(CNN) As the nationwide number of coronavirus cases nears 1 million people, Texas and other states are getting ready to reopen while others, such as Louisiana, the Lone Star State's neighbor to the east, are saying it's better to wait a while longer.

A University of Washington model frequently cited by the White House coronavirus task force suggests no state should open its economy before Friday.

Abbott expects barbershops, salons, gyms and bars to open by mid-May. He said the infection rate for Texans had been on the decline for the past 17 days and that soon the state will have more people who have recovered from Covid-19 than there are active cases.

Louisiana Gov. John Bel Edwards said he won't lift his state's stay-at-home order until after May 15.

"While Louisiana has seen positive, improving trends statewide in terms of new case growth and new hospitalizations, in several regions across the state, new cases and hospitalizations continue to increase or to plateau, according to data from the Louisiana Department of Health," the governor said in a statement.

Edwards issued a new order deeming that every worker in the state who has contact with customers must wear a face covering.

As of Monday, more than 988,000 people have been infected in the US, and 56,255 have died, according to Johns Hopkins University.

A Johns Hopkins chart displaying the five-day moving average of new cases shows ups and downs in the daily reports for the past three weeks since the curve apparently began to flatten.

In some states, mayors are going forward with reopening plans.

Miami Mayor Francis Suarez announced a road map to reopen the city in phases. While he did not announce the rollout date of this phased plan, he said that Miami-Dade county will reopen parks, waterways and golf courses before the city is ready for phase one.

Florida Gov. Ron DeSantis said he's not putting a date on when the state will reopen, even though its stay-at-home orders are set to expire Thursday.

"We are going to do everything in a smart way," DeSantis said. "I am less concerned about the date and more concerned about getting it right."

Other states have already started reopening, including Georgia, Texas Michigan , Hawaii and Alaska.

On Monday, restaurants in Georgia -- where the state health department says the seven-day average of new cases had been rising until mid-April but has fallen since -- were allowed to offer dine-in services for the first time in weeks.

And Friday, most counties in Iowa will be allowed to reopen restaurants, retail stores and gyms at 50% capacity, Gov. Kim Reynolds said. Reynolds said she's also lifting a ban on religious gatherings of more than 10 people.

But New York state won't be lifting restrictions this week, despite declines in the rates of hospitalization, intubation and deaths, Gov. Andrew Cuomo said Sunday.

The earliest the state will begin its first phase of reopening is May 15, but only in places that have seen a 14-day decline in hospitalizations, Cuomo said.

He said the state's multiphase reopening will start with construction and manufacturing at "businesses that have a low risk."

Some states have said they are considering letting hospitals do non-urgent surgeries again. Tennessee Gov. Bill Lee said at a news conference that elective medical procedures can resume Friday.

Daily cases in Tennessee appear to be level or slightly rising, according to a chart on the health department's website

Antibody testing ramps up

In Boston, Mayor Martin Walsh said 1,000 asymptomatic residents will undergo diagnostic and antibody testing to evaluate exposure to the virus in the city. The testing is expected to be done by Friday.

And beginning Tuesday, health workers will start visiting randomly selected homes in Fulton and DeKalb counties in the Atlanta area to conduct antibody testing through blood samples.

"This investigation will help us estimate the percentage of people in the community who have been infected with the virus that causes Covid-19," the Georgia health department said.

"All members of the households selected will be asked to participate, including children. Participation is voluntary, and you can ask investigation teams any questions you have before agreeing to participate."

The virus is too new, and "four months into this pandemic, we're not able to say that an antibody response means that someone is immune," said Dr. Maria Van Kerkhove, technical lead for the World Health Organization's coronavirus response.

"This is a very active area of research."

Van Kerkhove said that those infected with Covid-19 will likely have some level of protection.

"What we don't know right now is how strong that protection is, and if that's seen in everybody that is infected, and for how long that lasts."

Washington says it will grow testing supplies

President Donald Trump told reporters at the White House that there have been 5.4 million coronavirus tests done in the United States.

"We are lapping the world on testing and the world is coming to us," Trump said , though per capita testing rates remain behind other nations, and health officials say there isn't enough testing for states to safely reopen.

Director of US coronavirus testing Adm. Brett Giroir said the federal government will continue to help states procure supplies for coronavirus testing, despite new guidelines saying the government should be a "supplier of last resort" for tests.

"It's very important that I think we don't interrupt our commercial channels, because they're very efficient and this is what they do, but we do have to prioritize them," Giroir told reporters outside the White House.

"Some of the larger companies, the testing companies, we need to make sure that the states that have a certain machine or a certain test are adequately supplied until we get 10x the amount that we need."

Giroir described supplies like swabs as a "small, fragile ecosystem right now."

He said for a few months the federal government will get them and distribute them to states. He thinks the supply chain will be more robust by mid- or late summer.

As early as late next week, the aim is to be able to send supplies to states without them having to make requests.

"We're really starting to a more prospective way that everybody has what they need in terms of their testing plans, but we supplement," he said.

Researchers are looking into possible treatments

Preliminary results of a clinical trial for heartburn medicine in coronavirus treatment could come in the next few weeks, said Dr. Kevin Tracey, president of Feinstein Institutes for Medical Research at Northwell Health.

"We don't know if it has any benefit. We really don't. I swear we don't," he said. "People are hoping for anything. But we need to do this clinical trial."

Separately, preliminary results for a clinical trial of the experimental antiviral drug remdesivir could come out in a week or two, said Dr. Andre Kalil, a principal investigator in the trial. But final results are not expected until mid-to-late May.