“We still don’t know the state of our house,” said Justin Sylvest, 21, who lives with his girlfriend and their 11-month-old in Denham Springs, a town east of Baton Rouge that was among the hardest hit.

The three of them had been staying since Sunday at an emergency shelter on the vast grounds of the Lamar Dixon Expo Center in Gonzales, southeast of Baton Rouge. Sylvest said the shelter had provided everything his family needed, starting with formula for the baby and clean clothes.

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But a shelter’s still a shelter, a gymnasium lined with cots with no personal space or guaranteed quiet — all the more difficult for a young father who isn’t sure whether his family has a place to live or a way to pay the bills. He said he hadn’t slept much.

“I don’t even know when I’ll be able to go to work,” Sylvest said, taking a drag on a cigarette. “It’s going to be a lot getting back to normal.”

After two feet of rain began falling Thursday night, water rose quickly in Baton Rouge and then migrated east and south, leaving a vast swath of damage. At least 40,000 homes have been damaged, according to Gov. John Bel Edwards (D). The death toll has risen to 13.

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Roads remain flooded and closed, while schools, businesses and government offices have been shut down for days. The country has not seen a natural disaster this bad since 2012, when Hurricane Sandy pummeled the East Coast, according to the American Red Cross.

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“The current flooding in Louisiana is the worst natural disaster to strike the United States since Superstorm Sandy,” Brad Kieserman, vice president for disaster services operations and logistics for the Red Cross, said in a statement. “The Red Cross is mounting a massive relief operation, which we anticipate will cost at least $30 million and that number may grow as we learn more about the scope and magnitude of the devastation.”

Many scrambling to escape the water or witnessing the chaos from afar have wondered why the flooding has not gotten more widespread national attention. William W. Craig Fugate, administrator of the Federal Emergency Management Agency (FEMA), referred to those concerns at a news briefing in Baton Rouge on Tuesday, but he assured residents that the federal government was deeply aware of the scope of what happened.

“This is a very large disaster impacting tens of thousands of people,” Fugate said. “Irregardless of what it may be getting in the national coverage, we know this has been a significant impact here in Louisiana.”

President Obama declared the flooding a major disaster, and so far, 20 parishes have been added to that declaration, officials say. More than 70,000 people in the state have registered for FEMA assistance.

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Obama spoke with Fugate on Wednesday morning for an update on the flooding response, the White House said. During the discussion, Obama told Fugate “to utilize all resources available to assist in the response and recovery,” according to Jen Friedman, the deputy White House press secretary.

Homeland Security Secretary Jeh Johnson is scheduled to visit the region on Thursday and will meet with state and local officials to review the response there, a spokeswoman for the department said.

For Phonecia Howard, whose house was all but destroyed when Hurricane Katrina hit in 2005, she looked out her window in East Baton Rouge Parish and had one thought while watching four feet of water creeping up her lawn.

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“I was just thinking not again,” she said Wednesday. “This cannot happen again.”

Her family fled their New Orleans home at 4 a.m. the day before Katrina slammed into the Gulf Coast. They made the decision to head for Baton Rouge, to take refuge from the storm with family, settling in a neighborhood that had never flooded.

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All of the memories from Katrina — ripping out sheet rock, stepping over warped hardwood floors, having to replace all their possessions right down to the last measuring cup — raced through her mind as she waded into her yard this past weekend and stepped into a boat waiting to take her to safety.

“I was praying, just ask God to spare us one more time,” she said.

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Authorities are seeking to keep people off the streets at night, raising the specter of looting in a region where scores of homes have been abandoned.

The East Baton Rouge Sheriff’s Office said in a statement posted on Facebook that between Monday night and Tuesday night, about 10 people had been arrested for looting in that parish. The tally included four men who the sheriff’s office said broke into a Dollar General store and stole $750 worth of supplies. The sheriff’s office announced a curfew between 10 p.m. and 6 a.m.

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First responders — many of whom face their own crises at home — have been racing to keep up with calls for help and rescue. Officials said it’s unclear how many people are missing in neighborhoods that are still flooded.

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“I don’t know that we have a good handle on the number of people who are missing,” Edwards said at a news briefing Tuesday afternoon. He said it was likely that many who are missing are safe but unable to communicate with their loved ones.

The number of those stranded and still needing rescue “was next to impossible to say,” said Mike Steele, a spokesman for the Governor’s Office of Homeland Security and Emergency Preparedness, “and it’s changing every minute.”

Teams are going to search as many as 30,000 homes and buildings in at least five parishes over the next two weeks, said H. “Butch” Browning, the state fire marshal, whose office is coordinating the urban search and rescue effort.

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“We are really challenged in situations like this, where you have such widespread damage,” Browning said. But he said he anticipated finding far fewer bodies than were found during a similar effort after Hurricane Katrina.

When Katrina hit, people were facing not only rising water but also high winds and a tidal surge. “We won’t see that type of death toll at all,” Browning said.

In some neighborhoods, where water has receded, the damage is only now becoming clear as residents return to begin cleaning up. The curbs in the Sherwood Forest Oaks neighborhood of Baton Rouge were lined Tuesday afternoon with the detritus of people’s lives: couches and mattresses, flat-screen televisions and dressers, all waiting for a garbage truck to come.

On Wednesday, Jewels Simpson was wandering around what remains of her home in central Louisiana, looking at broken bookshelves, crumbled furniture and belongings thrown from room to room.

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“The home looks as if you picked up a snow globe and shook it,” Simpson said. “My refrigerator was on its back … My chair in my office, my desk has only two legs left.”

Others had been chased from place to place by water that kept coming. Christine McFarland’s eyes grew wide as she told the story of her escape from the flood on Saturday. That morning, there had been no standing water at her apartment complex in Baton Rouge — just rain that was falling hard but hardly seemed extraordinary. But then the water started rising, fast. Within an hour, she said, it was up to her chin, and she and her daughter nearly had to swim out of the apartment building.

“We have never been through anything like that,” McFarland said Wednesday. “It was very scary.”

They were able to walk to a place where the water hadn’t risen yet, where her daughter had parked her car. From there, they took refuge at another family member’s house in Galvez, until Galvez also flooded. Then they headed to a hotel in La Place, a half-hour east of Baton Rouge and away from the worst of the water. That is where they have been since Sunday, trying to come to grips with a world turned upside-down overnight.

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“You’re in shock. You’re thinking, what just happened?” McFarland said.

McFarland said she can deal with the loss of her Lexus SUV and things inside in her apartment. She lived on the first floor, and the property managers have told her that the water ruined everything. But what she is having trouble with, what has been making it impossible to sleep, is the thought that at age 59, she has no place to go. No place that is hers.

“I feel so homeless. I feel like where do I go from here?” she said, tearing up. “I need a home.”

Inside one home in Baton Rouge, the air was humid and smelled of rotting food. The floors were covered in a thin layer of mud, and a refrigerator lay on its side, tossed by water that had risen to shoulder height, according to the marks left on the walls.

Josh Raley, 29, an associate pastor at the Community Bible Church in Baton Rouge, was helping a church member haul armful after armful of ruined things outside. “If Hurricane Katrina taught us anything, we’re looking at six to nine months before anything gets back to normal, and probably longer,” he said.

Sandi McGrew spent most of the first few days of the storm trying to keep her animals — including a dozen horses and four dogs — safe. Two of the horses died, so she had to tackle the question of how to dispose of their bodies.

But by Tuesday, she had time to reflect on what had happened. She was living on the second floor of her ranch, which she usually rents out to tenants; her own home, on the first floor, was devastated.

The scene downstairs “reminds me of the Titanic,” she said. “Everything floating. Things that were in one room are now in another. I lost everything.”

“I’ve been so focused since the water started rising on the safety of the horses that I couldn’t think about my things. The horses are all right. Now what do I do? I don’t really know where to go from here.”

Berman reported from Washington. Sarah Netter in Slidell, La., contributed to this story.

[This story, first published at 9:21 a.m., has been updated and will be updated throughout the day.]