An increase of rapes in New York City this year is being fueled largely by crimes that occurred as far back as 30 years ago but are being reported for the first time by victims likely emboldened by publicity over allegations like those facing actor Bill Cosby, according to police and a victim’s advocate.

The old rape cases are being added to 2015 NYPD statistics through Dec. 12 that show 1,361 rapes, an increase of about 5.3 percent over last year’s total of 1,292. If those cases from before 2015 are removed, the city has actually experienced a 6 percent decline in rapes from last year, according to police officials.

The amount of old rape complaints have increased NYPD statistics significantly since 2012. In 2014, older rape cases amounted to 11 percent of the yearly Compstat number.

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This year, 21 percent of the rapes occurred before 2015, said Dermot Shea, the NYPD’s deputy commissioner for operations.

In at least one case, the alleged rape took place more than 30 years ago. Others occurred well over a year ago, going as far back as 20 years, Shea said. Police reporting methods require that crimes occurring in previous years and reported for the first time in 2015 be recorded in the current year.

Shea, who oversees much of the NYPD crime-data collection, said he has not done an in-depth analysis of rape-complaint victims this year but added that the statistical hike comes in large measure from increased department outreach over the years to sex-crime victim groups and schools.

Media publicity about high-profile rape cases has fueled some of the reporting, said Min Um-Mandhyan, director of development and communications at the New York City Alliance Against Sexual Assault.

“A lot of media attention on [sexual assault] has allowed victims to feel more in control . . . they are not afraid to come forward,” Um-Mandhyan said. “It gives them control and closure.”

Asked if publicity about cases like that of Cosby, accused of rape by a number of women, is responsible for increased reporting in the city, Shea said the effect of the Cosby case was a “logical” conclusion but he couldn’t say with certainty.

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Cosby has denied the allegations and has filed lawsuits against a number of his accusers.