to see hospitalizations increase at a very fast rate,” said Lauren Ancel Meyers, a professor of integrative biology who leads the University of Texas at Austin COVID-19 Modeling Consortium. “It is definitely time to take some kind of action. It is time to be alarmed.”

Even as new cases and hospitalizations soar, the number of daily deaths in Texas has remained relatively low. On Tuesday, the state reported nearly 7,000 new cases, a record, but only 21 new deaths. All told, New York state has reported nearly 25,000 confirmed deaths from COVID-19. Texas has recorded fewer than 2,500, including 378 in Harris County, which includes Houston.

But experts caution that rising hospitalizations today will likely result in a spike in deaths in the coming weeks, and those who require ICU care for COVID-19 but recover often leave the hospital with lasting health problems.

Meyers and others said that while hospitals across the United States generally are more prepared than they were in March and April — personal protective equipment is more plentiful, advances in therapeutics have helped patients and ventilators aren’t in short supply — the lack of government measures to slow the spread in Texas and other states puts them at a disadvantage.

Texas was one of the first states in the nation to ease social distancing mandates, beginning two months ago when daily coronavirus cases remained relatively low compared with some states. Restaurants reopened first, with gradually loosening capacity restrictions; bars, hair salons, bowling alleys and other businesses soon followed. In Houston, where Gov. Greg Abbott had until recently blocked local officials from issuing public mask requirements, it was common to see the majority of people shopping at neighborhood supermarkets or big-box hardware stores with no face coverings.

But to date, Abbott has resisted a return to the lockdown, other than an order last week closing bars and further limiting the capacity at restaurants. This week, after the top elected leader in Dallas County asked for the authority to issue a new stay-at-home order locally, Abbott dismissed the idea, saying the official was asking to “force poverty” on people.

“Closing down Texas again will always be the last option,” the governor said last week, emphasizing his commitment to protecting the state’s economy.

Experts noted that it can take two weeks or longer for social distancing measures to lead to decreases in cases and hospitalizations.

“The hospitalizations you see today, they’re not just going to linearly increase in the next two weeks,” said Dr. Clay Johnston, dean of the Dell Medical School at the University of Texas at Austin. “They’re going to accelerate. When you overwhelm the hospitals, you’re in big trouble. That to me is the impossible task that the governor faces. It’s like steering a giant tanker through a tiny strait without any maps.”

Although hospital executives in Houston stress that they have the ability to add additional intensive care beds in the region to meet the growing demand — for a few more weeks, at least — the strain on hospitals is already being felt in other ways.

Houston Fire Chief Samuel Peña said his paramedics sometimes have to wait for more than an hour while emergency room workers scramble to find beds and staffers to care for patients brought in by ambulance — a bottleneck that’s tying up emergency medical service resources and slowing emergency response times across the region.

Part of the problem, Peña said, is that when his crews arrive at a hospital with a patient suspected of having COVID-19, the hospital may have a physical bed open for them, but not enough nurses or doctors to staff it. That’s a problem that’s likely to deepen as a growing number of medical workers have been testing positive for the virus, according to internal hospital reports. Just as New York hospitals did four months ago, some Houston hospitals have posted on traveling nurse websites seeking nurses for “crisis response jobs.”

“If they don’t have the nursing staff, then you can’t place the patient,” Peña said. “Then our crews have to sit with the patient in the ER until something comes open. It has a huge domino effect.”

The crisis in Houston has accelerated rapidly in recent weeks, at times resulting in muddled messaging from both hospital leaders and public officials.

On June 24, several hospital executives affiliated with the Texas Medical Center — a sprawling medical campus that’s home to most of Houston’s major hospital systems — issued a statement warning that COVID-19 hospitalizations were growing at an “alarming rate” and could soon put an unsustainable strain on hospital resources.

But the following day, after Abbott issued an executive order directing hospitals to limit elective surgeries — a measure intended to preserve hospital capacity but one that also hurts hospital revenues — the CEOs of four hospitals in the medical center abruptly dialed back their earlier warnings at a hastily organized news conference. They said they hadn’t meant to alarm the public. The hospitals still had room to add ICU beds, they said, both to treat COVID-19 and to continue caring for other patients.

“I think the Texas Medical Center’s purpose was to really urge people to do the right things in the community, and do so by talking about capacity, but really ended up unintentionally sounding an alarm bell too loudly,” Dr. Marc Boom, president and CEO of Houston Methodist, which is part of the Texas Medical Center, said at the news conference. “We clearly do have capacity.”

The shifting messages upset Harris County Judge Lina Hidalgo, the county’s top elected official. She vented her frustrations Monday during a virtual news conference from her home, where she’s on self-quarantine after a member of her staff tested positive for the coronavirus. Hidalgo said the “diluted” messaging from some hospital leaders “weakens our community’s ability” to stop the virus.

“The goal is not to have doctors and nurses that we’re bringing in from out of town,” Hidalgo said. “The goal is not to have basic general population beds that we need for dialysis and heart attacks and strokes and pregnant women who need to give birth turned into ICU beds. The goal is not to see how much room we can make for people to go and be there and die in a hospital bed. That is not the point of any of this.”

In an interview Tuesday, Boom said he didn’t intend to suggest that there wasn’t reason to be deeply concerned about the number of COVID-19 patients filling hospital wards. He said he and other executives were trying to thread the needle between sounding the alarm about the growing but still manageable strain on hospital resources, while trying to reassure people who might need to come to the hospital for other ailments.

“Honestly, in a way, it’s backfired, and I’m very sorry for that because what has happened has actually been the exact opposite of what we were trying to accomplish,” he said of his attempt to clarify the earlier warning about hospital capacity. “I never wanted to confuse the public. The message really was, ‘Hey guys, we don’t want panic, because when people panic, bad things happen.’”

Hospitals in Houston and elsewhere in the country temporarily halted outpatient visits and elective surgeries in March and April as the coronavirus pandemic took hold on the East Coast — a move that not only hurt hospital revenues, Boom said, but also forced many patients to delay critical procedures, including heart surgeries.

Boom and other hospital leaders said the earlier restrictions also led some patients to avoid going to the hospital after suffering symptoms of heart attacks or strokes, leading to potentially deadly delays in care.

Vivian Ho, an economics professor at Rice University, said hospitals want to protect their fiscal health and the health of patients, both those with COVID-19 and those with other conditions, while also preventing themselves from becoming overwhelmed down the line.

Elective surgeries deliver a far better financial return than ICU wards full of patients with COVID-19.

“They would prefer to tell the public that this is extremely dangerous,” she said, “but they can’t, in part, because they have to keep performing these elective surgeries, and for the most part, that is safe.”

Not all hospitals are equally equipped to respond to a surge in COVID-19 demand, accompanied by a loss of more profitable business, Ho said. Hospital systems like Houston Methodist have “the financial resources to sort of convert anything into an ICU just because they have more money, more cash on hand,” she said.

Houston’s public hospitals, Ben Taub and Lyndon B. Johnson, don’t have those same resources.

“The problem is that, of course, there are going to be more patients who are going to be going to Ben Taub” because the virus is disproportionately affecting Black and Latino people in low-income communities, and Ben Taub is traditionally the safety net for those without health insurance, Ho said. “I don’t know to what extent they are able to send patients to the other hospitals.”

Harris Health System officials said that capacity limits at both of its public hospitals have forced doctors to transfer coronavirus patients elsewhere, including sending some to hospitals in nearby cities.

The Sunday note to the staff at Lyndon B. Johnson said that the hospital had reached maximum occupancy in its COVID-19 units. That day, nearly 50% of the patients tested for the virus had it, more than double the rate from a week before. The hospital had run out of remdesivir, an antiviral drug that’s shown some effectiveness in treating COVID-19. And for now, all elective surgeries were being canceled to preserve bed and staffing capacity.

There appeared to be no letup in sight; the note to the staff warned that Monday would likely be worse.

“Sunday,” it said, “is typically a lower volume day.”

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