BATON ROUGE — Louisiana Gov. John Bel Edwards said Monday the state may have reached its peak of coronavirus infection, but warned the trend could be undone if people don't follow his stay-at-home order.

"We believe we might be seeing the beginning of the flattening of the curve," Edwards said, noting "our fear" is people will think they can relax the mitigation and social distancing measures "that brought us to this point."

"While all numbers are still high we're starting to see real signs these mitigation measures are starting to yield real results," he said. "The data points we're seeing will only become a trend if we continue to following the stay-at-home order. We have to keep it up."

© Greg Hilburn/USA Today Network Louisiana Governor John Bel Edwards and Louisiana Attorney General Jeff Landry conduct a press conference Monday to update the public on the coronavirus crisis.

Louisiana's Department of Health on Monday reported 35 more coronavirus deaths, but the number of hospitalizations and patients needing ventilators showed only small increases.

That could portend fewer projected deaths in the state, which would confirm new modeling data from a source used by the White House.

More: Coronavirus: White House model updated with mitigation shows La. deaths reduced to 746

The health department reported 1,857 new cases for a total of 14,867 in 62 of the state's 64 parishes, while the death toll rose to 512.

But the total number of those needing hospitalization rose by only six to 1,809, while the number of those needing ventilators rose by only two to 563.

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The University of Washington's Institute for Health Metrics and Evaluation adjusted it's projections for Louisiana coronavirus deaths from 1,834 to 746, an indication that the governor's stay-at-home order and social distancing are making a difference.

Edwards said the University of Washington model and the state's model don't match exactly, "but it looks like things might be moving in a positive direction."

"As to the question of whether we have peaked, that's still unclear," Edwards said.

The governor said the hard-hit New Orleans area is no longer projected to run out of ventilators or hospital beds this week. Edwards said he doesn't have a new projected date to exceed capacity of ventilators and beds.

Edwards said 70% of the Louisiana patients who have died with COVID-19 are black, a disparity he called "disturbing" that will be tracked and published on the health department's website.

Louisiana coronavirus: 35 more die; rate of hospitalizations, ventilation slows

The agency's top coronavirus expert Dr. Alex Billioux said that's likely a result of Louisiana's black population suffering with a disproportionate number of underlying conditions contributing to COVID-19 deaths like diabetes, high blood pressure and obesity.

"Sadly, we know there is a significant racial health disparity in the state," Billioux said.

Louisiana Attorney General Jeff Landry also joined Edwards at the press conference to announce he has secured 475,000 hydroxychloroquine tablets as well as the antibiotic azithromycin.

LSU is using the medicine in clinical trials in Shreveport and New Orleans to see if the combination is beneficial for COVID-19 patients.

More: LSU Health Shreveport among first in US to offer nitric oxide clinical trials for COVID-19

Edwards said he will begin wearing a non-medical mask if he's out inspecting facilities like the field hospital in the New Orleans Ernest Morial Convention Center after the Centers for Disease Control issued that recommendation over the weekend.

"If and when I go out in public at a facility you will see me in a mask," said Edwards, who recommended the same for Louisiana residents.

Greg Hilburn covers state politics for the USA TODAY Network of Louisiana. Follow him on Twitter @GregHilburn1.

This article originally appeared on Monroe News-Star: Governor John Bel Edwards: Louisiana may be flattening the coronavirus curve