Louisiana Governor John Bel Edwards said at a press conference Thursday that the number of confirmed coronavirus cases across the state has surged. He also warned that if the state does not start flattening its curve, New Orleans could run out of key medical supplies by early April.

According to Edwards, as of Thursday, Louisiana has at least 2,305 positive cases of COVID-19 and 83 deaths — 18 of which were reported since Wednesday. Edwards said that a 17-year-old from New Orleans is among the dead, calling it a "very disturbing piece of information."

The virus has taken a strong hold on the state, particularly in New Orleans. Officials estimate that New Orleans could run out of life-saving ventilators by the first week of April. Edwards echoed that warning on Thursday, and said that if the state does not flatten its curve soon, the city could run out of ventilators as early as April 2, and potentially be out of hospital beds by April 7.

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"It's not conjecture, it's not some flimsy theory, this is not a scare tactic, this is what is going to happen," he said.

Doctors and elected officials believe the skyrocketing number of cases is connected to Mardi Gras, the month-long celebration that typically draws huge crowds to the city in February, CBS News correspondent Omar Villafranca reports.

Bourbon Street, the iconic thoroughfare in New Orleans' French Quarter neighborhood, was shut down earlier this month. The French Quarter stayed open during Hurricane Katrina in 2005.

On Thursday, however, Governor Edwards stressed that cases of coronavirus are spread across the state. He said that cases have now been confirmed in a vast majority of the state's parishes, not just metropolitan areas.

"Nobody should look at this situation and think this doesn't involve me... this coronavirus is in your neighborhood," Edwards said. "There is no place where it isn't. There are places where we haven't detected it yet."

The governor pleaded for people to follow social distancing guidelines and limit trips for groceries and other essential items. "All you have to do to save lives is stay home," he said.

At his daily press briefing on Thursday, New York Governor Andrew Cuomo said that Louisiana is a "hotspot" for the virus. New York has 37,258 confirmed cases of the coronavirus. That's by far the highest number of any state — but New York has also deployed the most tests of any state.

"(Louisiana) has a cluster that is growing and the people in Louisiana and in New Orleans are in our thoughts and prayers," Cuomo said. "We know what they're going through. And we feel for them, and we pray for them, and we know the difficulty they're under because we're dealing with the same type of situation. So our best to them. Anyway we can help them, we stand ready."

Edwards said that Louisiana's medical system would not be able to handle the surge in cases projected to come without social distancing.

"We cannot surge the (medical) capacity to meet the need if we do not bend the curve. We cannot," he said.

"There is no reason why the things that you see coming out of Italy, wouldn't happen here in Louisiana if people don't engage seriously in these mitigation measures," he added.