Louisiana Gov. John Bel Edwards said Monday he’s concerned that residents may be relaxing their social distancing practices and not following the state’s stay-at-home order as the state sees improving numbers in its coronavirus outbreak, warning that the state will see another spike if people don’t take the restrictions seriously.

The governor, speaking at a press conference after touring parts of northeast Louisiana that storms ripped through Sunday, said he has received anecdotal reports of people gathering over the Easter weekend in violation of his order barring gatherings of 10 or more and urging people to stay home.

“All it takes to have a spike in cases and go back in the other direction is for too many people to violate the order, too much social contact to spread this disease,” Edwards said. “So I’m asking everyone to do better.”

“There are too many people moving around,” he added.

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After seeing its rate of detected cases and deaths grow at one of the fastest clips in the country, Louisiana has seen a tapering off in recent days, leading state officials to conclude the stringent restrictions are working as intended. On Monday, the state confirmed 44 more deaths, bringing the death toll to 884 statewide. In total, the state has confirmed 21,016 cases of coronavirus, after adding 421 on Monday.

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The New Orleans area was previously on track to run out of hospitals and ventilators in early April, according to state modeling, but the pace of hospitalizations has slowed. Fifty more coronavirus patients were in hospitals Monday compared to a day before, and three more people were on ventilators, both of which Edwards said did not represent “alarming growth.”

Louisiana has had an outsized number of parishes atop a dubious list of counties across the country with the highest death rates per capita, according to data compiled by University of Louisiana at Lafayette economist Gary Wagner. But Wagner said Louisiana parishes have dropped on that list, as several counties in Georgia have risen.

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St. John the Baptist Parish, which has ranked No. 1 on that list in recent days, was overtaken by Terrell County, Georgia. Orleans, St. James, St. Charles, Iberville, Plaquemines and Jefferson were still on the top 20 list as of Monday, according to Wagner’s research, though he noted Louisiana parishes are falling on the list.

Edwards said the data reported in recent days continues to be encouraging, and he pointed to the fact that the state confirmed 44 deaths Monday after reporting 70 twice last week.

The governor noted that people with underlying health conditions, especially high blood pressure, diabetes and kidney disease, are more susceptible to the disease caused by the virus, COVID-19. And the state continues to see a stark racial disparity, with black people comprising at least 60% of deaths as of Monday. While that’s down from 70% reported by the state last week, the state was still determining the race of 9% of deaths.

East Baton Rouge Mayor President Sharon Weston Broome said in a statement she is encouraged that many of the area's residents are staying home, but said there is "plenty of room for improvement."

"For instance, I see a lot of vehicles on the roadway and I’m concerned too many people are disregarding the Governor’s Stay at Home order," Broome said. "Only essential workers should be regularly leaving their homes at this point. The rest of us should be staying home, with the exception of a daily walk through the neighborhood or a weekly trip to the grocery store or pharmacy."

Broome added many businesses have taken steps to enforce social distancing and good hygiene, like floor markers and sneeze guards. She has also received reports of other businesses "not doing enough."

New Orleans Mayor LaToya Cantrell's office did not respond to requests for comment.

The governor said it is “too early to know” whether Louisiana’s stay-at-home order will expire on April 30th, as currently scheduled. He has repeatedly indicated the restrictions could last longer, and he described the next phase as a “transition period,” with things not returning to normal until there is a viable vaccine, which could be a year away.

In the meantime, the state is not cracking down with police or National Guard to enforce its stay-at-home order, though some local leaders have had police break up gatherings. Instead, Edwards and other officials have pleaded with religious leaders, business owners and residents to heed the order, which lists essential businesses that can keep operating but shutters others, like bars, casinos, gyms and movie theaters.

“We hope we don’t have to rely on enforcement,” said Alex Billioux, assistant secretary of the state’s Office of Public Health. “But ask people to self-police, ask people to be mindful of the 10-person limit.”

However, Edwards’ administration and Attorney General Jeff Landry, a Republican, have begun investigating at least two abortion clinics in Baton Rouge and Shreveport to determine if they are violating the order by performing abortions. The state health department told providers to postpone “elective” procedures to conserve personal protective gear for hospitals.

To begin opening the state back up, Edwards has said officials need far more diagnostic tests, along with serological tests that could tell whether people have immunity to the virus. The state appears to be gaining some ground on both of those fronts.

LSU Health Shreveport has opened a new lab that can process 1,500 coronavirus tests a day, with results in 24 to 48 hours, much quicker than commercial labs that often take days to get results. The lab will start accepting samples from around the state and even out-of-state samples once Louisiana’s peak has occurred.

The school also recently administered the first convalescent plasma therapy in Louisiana to a coronavirus patient. The treatment, which is being tested in other parts of the country, takes plasma from people who have recovered and injects it into patients battling COVID-19.

The federal government is also expected to make an announcement about the serological tests this week, Edwards said, though it was not clear what the news would be.

LSU in Baton Rouge also announced Monday it would use the Pete Maravich Assembly Center to make gowns and face shields for health workers amid a shortage of personal protective equipment at hospitals around the state and country.