By CBSLA Staff

LOS ANGELES (CBSLA) — Los Angeles County health officials on Saturday reported 10,537 new confirmed cases of COVID-19 and 269 more deaths.

The county this weekend also surpassed 15,000 coronavirus deaths.

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More than a third of those deaths have come after Christmas, which is what health experts feared after people disobeyed local guidance by gathering.

As of Friday, the most recent figures showed that 441,140 doses of the coronavirus vaccine have been administered in L.A. County, according to Dr. Paul Simon, the county Department of Public Health’s chief science officer, although he said that number is likely much higher due to delays in tallying vaccination totals.

Health Access California tells CBS2/KCAL9 that about 10 million Californians are now eligible for the vaccine, but the state only has about three million doses available.

“We need a lot more vaccine to get anywhere close to meeting this category before we get into another phases and tiers,” said Anthony Wright, Executive Director of Health Access California.

Officials say part of the problem with administering the doses we do have is the heavy load of coronavirus cases.

During the pandemic in L.A. County, the totals are 1,064,887 COVID-19 cases and 15,162 coronavirus-related deaths to date.

As of Saturday, there were 6,881 people with COVID-19 currently hospitalized in L.A. County, and 24% are in intensive care.

READ MORE: OC Receives More Than 83,000 COVID-19 Vaccine Doses In Single Day

“Those nurses and front line hospital workers that would be giving vaccines are actually doing double shifts treating COVID patients, so that’s an issue,” Wright said.

Hospitals remain busy across Los Angeles County despite news that the coronavirus case rate has actually declined.

“Case rates are lower so there’s more bed availability but we are still seeing carry-over from the very high case rates a couple of weeks go,” Wright said. “But we have very stick people in ICU and those are the ones passing away.”

While the county has ramped up vaccination efforts, doctors say we still have a ways to go.

“There’s over 100,000 people in L.A. County who are getting vaccines every day, which is great but it’s a huge population so it just takes time,” said Dr. Michel Hochman with USC Keck.

The recommended time period for the second vaccination dose is the 21-day mark, but doctors say for people who have received a first shot and are able to get the second one within a week, they should.

The resources listed below can provide information about the pandemic and best practices for staying safe:

For information about how to get a free coronavirus test in L.A. County, visit https://corona-virus.la/covid-19-testing.

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(© Copyright 2020 CBS Broadcasting Inc. All Rights Reserved. City News Service contributed to this report.)