The county's transmission rate, referred to as the R number, has reached 1.27 - the highest since the early days of the pandemic in mid-March.
"With an R this high the cases really can multiply quite quickly," said Dr. Christina Ghaly, director of the county Department of Health Services.
The transmission rate is a measure of how many additional people are likely to get infected from a single person who is currently sick. Any number over 1.0 means the current case rate is increasing.
So for example for every 10 people who are sick today, an R of 1.27 means there will be about 13 people infected in five days - and 20 in two weeks, Ghaly said.
That means a doubling of cases every two weeks or a quadrupling within a month, she noted.
"Doubling or quadrupling these numbers could stretch our healthcare systems severely," Ghaly said.
The county reported 4,311 new coronavirus cases on Wednesday, as well as 49 new deaths. Total cases since the start of the pandemic stands at 378,323.
Wednesday's figure follows the new one-day record the county set Monday, with 5,124 new cases.
The county has reported 7,543 deaths since the start of the pandemic. By comparison, the latest flu season saw 3,133 deaths.
Last week the county was seeing about 200 new hospitalizations per day. This week the county is approaching 300 new hospitalizations each day, a 50% increase in just one week. If the trend continues, the county could see up to 1,000 hospitalizations per day, she said.
That means "this virus is very much still spreading," she said. The spread is not just limited to young healthy people who won't get sick or won't need to go to the hospital."
The county estimates that 1 out of every 145 residents out in the community are currently infectious. That number doesn't include people who are already in the hospital or isolating at home - "This is people out and about and infecting others," Ghaly said.
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So, for example, if people ignore warnings and hold Thanksgiving dinners with large groups of family members of 15 or more people - 1 out of 10 of those gatherings is likely to have a sick person who will infect others.
"The county has warned repeatedly against public and private gatherings as we all prepare for Thanksgiving," she said.
As of Wednesday night, Los Angeles County is shutting down outdoor dining for at least three weeks in an effort to help contain the spread.
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County health director Dr. Barbara Ferrer said earlier this week that a new stay-at-home order may be needed to help contain the spread. Discussions on whether to issue a new order remain ongoing with the county Board of Supervisors.
California has reported more than 1.14 million cases, with 18,350 new cases confirmed Tuesday alone. The state's 7-day positivity rate has increased to 6.5%. The state has seen 18,875 deaths.