(CNN) Two days after announcing coronavirus cases were climbing at a frightening clip -- notably in two parishes that make up most of metro New Orleans -- Louisiana Gov. John Bel Edwards made a plea for a major disaster declaration Tuesday.

The declaration would provide various agencies with additional federal resources as they combat the pandemic

"I have determined that this incident is of such severity and magnitude that effective response is beyond the capabilities of state and local governments," Edwards wrote in a letter to the White House

This follows his assertion during a Sunday news conference that "there is no reason to believe that we won't be the next Italy. ... We have the fastest growth rate of confirmed cases in the world in the first 13 days right here."

Parishes rank among the worst

Late Monday, The Times-Picayune/The New Orleans Advocate published a story reporting that with the focus on California, New York and Washington locales, New Orleans had been overlooked, despite having some of the highest infection rates in the nation.

Health workers screen for Covid-19 at West Jefferson Medical Center in Marrero, Louisiana, on Tuesday.

The numbers move quickly as Covid-19 spreads, but CNN's own analysis of county-level data collected by Johns Hopkins University showed that as of noon Tuesday (1 p.m. ET), Orleans and Jefferson parishes were two of the deadliest places to contract the virus.

A quick look at the deaths per 100 cases (in counties with 100+ cases):

King County, Washington -- 7.4

Santa Clara County, California -- 4

Orleans Parish -- 3.5

Palm Beach County, Florida -- 3

Dallas County, Texas -- 2.6

Fairfield County, Connecticut -- 2.2

Snohomish County, Washington -- 2.1

Jefferson Parish -- 2

For comparison, New York City has a death rate per 100 cases that's less than half of Jefferson Parish's.

To be sure, Jefferson and Orleans parishes are much smaller than the counties with which they're being compared above.

Breaking down the numbers by deaths per 100,000 residents -- again, using only counties with 100 or more cases -- Jefferson and Orleans parishes ranked No. 1 and No. 5 respectively, as of noon Tuesday.

'Stay home'

Last week, New Orleans Mayor LaToya Cantrell issued a stay-at-home order for her city, closing businesses and banning gatherings of more than 10 people.

"If you don't have any essential function or cannot safely maintain social distancing, you need to stay home," Cantrell said Friday. "Don't look for ways for the rules to not apply for you. ... Stay home."

The city has created a special police team to enforce order and respond to reports of large gatherings. Establishments that don't comply with the order could permanently lose their business licenses, the New Orleans Police Department said in a tweet.

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As of 3 p.m. ET on Tuesday, only California, New Jersey, New York and Washington had more cases than Louisiana, which had almost 1,400. Forty-six people have died, according to CNN's 3 p.m. tally.

Could patients overwhelm hospitals?

Another startling number, Edwards said: The state saw its number of cases jump tenfold one week.

Even more worrisome, Louisiana could reach its health care capacity within days if the cases continue to rise at the current pace, the governor said.

"If we want to flatten the curve we have to take more aggressive mitigation measures now and limit social contact now," he said Sunday. "We've got to take action now."

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Tulane Medical Center, Louisiana State University Health and Ochsner Medical Center did not immediately respond to CNN's request for comment on Edwards' concerns about available hospital beds.

Louisiana Children's Medical Center Health, a system encompassing four hospitals, had no comment on the governor's remarks. A spokeswoman declined to say how many of its employees had been tested or had tested positive for coronavirus.

Elderly hit hard

Of particular concern for health officials is Lambeth House , a retirement community in New Orleans that had two dozen cases as of Friday, according to Dr. Alexander Billioux, assistant secretary of health for the state's Office of Public Health.

Seven deaths have been linked to the Lambeth House cluster , Billioux said.

"Lambeth House is truly a community of people who care deeply about one another," said Christina Fay, board director of Lambeth House. "The intensity of sadness that accompanies what our community is currently enduring is almost indescribable."

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At least seven nursing homes in the state have reported cases, Billioux said. The health department is in daily contact with the facilities and monitoring the situation, Billioux said.

As part of his Sunday order mandating that residents stay home, Edwards instituted restrictions on visiting retirement communities.