Some 328 immigrants from China have been caught crossing the border illegally so far this year, according to Homeland Security data that raises the prospect a coronavirus carrier could sneak into the country via the U.S.-Mexico border.

Three other people from South Korea — another country with rapidly spreading cases — have also been arrested at the border, as have 122 people from the Dominican Republican, where the coronavirus has now been detected.

All told, more than 1,000 migrants a day are caught attempting to sneak in illegally from Mexico, which detected its first case last week, and since has identified five others.

And if that many are being caught each day, an unknown but significant number are getting through undetected, Border Patrol agents say.

“The journey to the U.S. border puts migrants in poor conditions,” a Homeland Security official told The Washington Times. “We don’t know if they have come into contact with someone who has the flu, there is no passport, medical history, or travel manifest.”

President Trump last week had floated the possibility of closing border crossings between the U.S. and Mexico, though this week he downplayed that option, saying he didn’t see the border as much of a vulnerability.

“We’re not seeing a lot of evidence in that area,” he said — though he added, “We’re closing it, I guess, automatically because we have a very strong border there now.”

Homeland Security officials, though, say it is a vulnerability.

Acting Homeland Security Secretary Chad F. Wolf raised the issue Tuesday with the House Homeland Security Committee, saying that illegal immigration presents a unique threat compared to legal travelers from China, who are being screened on arrival.

“The individuals that are coming in at our 11 airports that are being funneled, we have very good information of their travel history, of their medical history. We’re not going to have that same set of fidelity for the individuals if this continues to grow at the southwest border,” he said.

Mr. Wolf also said the spread of the virus in Mexico creates new complications, after the U.S. has forced tens of thousands of asylum-seekers to wait in that country while their cases are proceeding in American immigration courts.

Late last week a federal court issued a ruling that could result in thousands of them being admitted immediately.

The ruling was stayed, but Mr. Wolf said it could be a danger spot should the courts demand their entry.

Rep. Val Demings, Florida Democrat, chastised Mr. Wolf for drawing a connection between illegal immigration and the virus. “You were not, surely, suggesting that the problem that we are seeing in this country with the coronavirus is the result of — or was caused by undocumented immigrants coming across the south border. Is that what you’re saying?”

Mr. Wolf said he wasn’t pinning the current spread of the virus here on illegal immigration, but said the border is a risk factor.

Ms. Demmings demanded to know if he was ordered by higher-ups to tie immigration to the virus.

He said he was not.

So far none of the confirmed coronavirus cases in the U.S. have been tied to the border.

Coronavirus was identified last year in China, and has quickly frightened much of the world.

The U.S. has funneled travelers arriving from China into a select set of American airports, where they can be screened.

But that’s not possible with those crossing the border — particularly those who evade detection altogether.

There is no good public estimate of how many people avoid capture and make it to the interior, though some agents use a rough calculation of one got-away for every one that’s caught.

Many would-be undocumented immigrants from China try to enter by being smuggled in cars through the official border crossings, though an increasing number are now being snared by the Border Patrol after they’ve already gotten in.

In one case in January agents stopped a Chevrolet Silverado pickup truck and found 10 Chinese migrants piled on top of each other in the truck, along with five Mexican migrants. The truck driver had been trying to avoid detection by blending in with border wall construction crews.

One of the Chinese men said he was paying up to 40,000 Chinese Yuan to be smuggled into the U.S. — or about $5,750.

In another incident last month agents in Arizona spotted three Chinese migrants as they were picked up by smugglers. The Chinese men said their church had paid to smuggle them into Mexico, where another branch of the church connected them with smugglers who brought them into the U.S.

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