Unprompted, Watley makes his case to stay.

“I can’t go back,” he tells her, softly. “This is it. The last stand. Next one’s the box.”

He came here from a Brooklyn homeless shelter, where his oxygen tank was considered a fire hazard. It’s at least an hour by subway from the Montefiore Medical Center in the Northwest Bronx, where he receives treatment for blood cancer. Last time, he fainted on the train.

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Deirdre Sekulic, 42, doesn’t argue. Her job is guided by one belief: Sick people with no home cannot heal. Moral implications aside, that’s an expensive problem for the nation.

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“I might have an opportunity for you,” she says. “It could take a while, and it’s hard to tell what will happen. . . . But I need to know you’re interested.”

Sekulic heads Montefiore’s housing unit, which aims to find one-bedroom apartments for homeless patients who show up in the emergency room, again and again. The program is the only one of its kind in New York City.

Montefiore is also an unexpected cost-saving offshoot of the Affordable Care Act — and part of an experimental effort to treat health care as more than just medicine. The dual goal: Save lives, save money.

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The medical center is what’s called a Pioneer Accountable Care Organization, one of 19 in the country. More simply: It’s a network of doctors, nurses and social workers who team up to deliver continuous, coordinated care to patients — and, in the process, slash government spending.

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Its approach has been championed by some health economists as a cutting-edge way to save tax money. Last year, the Montefiore Pioneer ACO saved the government $24.5 million in Medicare spending, according to a Montefiore spokesperson. Because of a cost-cutting incentive built into the Affordable Care Act, which created the partnership, the medical center got to keep $13 million of that amount.

Nationwide, Pioneer ACOs saved the government $96 million last year, compared with $87.6 million in 2012, the Centers for Medicare and Medicaid Services said last month.

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Montefiore has about 2,500 medical providers in its network. An oncologist, a physical therapist and a social worker may treat the same patient, for example. Smaller Pioneer ACOs that serve populations with higher median incomes had much lower Medicare savings.

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How has one operation been so successful at cutting costs? It bridges the gap between patients and the often confusing world of health care, Sekulic said. Nurses regularly call patients to make sure they’re taking their medicine. Emergency room aides consult a medical history database for every visitor, to avoid repeating expensive tests such as MRIs.

Housing, one of the newest initiatives here, takes this idea a step further. Montefiore has housed only two patients, but it plans to push for more.

Pioneer ACOs have been able to save only a small chunk of government spending on its main three health-care programs — Medicare, Medicaid and the Children’s Health Insurance Program — which last year totaled $772 billion. But the idea is still young, a fledgling experiment, said Andrew Racine, Montefiore’s chief medical officer.

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In the Bronx, he said, the origins of illness are largely social. About 80 percent of Montefiore’s patients receive Medicaid or Medicare.

“It has to do with how people are housed, what transportation is available, their educational backgrounds,” Racine said. “Until and unless you have a system that’s attuned to these issues, you don’t have the possibility of keeping people healthy.”

Three years ago, the government gave Montefiore the designation of Pioneer ACO, reserved for hospitals that have long developed hands-on community care methods. The title feels like a mere formality, Racine said; The medical center has honed a grass-roots approach here for two decades.

“The question we’re asking ourselves is: If [the government] partners with medical facilities, which have a financial interest in keeping costs down, is that enough of an incentive to actually change the trajectory of costs over time?” Racine said. “You better know how it’s working, and why, so you can take those lessons and send them out more broadly.”

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One proposed fix: More demographic-specific research, more ACOs. What works in Brooklyn, even, may not float in the Bronx. “It is difficult to isolate the effects of differences in health spending intensity,” Sheiner writes, “from the effects of the differences in the underlying state characteristics.”

Today, one in five Americans, or about 65 million, receive benefits from Medicaid, the nation’s largest insurer. More than 49 million receive Medicare, which covers beneficiaries age 65 and older.

Montefiore does not focus ACA innovation tactics solely on Medicare recipients, although that’s the government’s primary metric of success, Racine said. The theory is: Diseases caught or prevented earlier should reduce future costs across the board.

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So does getting patients off the street.

**

Sekulic shows up at their apartments with MetroCards so they can travel to chemotherapy appointments. Co-workers say the Irish woman with thick, dark bangs will walk down any alley. Answer her door at any hour of night.

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She grew up poor in Dublin, where her mother ran a free after-school program for kids. Social work was her passion, she says, before she knew the term.

Sekulic is one of two dedicated social workers tasked with arranging one-bedroom apartments dubbed supportive housing, which come with curfew and guest restrictions, for Montefiore’s most vulnerable patients. She checks listings every night before bed.

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The applications take months. Sekulic hounds city agencies and nonprofits. She preps her patients for grueling interviews. “That’s the only way I get rooms.”

This year, Sekulic secured two apartments, funded partly by Medicaid. Two patients received their first set of house keys ever: a 26-year-old transgender woman, whose grandmother kicked her out as a child, and a 31-year-old man who slept on the streets before unchecked diabetes rendered him half-blind.

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Now, Sekulic is working on a third case: a home for Watley, the patient with blood cancer.

An ambulance first dropped him at the Montefiore emergency room and onto her caseload in November, when chest pains hindered his ability to breathe. He returned in December, diagnosed with multiple myeloma — the same disease that killed his mother. And again in March, with leg swelling. Again in June, unable to move.

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Watley received the bone marrow transplant in September. He remains in a Montefiore bed, resting for the next two weeks. A home, Sekulic said, could get him back on his feet.

“It has to do with how people are housed, what transportation is available, their educational backgrounds,” she said. “Until and unless you have a system that’s attuned to these issues, you don’t have the possibility of keeping people healthy.”

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And, ideally, keeping him away from the emergency room.

Homeless men in the United States visit the ER nine times more often than the rest of the population, according to the Agency for Healthcare Research and Quality. Homeless women are 12 times as likely. The average trip costs $1,233, according to research funded by the National Institutes of Health.

This, of course, amplifies the taxpayer burden. Montefiore’s housing mission has something to satisfy liberals and conservatives, Sekulic says. “If you don’t have a place to sleep, you won’t have the ability to take care of much else — and you’re going to be a much more expensive patient.”

The biggest challenge, she said, is signing the lease. That’s because the Bronx has about 8,000 supportive-housing units — and thousands more New Yorkers from all five boroughs are vying for them.

On Christmas Eve, Sekulic rushed to a Harlem agency to sign for the 26-year-old transgender woman, her first patient housed. The patient’s ER trips since dipped from nearly 50 in 2013 to just one this year, to patch an accidental wrist cut.

Watley, Sekulic fears, won’t be a competitive candidate. He served prison time for dealing drugs, she said. That was years after his mother died. After he became an orphan, sleeping on park benches.

The social worker will first find him a bed in a Bronx shelter, just in case. That would cut down his commutes to receive medical attention at Montefiore. Her top priority, though, is sending out Watley’s housing applications, following up daily, preparing him for prerequisite interviews.

Building managers probably will ask: “How do we know you won’t bring trouble?” Watley must promise, genuinely and repeatedly, to follow the law.

Sekulic will add: “He is sick, very sick. He will get much sicker without a home. He will run up medical bills. And then, he will die.”

**

In the hospital room that September day, Watley listens to Sekulic, eyes welling. He has never heard an offer like this. He’s reluctant to believe it.

She’s taking his case. Working, full-time, to find him a nearby one-bedroom apartment. His alone.

“You would have your own place,” the social worker says. “Your own keys.”

“What?”

“You gotta stay sober, though,” she continues. “Stay off the streets.”

Watley puts his hand on his heart. Closes his eyes.

“I want to beat this for my mom,” he says. “I feel her pushing me.”