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Payton, 56, confirmed the news to ESPN. He said he didn't feel great this past Sunday, took a test Monday and got the results back Thursday.
He is the first person connected to the NFL to have reported catching the coronavirus.
"This is not just about social distancing," Payton told ESPN. "It's shutting down here for a week to two weeks. If people understand the curve, and understand the bump, we can easily work together as a country to reduce it. Take a minute to understand what the experts are saying. It's not complicated to do what they're asking of us. Just that type of small investment by every one of us will have a dramatic impact.
"I was fortunate to be in the minority, without the serious side effects that some have. I'm lucky. Younger people feel like they can handle this, but they can be a carrier to someone who can't handle it. So we all need to do our part. It's important for every one of us to do our part."
Louisiana has at least 340 reported cases of coronavirus and at least seven deaths.
The coronavirus outbreak has affected hundreds of thousands of people across the globe and over the last two weeks brought sports to a complete standstill.
The NBA took the lead on the outbreak after one player contracted the disease. The league then decided to suspend the rest of the regular season. At least seven NBA players have tested positive for the coronavirus with most being asymptomatic.
The NHL also suspended its season over the coronavirus. One player reportedly tested positive for the disease. MLB delayed the start of its season because of the coronavirus. A handful of people have tested positive.
The NCAA canceled both the men’s and women’s basketball tournaments and the rest of the spring sports season.
The Centers for Disease and Control Prevention (CDC) recommended that gatherings of 50 people or more be prohibited for at least eight weeks. The White House recommended that people avoid gatherings of 10 or more.