New daily cases of the coronavirus have been dropping sharply in the United States for weeks -- but experts don't know if Americans will have the discipline to bring the epidemic truly under control.

After exceeding 70,000 confirmed infections per day in July, the country recorded 43,000 cases on Thursday.

Hospitalizations have fallen by a third, and the number of deaths, which has been more than thousand per day should logically follow.

"I do think we're going to start to see significant declines in the mortality across the country in the next... hopefully next week," said Robert Redfield, director of the Centers for Disease Control and Prevention during a talk hosted by the medical journal JAMA.

No one thinks the US is out of the woods. The incidence rate -- new cases per capita -- is still triple what is being observed in Mexico or France.

And there are huge regional disparities.

"We are beginning, I think, to turn the tide on what I call the southern outbreak in the nation," said Redfield.

There are however warning signs -- including the Midwest where cases are plateauing instead of falling.

"So Middle America right now is getting stuck," he added, citing Nebraska and Omaha.

Health officials fear a repeat of the spring, when, spurred on by President Donald Trump, states that were less affected in the first wave eased precautions too soon, which led to the summer surge in the south and west.

Back to school

Complicating the picture further, schools in several states, particularly those in rural districts, have started reopening their doors for in-person learning.

Early signs aren't encouraging.

Schools that opened up in hotspots in Georgia and Mississippi experienced outbreaks and were promptly forced into mass quarantines and closures.

"What we're seeing is unfortunately so far more of a cautionary tale," said Jennifer Nuzzo, an epidemiologist at Johns Hopkins University during a talk.

"If there are high numbers or increasing numbers of infections in the school feeder communities, it stands to reason that students and staff may be infected and come to school with an infection."

Major cities like Washington, Chicago, Houston, Los Angeles have opted for virtual starts.

Colleges and universities could be an even bigger challenge, since adults are thought to be more frequently infected than children and are more likely to fall seriously ill.

Alabama will reopen all of its campuses but will first test all students.

Elsewhere, the University of North Carolina at Chapel Hill and Notre Dame have gone back to distance learning after attempts at in-person classes were aborted following outbreaks.

Trump is in favor of a total reopening and a return to normalcy, but the federal government has left it to local authorities to assess the risks themselves.

No formal criteria have been set at the national level, leaving it to individual government officials to make suggestions that aren't formalized.

"If you are in a green zone where you have literally less than 10 per hundred thousand population then you could probably open the schools," Anthony Fauci, director the National Institute for Allergies and Infectious Diseases said in a talk hosted by George Washington University.

On the other hand, when there's over 100 cases per 100,000, it's a red zone, and "you really want to think twice if you want to get the children back to school."

Fauci and other experts are adamant that even before the arrival of a vaccine either later this year or early next, public health interventions like wearing masks, physical distancing, and avoiding crowds can break the back of the epidemic.

Patience is required: even if a vaccine were available in early 2021, the return to normal will take many months, the time needed to vaccinate the population and achieve herd immunity.

Ezekiel Emanuel, of the University of Pennsylvania, estimates this won't happen before November 2021.

Another item on many experts' wish lists is faster tests.

A study in early August put the average wait time for a result at four days, even though rapid, point-of-care diagnostic tests that give results in minutes are available in some places.

"Investment in new treatments and vaccines is smart, but where is the investment in other response efforts?" Natalie Dean, a biostatistician at the University of Florida said on Twitter.

"Getting cheap tests approved? Supporting our public health departments to trace and to analyze their data? There is so much more we can do right now."