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As Gov. Gary Herbert praised Utahns for lowering the rolling average of COVID-19 cases below 500 a day, Thursday’s case count went the other way — with another 587 Utahns testing positive for the virus, the Utah Department of Health reported Thursday.

It’s the highest daily case count in the past 12 days.

Herbert, at the state’s weekly media briefing Thursday, also announced he was streamlining the process for cities and counties to get his approval for local mask-wearing mandates.

Three more Utahns have died from COVID-19, bringing the state’s overall death toll to 330 people.

The three deaths were identified as a Davis County resident, between 45 and 64, living in a long-term care facility; a Salt Lake County man, also between 45 and 64, who was in the hospital when he died; and a Utah County man, older than 85, who was in a long-term care facility.

The state’s rolling seven-day average for new cases — the metric public health officials use to gauge trends — is at 449 cases per day. The average for the seven days before that, which included the Pioneer Day holiday, was 516 per day.

Herbert noted that he made a challenge on July 9 for the state to hit below 500 cases a day on the rolling seven-day average by Aug. 1.

“We have something to celebrate in our efforts to work together to bring down that rolling average,” Herbert said. “I’m not ready to spike the football, by any means. We still have a lot of tough sledding ahead of us.”

Herbert extended his challenge, with a new goal and deadline: To get the rate below 400 cases a day by Sept. 1.

“I think it’s something, if we all work together, we can do this,” Herbert said.

The state’s epidemiologist, Dr. Angela Dunn, also announced that Utah’s guidelines for public schools would no longer include a “modified quarantine” allowing attendance by students and educators exposed to people with COVID-19 but showing no symptoms themselves. In the case of students, the original guideline had left the decision up to parents whether or not to send their children to school.

“Guidance from @UtahDepOfHealth now clarifies that students and teachers should follow standard quarantine practices when exposed to COVID-19,” tweeted Gov. Gary Herbert.

Standard quarantine practice means staying home for 14 days.

Another 5,069 tests for the virus were processed in the last 24 hours, UDOH reported. The rolling seven-day rate of positive test results is at 10% — down a bit from Wednesday’s rate of 10.1%, but up from the 9.6% rate of a week ago.

Dunn said UDOH is “cautiously optimistic” about the drop in daily case counts, but the accompanying decline in testing remains a concern. If the positive test rate also dropped, she said, “that would give us even more confidence that we’re getting this under control.”

Herbert bristled at a reporter’s question whether the state had manipulated the case counts to get below the governor’s 500-per-day challenge. “That’s just patently false,” Herbert said. “Nobody’s jimmying any numbers. The numbers are what the numbers are.”

Herbert, who calls himself a proponent of local control, said his office will streamline the process that allows cities and counties to mandate mask-wearing. “All you need to do is notify us, and that they’re going to opt in,” Herbert said.

Such mandatory mask orders are in effect in Salt Lake, Summit and Grand counties, as well as the cities of Logan and Springdale. Herbert also has mandated the wearing of masks in state-owned buildings, which includes universities and liquor stores.

A law passed by the Utah Legislature in April made it illegal for local jurisdictions to pass health rules stronger than the state’s laws without Herbert’s approval.

Herbert said the “opt in” plan doesn’t mean he’s giving up on the idea of a statewide mask mandate. If daily case counts get wildly out of control, a mandate remains an option, he said, though he hopes he doesn’t need to order one. Rather, Herbert said, that when it comes to wearing masks, people should “do it because it’s the right thing to do.”

There are 190 people now in Utah hospitals with COVID-19, UDOH reported. Another 35 people were hospitalized on Wednesday, bringing the total number of people hospitalized since the pandemic began to 2,554.