Officials at BYU-Idaho said they are "deeply troubled" by reports that students on campus are intentionally trying to contract COVID-19 in order to recover and then sell their plasma, containing virus antibodies.

"The university condemns this behavior and is actively seeking evidence of any such conduct among our student body," the school said in a statement. "Students who are determined to have intentionally exposed themselves or others to the virus will be immediately suspended from the university and may be permanently dismissed."

However, according to a report in the Chronicle of Higher Education, there have been no substantiated examples of students intentionally contracting the virus. The concern may stem from a local article on about the rising demand for sales of plasma, the outlet reported.

Still, cases are definitely rising sharply in the state. Idaho's test-positivity rate spiked to 14.7% for week ending Oct. 8 -- twice the national rate of 5.9% during the same time period, according to an internal Health and Human Services memo obtained by ABC News. Idaho has the sixth-highest rate of infection in the country, the latest White House coronavirus task force report, obtained by ABC News and dated Oct. 10, shows.

The school, located in Rexburg, Idaho, is operated by The Church of Jesus Christ of Latter-day Saints.

Nick Saban, the head coach of the University of Alabama's football team, tested positive for COVID-19, sources told ESPN.

The 68-year-old was informed about his test by training staff and left the football facility immediately, ESPN reported. Alabama is set to play No. 3 Georgia in a huge, nationally televised game this Saturday.

"At this time, I do not have any symptoms relative to COVID-19, and I have taken another PCR test to confirm my diagnosis," the coach said in a statement. "I informed our team of my positive test at 2 p.m. today on a Zoom call and let them know offensive coordinator Steve Sarkisian will oversee preparations at the complex while I work from home."

Saban, the highest paid college football coach in the country at over $9 million a year, is the latest college football coach to contract the disease.

University of Kansas coach Les Miles at Kansas, Florida State University coach Mike Norvell and University of Arizona coach Kevin Sumlin have all tested positive for the virus this season.

Yesterday, the University of Florida announced it was pausing team activities citing a rise in coronavirus cases. Florida's game against LSU this weekend was subsequently postponed on Wednesday -- just days after Florida coach Dan Mullen said he wanted to pack his team's stadium with 90,000 fans.

Barron Trump, the youngest of President Donald Trump's five children, has contracted COVID-19, according to an article first lady Melania Trump wrote in an article published on the White House website where she described her experience in the battle against the virus.

Barron has "exhibited no symptoms" and has since tested negative, Melania Trump wrote. It is unclear when he contracted the virus.

The first lady says her own illness came "with minimal symptoms" but adds that they hit "all at once."

"It seemed to be a roller coaster of symptoms in the days after," she wrote. "I experienced body aches, a cough and headaches, and felt extremely tired most of the time."

Melania Trump has also since tested negative, she wrote. She did not reveal the details of her treatment, but thanked her caretakers and the Americans who wished her well while she was ill.

"Recovering from an illness gives you a lot of time to reflect. When my husband was taken to Walter Reed as a precaution, I spent much of my time reflecting on my family," she said. "For me personally, the most impactful part of my recovery was the opportunity to reflect on many things -- family, friendships, my work, and staying true to who you are."

"Barron's fine," the president told reporters as he departed the White House, making his way to Iowa for another campaign rally tonight

ABC News' Jordyn Phelps contributed to this report.

The number of Wisconsin COVID-19 hospitalizations is at an all-time high, Wisconsin Department of Health Services Deputy Secretary Julie Willems Van Dijk told reporters at a news conference Wednesday.

The state saw an increase of 3,107 cases since yesterday, bringing the total number of confirmed cases in the state to 153,578.

Fifty-seven of 72 counties in Wisconsin are meeting the threshold of very high disease activity levels, Van Dijk said, and every region in the state has one or more hospitals reporting staff shortages.
The death toll in Wisconsin currently stands at 1,536.

ABC News’ Rachel Katz contributed to this report.

The number of new COVID-19 cases recorded in the United States increased by double digits in week-over-week comparisons, while the number of new deaths from the disease continued to tick downward slightly, according to an internal memo from the U.S. Department of Health and Human Services that was obtained by ABC News on Tuesday night.

The memo, which is circulated to the highest levels of the federal government and is used to determine daily priorities for the agencies working on COVID-19 response, said 34 U.S. states and territories are in an upward trajectory of new infections, while 10 jurisdictions are at a plateau and 12 others are in a downward trend.

There were 351,270 new cases confirmed during the period of Oct. 6-Oct. 12, a 14.4% increase from the previous week. There were also 4,886 fatalities from COVID-19 recorded during the same period, a 1.5% decrease compared with the week prior. The national positivity rate for COVID-19 tests increased from 4.7% to 6.1% in week-to-week comparisons, according to the memo.

Meanwhile, 22% of hospitals nationwide have more than 80% of beds full in their intensive care units. That figure was 17-18% during the summertime peak, the memo said.

California's Sonoma County saw a 129.7% relative increase in new cases of COVID-19 between Sept. 29 and Oct. 6. The county confirmed 62 cases on Oct. 7 linked to outbreaks at schools and childcare facilities, according to the memo.

Kentucky reported on Oct. 7 its highest number of COVID-19 patients in ICUs since May. As of Oct. 6, the state's seven-day average for ICU bed occupancy was 80.6%, with 43.7% of adult ICU beds occupied by COVID-19 patients, the memo said.

Montana hit a peak of 504 new COVID-19 cases confirmed on Oct. 6. Daily hospital admissions in the state have increased from 40 in mid-September to more than 60 per day, with greater than 80 on Oct. 5 and Oct. 6. Montana's seven-day hospitalization rate continues to rise from 15.7 per 100,000 population on sept. 29 to a four-month high of 20 per 100,000 population on Oct. 6. Local officials report that hospitals are closed to or at capacity and have started redirecting patients, according to the memo.

New Jersey's seven-day COVID-19 case rate increased 20.6% to 539.5 cases per 1 million population between Sept. 29 and Oct. 6. The state has 71.7% of inpatient hospital beds occupied, with 56.4% of ICU beds full. At least 100 schools in New Jersey have teachers or students who have tested positive for COVID-19, the memo said.

New York recorded on Oct. 6 its highest number of total hospitalizations since July 22. The state has 79.5% of inpatient hospital beds occupied, with 62.4% of ICU beds full.

Utah reported more than 1,000 COVID-19 cases per day for six of the seven days last week. At the same time, week-to-week testing in the state has decreased slightly by 1.2%. Utah's positivity rate for COVID-19 tests, however, has remained stable at 14%.

ABC News' Josh Margolin contributed to this report.