The COVID-19 positivity rate in the city is currently 8.4%, down slightly from 8.8% last week, Turner said in a Monday afternoon briefing. The city reported 685 new cases, bringing the total to 97,703. And no new deaths were reported, with the total still at 1,436.
"I would not be surprised [about] an uptick [in the number of COVID-19 cases] after Thanksgiving," he said.
The mayor announced his staff, the Houston Police Department and the Houston Fire Department will enforce COVID-19 business regulations laid out by Texas Gov. Greg Abbott.
"My staff is trying to work my schedule and getting me out and about [the city] to let me take a look at what's happening," Turner said. "If by chance you see me coming [into your business], it's not to socialize with you. If I see nothing but a community [virus] spreader event, the last resort is we will shut businesses down. Please consider yourself forewarned."
Chief Samuel Pena added his firefighters have responded to about 20,000 occupancy complaints since mid-March.
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"That's about 90-100 complaints per day," Pena said. "The majority are handled on the spot. Managers have been receptive. In the end, we want to help businesses keep lights on, but we need their assistance to make sure they're enforcing what's in the governor's order."
"We're trying to strike a balance between public health and businesses open," Turner said.
Turner also echoed the guidance by many health experts across the country for anyone who traveled over the weekend or had people visit who don't live with them.
Experts say if you were in a high exposure situation, it is recommended to get tested around four to eight days after exposure. Harvard Health says if you get tested right after an infection, you're likely to get a false negative because there are not enough viral particles in your nose or saliva. So if you celebrated during Thanksgiving, a good time to get tested would be between Tuesday, Dec. 1, and Friday, Dec. 4. They also recommend you quarantine while you're waiting for your test in case you do have COVID-19.
SEE ALSO: Why you should get tested for COVID-19 after Thanksgiving
You can find a free COVID-19 testing site near you in Houston or Harris County.