Tuesday, the first three positive tests were reported in the county.
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Only about 170 people live in Loving County, making it the lowest population in the contiguous United States.
This means all 254 counties in Texas now have COVID-19 cases.
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Loving County is just under 200 miles from El Paso, Texas, which has exceeded 1,000 daily cases several times during the last two weeks.
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The outbreak was responsible for another 14 deaths reported last Wednesday, and active cases in the border area are now at more than 29,000. Nearly 1,100 patients are hospitalized, including 279 in intensive care, according to the latest government statistics.
El Paso County has temporarily shut down nonessential businesses for at least three more weeks in order to control the spread.
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