LOS ANGELES (AP/CBS13) — California’s death toll during the coronavirus pandemic remains alarmingly high, topping 49,000 this weekend, even as the rates of new infections and hospitalizations continue to plummet across the state.

The number of patients in California hospitals with COVID-19 slipped below 7,000, a drop of more than a third over two weeks, the state Department of Public Health reported Sunday.

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The 6,760 new confirmed cases are more than 85% below the mid-December peak of about 54,000. Total cases are approaching 3.45 million.

California reported another 408 deaths, bringing the total since the outbreak began to 49,105 — the highest in the nation.

Despite the grim death count, the positivity rate for people being tested has been falling for weeks, which means fewer people will end up in hospitals.

In Los Angeles County, the state’s most populous, the daily test positivity rate was 3.8% on Saturday, public health officials said.

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Herd immunity is reached when so many people have immunity that a virus cannot find new hosts and stops spreading, resulting in community-wide protection. The effects may be greatest in places that endured the worst COVID-19 surges, including Los Angeles in the fall and early winter.

More from CBS Sacramento:

Residents were urged to continue to avoid close contact with anyone outside their household while wearing masks and observing social distancing rules when outside.

“We must remain diligent with our safety measures even though we see overall decreases in cases, hospitalizations and deaths,” Barbara Ferrer, LA County’s public health director, said in a statement. “Let’s keep our guard up because we know letting our guard down will lead to more cases and, tragically, more deaths again.”

California continues to struggle with vaccine shortages that are hindering efforts to inoculate substantial numbers in the state of nearly 40 million residents. Newsom on Sunday said over 7.3 million vaccines have been administered. But county vaccination centers aren’t operating close to full capacity because there aren’t enough doses.

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The state is shifting to a new vaccine distribution system run by insurer Blue Shield, which will take some decision-making power away from counties.