They’re sick of the rat race.

The Upper West Side’s booming rat population is getting a helping hand from an unlikely source: the sanitation department, residents in the posh neighborhood claim.

In the midst of a booming rat population, the Department of Sanitation pulled 110 litter baskets from the Upper West Side in the past 12 months, according to new data obtained by The Post.

The lack of litter baskets is causing trash to overflow onto the streets around the remaining cans — and the unwanted vermin are feasting on the spoils.

“It’s disgusting to be working next to overflowing garbage all the time,” Zillur Rahman, who owns a newsstand at Amsterdam and 79th Street, told The Post on Tuesday.

“There are so many rats sometimes.”

The Upper West Side has the highest concentration of rat complaints — one in five rat sightings citywide — according to 311 calls analyzed by nonprofit watchdog group OpenTheBooks.com.

“The rats are running wild in this fancy area,” they wrote in their May report on New York’s rat population.

The Upper West Side also had some of the city’s highest rat complaints in 2018.

It’s no surprise, then, that the decision to pull dozens of litter baskets has both residents and Assemblywoman Linda B. Rosenthal (D-Manhattan) scratching their heads.

“I don’t think removing garbage cans does what they think it is supposed to do,” Rosenthal said, adding her office receives constant calls about the overflowing trash.

Sanitation blamed residents for abusing the litter baskets by filling them with household trash — and claimed removing the bins actually led to cleaner streets.

But angry residents said they weren’t consulted and are sick of living in a rat-infested ‘hood.

“There are some corners drowning in filth because of this absolutely silly policy,” Aaron Biller, president of civic group Neighborhood in the Nineties, told The Post.

“To think they’d do something like this when we’re trying to fight the rats,” he added.

The basket loss was five times the number in Prospect Heights, where 17 cans were taken away between July 2018 and July 2019.

Frustrated longtime resident Mary Andrews said her calls to officials had fallen on deaf ears.

“I am sick of it,” said the math teacher, 60. “The rats are all over the place and they’re aggressive. It’s disgusting.”

“It’s just become dirtier and dirtier since de Blasio came into office,” she added. “I am furious about this and nobody seems to care. We don’t have enough litter baskets.”

The neighborhood has an ongoing vermin issue that came to a head in 2017 with reports of rats jumping into strollers at Central Park playgrounds.

Mayor Bill de Blasio announced a $750,000 rat eradication plan, but it looks like the unwanted residents have yet to move out.

Rosenthal has convinced the Sanitation Department to reinstall several baskets they removed by taking officials on a walk-through of the worst-hit areas in February. She has another scheduled with them on Thursday.

Rodent sightings reportedly have soared 38 percent citywide since 2014, with scientists blaming milder winters and new property developments.

A Sanitation Department spokeswoman insisted the UWS remained spotless with a “near perfect” sidewalk cleanliness rating of 99 (out of 100). Biller disagreed.

“That rating is garbage,” he said. “Imagine if you allowed restaurants to give themselves ratings for their cleanliness. It’s literally that absurd.”

Additional reporting by Oumou Fofana