Time is running out for a 20-year-old ­Pakistani exchange student who has been in a coma at a Duluth hospital for three months.

Medically, Muhammad Shahzaib Bajwa is doing better than expected, his brother said Wednesday. He’s breathing on his own, squeezing his mother’s small hand.

But St. Mary’s Medical Center, which has cared for Bajwa since a November car collision with a deer, is trying to send him back to his home country of Pakistan, Shahraiz Bajwa said. He’s fighting to keep his younger brother in the United States, despite a soon-to-expire ­student visa and quickly multiplying medical bills.

“The heath care’s not so good there,” Shahraiz Bajwa said in a telephone interview. “But the flight itself — which is more than 24 hours — is too much. Anything can happen to him in the middle of nowhere.”

Such “medical repatriations” of foreign ­citizens are “widespread but barely publicized” according to a 2012 report by two advocacy groups. Hospitals put ill, injured or even comatose patients on flights to their home countries, often without consulting federal agencies. But a spokeswoman for Essentia Health, which runs the hospital where Bajwa is staying, said the Duluth-based health system has been ­working with the U.S. State Department, which rejected a request to extend Bajwa’s visa.

Shahzaib Bajwa was riding with friends from Minneapolis to the University of Wisconsin-Superior — where he was studying anthropology and sociology for a semester — when their car hit the deer. Antlers delivered a severe blow to his head.

He was talking when he got to a hospital in Cloquet, his brother said, but then choked on his own blood and went into cardiac arrest. After being resuscitated, he ended up at St. Mary’s Medical Center in Duluth, where he’s been comatose since.

Essentia Health has been “tremendous” and “cooperative,” said Shahraiz Bajwa, who flew to Duluth shortly after the accident. But they’ve also been pushing Muhammad’s mother to sign a consent form to send him to a clinic in Pakistan.

“The whole situation is very tragic and difficult for us,” Shahraiz Bajwa said.

With proper medical care, his brother has a chance, Shahraiz Bajwa believes. “Doctors said he would not be able to survive a month,” he said. “But he has come this far.”

His brother had taken out travel insurance capped at $100,000 for emergency medical care, Shahraiz Bajwa said. So far, he said, expenses have surpassed $350,000. The family, from Faisalabad in Punjab Province, has had no health insurance, because there’s “no such thing in Pakistan,” Shahraiz Bajwa said.

Shahzaib Bajwa’s student visa is set to expire Feb. 28, said the family’s attorney, Saiko McIvor, with the Minneapolis-based law firm Dorsey & Whitney. It’s already been extended once, she said. “I basically begged the U.S. State Department to extend it … which they did.”

Seeking another extension

McIvor is working to get another extension — which could be tough because Bajwa is no longer enrolled at the university — or a different type of permission. But that would fix only one of two problems, she said. “That doesn’t solve the situation of where he’s going to be.”

While hospital officials are “doing their best to accommodate the family,” McIvor said, it’s also dealing with medical bills the family won’t be able to pay.

Hospitals are required to provide emergency care to patients “regardless of their immigration status,” according to a report from the Center for Social Justice at Seton Hall Law School and New York Lawyers for the Public Interest. But “this obligation terminates once a patient is stabilized.”

Because the U.S. State Department is not renewing Bajwa’s visa, “he is not legally allowed to stay in the country,” Maureen Talarico, an Essentia Health spokeswoman, said in a statement.

‘Unfortunate situation’

“St. Mary’s Medical Center has been working with the State Department, which is making arrangements for Mr. Bajwa’s medical transport home,” she said. “This is an unfortunate situation and his caregivers are working closely with Mr. Bajwa’s family to ensure the smoothest transition possible.”

She declined to answer other questions Wednesday: “There’s very little I can say simply because of patient privacy rights.”

The State Department did not return requests for comment Wednesday. U.S. Immigration and Customs Enforcement said in a statement that the agency has “no role in a health care provider’s private transfer of a patient to his or her own country of origin.”

In his few months at Wisconsin-Superior — right across the border from Duluth — Shahzaib Bajwa had become a kind of cultural ambassador on campus, his brother said. He had been scheduled to speak at a gender equity club event in late November “about the role of women in Pakistan and his own experiences in the Pakistani feminist movement,” an online post says.

On his Facebook page, he posted photos and thoughts on trips to Las Vegas, the Grand Canyon and Lake Superior’s North Shore.

His mother, Tanzeela Bajwa, arrived in Duluth two weeks after the accident and has been praying at his side since.

Shahraiz Bajwa has worried about her since his father’s death in 2005. Having Muhammad in the hospital has been “very hard,” he said. “I’m a young person, a man. I can deal with it. She’s emotionally very attached to my brother.

“If something were to happen to her …” he added, trailing off.