By Holly Yan and Madeline Holcombe, CNN

(CNN) -- New Covid-19 hot spots keep popping up across the US, with worrying trends in the Midwest and at colleges nationwide.

More than 25,000 cases of Covid-19 have been reported from colleges and universities in 37 states, according to a CNN tally through Wednesday.

But it's not just college students getting more infections. The number of new cases among children has jumped 17% in two weeks, according to the American Academy of Pediatrics and the Children's Hospital Association.

While Covid-19 deaths are rare among children and young adults, many young people are suffering long-term effects from the disease. And even those without symptoms can easily spread coronavirus to others.

That's why colleges and universities shouldn't send infected students home, said Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases.

"Keep them at the university in a place that's sequestered enough from the other students. But don't have them go home, because they could be spreading it in their home state," Fauci told NBC's "Today" show in an interview aired Wednesday.

Campuses shouldn't shut down after an outbreak because it would scatter and spread the virus further, Fauci said. "It's the worst thing you could do," he said.

70,000 new child cases in 2 weeks

From the beginning of this pandemic through August 27, more than 476,000 children have been infected, according to the report from the AAP and the hospitals group.

Children at that time represented 9.5% of all coronavirus cases, up from 9.3% a week earlier, the report said.

And from August 13 through August 27, 70,330 new child cases were reported, it said. That's a 17% increase in child cases over two weeks.

Nationwide, more than 6 million people in the US have been infected with the coronavirus, and more than 184,000 have died, according to data from Johns Hopkins University.

Trouble in the Midwest

No Midwestern state has seen a drop in new cases this past week compared with the previous week, according to data Wednesday morning from Johns Hopkins University.

Iowa and South Dakota are two of the six states across the country that have seen at least a 50% increase in new cases this past week.

Track the virus in your state and nationwide

In Iowa, "the uptick in people is from a younger cohort of people," said Dr. Ravi Vemuri, an infectious disease specialist at MercyOne medical center.

In Iowa City, home of the University of Iowa, Mayor Bruce Teague said people are racing to get the virus under control. The return of college students helped fuel the spread, he said.

"We have a 30% positivity rate just within a 24-hour period," Teague told CNN on Wednesday. "So we have some major concerns that we must address. We've got to get a little bit ahead of the game because we're definitely looking in the rearview mirror and trying to catch up. And our efforts are not totally where they need to be."

Teague issued a face-mask mandate for Iowa City back in July, but the state has not followed suit -- despite a dire report from the White House coronavirus task force.

The report, dated sSunday, said Iowa is in the "red zone" with the highest rate of cases in the US, which increased 77.4% from the previous week. It also said Iowa had the fifth-highest test positivity rate in the country.

The task force called for a mask mandate, the closure of bars and a plan from universities as the pandemic intensifies in the Midwest.

The White House task force releases state-by-state reports each week to governors' offices, but has declined to make them publicly available. CNN obtained the Iowa record, first reported by the Des Moines Register, from the state Department of Public Health.

Symptoms can last much longer than expected

The US Centers for Disease Control and Prevention has said most people who tested positive for Covid-19 can return to work or school 10 days after the onset of symptoms, unless the illness requires hospitalization.

But new research suggest the virus and its symptoms are often nowhere near finished by that benchmark.

Patients might need to wait over a month before being retested to know whether they have cleared the virus, according to research published Tuesday in the British Medical Journal.

The study also suggests about 1 in 5 negative test results are actually false negatives, meaning many infected people are still spreading the virus without knowing it after testing negative.

And even after testing negative, many patients have said their symptoms last months longer. Such symptoms include brain fog, body aches, mood problems and the loss of smell.

"We think that this long-term damage may in part be due to vascular damage -- kind of a footprint that the virus leaves even when it's gone from the body," said Dr. William Li, president and medical director of the nonprofit Angiogenesis Foundation.

Researchers have found the virus damaging blood vessels that connect the entire body, Li said. It isn't clear when "long haul" patients will be back to the lives they had before, he added.

$5 tests are expected this month

An insufficient number of tests -- combined with dayslong waits to get results -- has been a major roadblock to controlling Covid-19 in the US, health experts have said. But this month, $5 rapid tests will be distributed to states, said Adm. Brett Giroir, the head of US Covid-19 testing efforts.

The nasal swab antigen test does not require an instrument to read it and comes with a free smartphone app so the health care provider can record the test results and automatically send it to public health systems.

Giroir said 48 million tests a month will be available to the US.

Testing availability and speed has improved in the US, particularly since the disastrous spring delays. Giroir said 91.9% of results from major referral labs -- which perform about half the tests in the US -- were completed within three days. The mean turnaround time in August for large referral labs was 2.27 days.

But that 2.27-day average wait time means infected people can infect others unknowingly -- especially if they're asymptomatic or pre-symptomatic. Public health officials and lab industry experts have repeatedly asked the federal government to take a stronger leadership role in coordinating testing supplies.

Coronavirus found in university sewage system

Officials at the Utah State University have issued mandatory testing and quarantine for 287 students across four residence halls after they found elevated amounts of the virus in sewage samples.

The mandatory quarantine is effective immediately and will continue until the test results are returned. USU has also activated a Covid Care Team to arrange for resources to assist the affected students, including meal deliveries.

"This testing isn't new to Utah, it started shortly after the pandemic began and has been successful in monitoring the spread of the disease," said Amanda DeRito, a director with the university.

"The benefit of testing the water is that we get a snapshot into what is happening on campus and can quarantine even before a student becomes symptomatic. It is also less invasive."

States go in opposite directions with reopening

Some state and local officials are toughening measures to control the virus while others are moving forward with reopening.

Oregon Gov. Kate Brown has extended a state of emergency to November 3.

"When I last extended the COVID-19 state of emergency in June, I told Oregonians that we were at a crossroads: we could work together to stop the spread of COVID-19 in Oregon, or we could watch infections and hospitalizations spike," Brown said in a statement.

"Until there is an effective vaccine for COVID-19, this disease can spread like wildfire if we let our guard down."

But elsewhere, officials are relaxing measures.

San Francisco officials announced the city would move to Phase 2, which would allow hair salons, nail salons, massage parlors and gyms to resume outdoors in the coming days. More entertainment sites and houses of worship will be able to open with limitations in the coming weeks.

And North Carolina Gov. Roy Cooper said Phase 2.5 of its reopening will start Friday, which will increase maximum gatherings to 25 people indoors and 50 outdoors. Playgrounds will be opened, along with museums and aquariums at limited capacity.

"We're encouraged to see North Carolina holding steady on most and decreasing on some of our key data metrics," Cooper said. "Because of our stable numbers, today we're ready to take a careful step forward."