More than 20 people were arrested Thursday on federal charges connecting them to a series of Medicaid and other health-care schemes that prosecutors say cheated taxpayers out of tens of millions of dollars.

In announcing five federal indictments against 12 people and related D.C. Superior Court charges against 13 people, U.S. Attorney Ronald C. Machen Jr. said federal law enforcement officials had pulled off the largest health-care fraud takedown “in the history of the District of Columbia.” Prosecutors, FBI agents and others had investigated the fraud for years — much of it allegedly emanating from corrupt operators of home-care agencies and personal-care assistants, he said — and uncovered a problem that they say has permeated a component of the city’s health-care system.

“Today’s operation makes clear that Medicaid fraud in the District of Columbia is at epidemic levels,” Machen said. “But we’re fighting back.”

Those charged are accused of running separate — and sometimes competing — schemes to bill the government for in-home health-care services that were not provided. A Bowie woman also was accused of racking up more than $75 million in billings after she had been barred from being a part of federal health-care programs.

Machen said that the schemes were not “overly complex” but that the groups “had it down to a science.”

According to the indictments, the alleged swindlers — who included operators and workers at home-care and nurse-staffing agencies — recruited Medicaid recipients to claim that they needed expensive in-home health care, even coaching them on how to exaggerate their symptoms to persuade doctors to sign off on treatment plans. The accused would then pose as the Medicaid recipients’ personal-care assistants, having them sign time sheets while they billed the government, according to the indictments.

The Medicaid recipients, though, did not need in-home care, according to the indictments. Those charged merely gave them a cut of the proceeds — usually a few hundred dollars at a time — and pocketed the rest, according to the indictments.

“Doctors wrote prescriptions for these visits,” said Valerie Parlave, the assistant director in charge at the FBI’s Washington Field Office, “but no care was ever given.”

Machen said the alleged swindlers were able to take “millions” from the District’s Medicaid program — which is mostly federally funded but run by the city — although investigators were still calculating the precise amount. He said law enforcement officials were partially inspired to investigate the fraud when they noticed an unusual increase in the amount of money being paid out for personal-care services.

In 2006, Machen said, 2,500 Medicaid beneficiaries billed the government $40 million for personal care services. By 2013, he said, 10,000 beneficiaries were billing the government for $280 million.

“It was a number that skyrocketed so much, so quickly that we obviously had to look at it,” Machen said, “and we uncovered a huge fraud in the process.”

Prosecutors said that as part of the probe, they seized several luxury cars, including a 2013 Mercedes GL450 and a 2013 Porsche Panamera.

The investigation was not limited to networks of those billing for in-home services they did not provide. Prosecutors said they also charged the 51-year-old Bowie woman, Florence Bikundi, alleging that she hadmore than $75 million in D.C. Medicaid billings after she was barred from participating in federal health-care programs.

Bikundi, prosecutors said, used various names to hide the fact that her nursing licenses had been revoked and that her health-care companies were not eligible to receive Medicare or Medicaid payments. Machen said that investigators are still looking into whether Bikundi provided the services for which she billed the government.

Online court records did not list an attorney for Bikundi on Thursday afternoon, and efforts to locate family members were unsuccessful.

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