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With 458 new coronavirus cases reported on Saturday, Utah’s rate of new cases went up slightly, as the state’s death toll from the virus remained at 407, the same as Friday.

For the past week, Utah has averaged 366 new positive test results per day, the Utah Department of Health said. Gov. Gary Herbert had said he wanted the state to get below 400 new cases per day by Sept. 1 — and with just two days to go, new cases would need to continue to rise to miss that target.

Since public schools began opening on Aug. 13, there have been seven outbreaks in schools, affecting 54 patients — with one new outbreak, eight new cases and one new hospitalization reported by the state health department in the past day.

The Uintah School District also announced on Saturday that a second confirmed case of COVID-19 had been confirmed at Discovery Elementary School. But it said contact tracing showed neither person contracted the virus at the school and the TriCounty Health Department had concluded the cases were not related.

Those who were in “direct, prolonged contact” with the two people have been notified, the school district said. State policy calls for students and staff who have been in close contact to stay home for 14 days.

A quarter of the slightly more than 200 COVID-19 cases reported in the region — in Uintah, Duchesne and Daggett counties, and among members of the Ute Indian Tribe — have been residents age 25 or younger, the TriCounty Health Department said.

Since the beginning of the pandemic, there have been 99 patients infected in 18 school outbreaks, with an average age of 18. Six of those patients have been hospitalized; none have died.

There were 2,815 new statewide test results reported on Saturday, below the weeklong average of 4,028 new tests per day. The rate of tests with positive results was at 9.1%, up from Friday. State epidemiologist Dr. Angela Dunn has said a 3% positivity rate would indicate the virus is under control.

Hospitalizations did not change significantly on Saturday, with 119 Utah patients concurrently admitted, UDOH said. On average, 124 patients have been receiving treatment in Utah hospitals each day for the past week — continuing a decline from the peak average of 211 patients hospitalized each day at the end of July.

In total, 3,057 patients have been hospitalized in Utah for COVID-19, up 16 from Friday.

Per population, the virus appears to be spreading the most rapidly in Utah County, where there have been, on average, 16.5 new cases a day per 100,000 people for the past week. Utah County is followed by Salt Lake County, at 13.3 new cases daily per 100,000 people, and then Summit County, where new cases are slowing after an August outbreak at a private party.

The virus also appears to be becoming more prevalent in Davis County, where the average number of new cases has risen from 25 per day to 36 per day over the past week and a half — or from seven to 10 new cases daily, per 100,000 people.

Of 51,406 Utahns who have tested positive for COVID-19, 43,342 are considered “recovered” — that is, they have survived for at least three weeks after being diagnosed.