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While COVID-19 vaccine supply remains scarce, Los Angeles Mayor Eric Garcetti said Wednesday that there could soon be enough doses for everyone, leading to a phasing out of the tiered system.

Coronavirus infections in Los Angeles County have dropped 19% since last week and hospitalizations 28% in the same time period, the mayor said in a news briefing Wednesday. And intensive care units are at their lowest numbers since the beginning of December.

The mayor’s briefing comes after vaccination sites reopened across the city Tuesday following temporary closures due to weather-related shipment delays. Inoculations resumed Tuesday at all city-operated sites, with 17,572 doses administered in just one day.

Angelenos whose appointments were postponed last week were said to be prioritized this week to get the vaccine.

The city is providing primarily second dose appointments this week, Garcetti said, and a limited number of first-dose appointments.

A total of 367,206 COVID-19 doses have now been administered by the city, the mayor said.

Starting March 1, L.A. County will open up vaccine eligibility to educators and child-care workers; food and agriculture workers, including grocery store employees; and law enforcement personnel and other emergency responders.

And, looking ahead, Garcetti said Wednesday that vaccine eligibility for all residents may come sooner than expected.

“I look forward to the day, and I think it’s coming sooner than we can imagine — in a month, month and a half, maybe two months max — where I think all of these tiers basically go away, because we’re gonna have so much vaccine supply in this country,” he said.

But while supply remains limited, data released by the county shows stark disparities among those inoculated, while highlighting gaps across the county’s communities.

Garcetti said Wednesday that the city has partnered with trusted community organizations to administer shots in vulnerable neighborhoods in South Central and East Los Angeles, as well as in the San Fernando Valley.

The city is expanding the number of mobile vaccination clinics in communities hit hardest by the pandemic, and is now offering Saturday hours to accommodate more people who work Monday to Friday, Garcetti said.

When asked about the misuse of the state’s vaccine access codes that were meant for underserved communities but were used by wealthier outsiders, Garcetti said he doesn’t have jurisdiction over those L.A. sites because they’re run by the state.

“In terms of consequences, there aren’t any, you know, specific consequences, but it isn’t the right thing to do,” he said, explaining that some people didn’t know they were using an access code reserved for specific groups of people.

“So I wouldn’t punish somebody who simply is trying to do what everybody’s doing,” he said. “I would just tweak it, close it up, change the system if necessary and that’s what we’ve done with success.”

He said the system was successful in targeting doses for those who qualify but the state will likely make changes to address the issues.

The mayor also urged residents not to fall for scams after reports of people impersonating vaccination workers in scrubs, setting up fraudulent sites to try to take people’s personal information.

“Don’t fall for these tricks. And please report them if they happen to you,” Garcetti said. “No one legitimate will ever ask you to pay money for a COVID vaccine. Nobody.”

Earlier Wednesday, the mayor signed into law the first ever paid parental leave policy for Los Angeles, which is the third largest employer in the city. The leave includes six weeks of fully paid parental time off.