It was the third straight day the city has not had a fatality from the virus, though 27 more cases were identified.
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"That's very positive news. Our hope is that we can continue to move in this direction," Turner said. "We still need people to stay home and to engage in social separation and distancing and wear face coverings."
Turner's comments were the first after word that Harris County would order face masks will be required to be worn in public. Turner and other elected officials have worn masks in public for weeks.
"It's an added layer of protection and mitigation," Turner said. "I feel wonderful, but that doesn't mean that I'm not infectious."
The city's death toll remains at 34, and health officials still say cases have not peaked yet.
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"This virus is breaking all the rules," Houston Health Department director Dr. David Persse said. "The phenomenon of people not having symptoms and being able to spread the virus is not unheard of, but to the degree that this virus can do that is previously unseen."
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