ATLANTA — As state after state begins to reopen, local health departments charged with tracking down everyone who has been in close contact with those who test positive for the new coronavirus are still scrambling to hire the number of people they need to do the job.

They are often hundreds — even thousands — of people short of targets for their contact-tracing programs. Public health experts have consistently said robust programs to test more people and trace their contacts are needed for states to safely reboot their economies and prevent a resurgence of the virus.

Cook County, Ill., has just 29 contact tracers serving 2.5 million people living in suburban communities around Chicago, an Associated Press review found. Los Angeles County, which at more than 10 million people has a population slightly greater than the state of Michigan, has just 400 of the estimated 6,000 contact tracers it will need under California’s criteria for a broader reopening.

With 2.7 million residents and roughly 100 to 300 new COVID-19 cases a day, Miami-Dade County has 175 people tracking down those who were potentially exposed to the virus.

“The whole point of the lockdown was to buy time to have a better way to keep numbers down,” said Jeremy Konyndyk, who led the humanitarian response to the Ebola outbreak in West Africa during the Obama administration. “And that’s why so many of us are screaming ourselves hoarse about testing and tracing.”

Public health experts say contact-tracing systems should be in place before cases become widespread so every new infection can be tracked and the person’s contacts identified, tested and isolated from the rest of the community.

Until recently, there had been scant federal guidance on what contact tracing should look like, and there is still no coordinated federal strategy. While other countries are taking a national approach, the U.S. is leaving it to states to devise their own programs.

The result has been a patchwork of efforts. The AP review in late April found little consensus among states on basic questions such as how many investigators are needed.

Officials in Cook County, which has the highest number of cases in Illinois, have said they need at least 200 additional contact tracers and as many as 400 to supplement the work of the 29 currently on staff.

While there is no federal formula for how many of the disease detectives are needed, public health experts have said one contact tracer is needed for every 1,000 to 3,000 residents.

Under California’s criteria for a broader reopening, counties should have 15 people trained in contact tracing for every 100,000 residents. The state is helping, working to train 10,000 to 20,000 tracers, but most large counties are falling short.

San Diego County, home to 3.3 million people, had 171 contact investigators on the job, with plans to have 450 as soon as possible. In Orange County, which has about 3.1 million residents, about 75 staffers are assigned to trace contacts.