The University of Texas at Austin reported 42 new COVID-19 cases among students on Wednesday, bringing its total caseload to 72 since classes began last week.

This jump follows confirmation on Monday that two students living in on-campus residence halls had tested positive for the disease. Last weekend, residents of the off-campus Scottish Rite Dormitory received notification that one of their peer residents had tested positive for COVID.

UT Austin's COVID-19 dashboard shows 42 new cases among students were reported Wednesday.(UT Austin COVID-19 Dashboard)

The university said in early August that it aimed to test up to 5,000 asymptomatic members of its campus community each week. Since Sunday, the university has tested 1,072 students, faculty and staff, with 18 returning positive results, according to its public dashboard.

This puts the university's positivity rate at around 1.6%. In comparison, Travis County reported a positivity rate of 6.2% last week.

Researchers at UT Austin's own COVID-19 Modeling Consortium conservatively estimated between 82 and 183 students would return to campus with the disease during the first week of classes.

The research team, led by consortium director and professor of integrative biology Dr. Lauren Ancel Meyers, arrived at this estimate by assuming 22,000 students will return to campus—less than half of the university's total enrollment —and that 0.5% of them will be infected, based on the estimated prevalence of COVID-19 in the Austin metro and students' home counties in mid-August.

"Contacts between residents end returning students may exacerbate risks, fuel transmission and deplete public health resources," the researchers wrote in a report published on Aug. 20.

Before classes even started, there was backlash online as a photo circulated on social media showing an off-campus gathering of Greek life members.

In an Aug. 21 email sent to the campus community, UT Austin Interim President Jay Hartzell said the university will consider a number of metrics in deciding whether to move more classes online or close buildings on campus in the coming weeks.

Other area colleges are also reporting COVID cases in the wake of their reopening.

St. Edward's University, a private Catholic school in South Austin, reported seven positive results out of 2,173 tests conducted during the week ending Thursday.

Between July 6 and Aug. 28, Austin Community College reported eight cases among students and four among employees.

Huston-Tillotson University, a private historically Black university in East Austin, is conducting its fall semester entirely online.

A number of colleges and universities across the country—including the University of North Carolina at Chapel Hill and the University of Notre Dame—recently shifted to online instruction after outbreaks occurred on their campuses.