As immigration opponents continue to froth over the caravan making its way from Central America toward the United States, some are floating the idea that asylum-seekers will bring disease with them—including one that was wiped out nearly 40 years ago.

The right-wing magazine The New American ran a story over the weekend headlined: “Will Migrant Caravan Kill Your Child—With Disease?”

“What about diseases?” Fox & Friends co-host Brian Kilmeade asked Monday. Later, Fox News contributor Sidney Powell suggested that the current outbreak of acute flaccid myelitis (AFM) affecting children was because of migrants—prompting host Lou Dobbs to correct her on air.

And former immigration agent David Ward, also appearing on Fox, cited a disease that doesn't actually exist anymore.

“We have these individuals coming in from all over the world that have some of the most extreme medical care in the world,” Ward said. “And they're coming in with diseases such as smallpox and leprosy and TB [tuberculosis] that are going to infect our people in the United States.”

It's next to impossible for the migrants to have smallpox, the last known case of which was seen in Somalia in 1977. The uncurable disease, characterized by painful pustules that erupt on skin and internal organs, was declared eradicated in 1980 after  an aggressive worldwide vaccination campaign. The only remains of it (as far as public health officials are aware) are in Russia and an undisclosed U.S. lab controlled by the Centers for Disease Control.

Some researchers have looked at the virus’s potential replication and dissemination as a bioterror weapon. One Canadian researcher sparked controversy by claiming to have replicated the disease by ordering DNA fragments through the Internet, stitching them together and creating horsepox, a variant that doesn’t affect humans.

But the chance of migrants carrying smallpox over the border, without the involvement of state-sponsored terrorism, is practically zero.

Ward's concerns about leprosy and tuberculosis are more plausible but still no reason for panic. The World Health Organization declared leprosy “eliminated as a public health problem” in 2000, though some pockets—most notably in India and Brazil—remain. Central America has reported scattered cases in the years since then.

Tuberculosis is a worldwide public health issue, but already exists in the U.S. and is treatable by antibiotics, according to the World Health Organization.

After Ward’s comment, Fox’s press office sent out a clip it billed as Charles Payne clarifying the issue for viewers.

But Payne only referred to leprosy and TB and did not mention the ludicrous smallpox comment. Even then, he did not disavow Ward’s comments, saying only: “We have no way of independently confirming this.”

Meanwhile, Dobbs’ guest seized on public fears about a different condition, AFM, a mysterious ailment that spiked in the U.S. this year with 72 confirmed cases so far.

It came up as Powell, a former federal prosecutor calling for a crackdown on migrants, said the U.S. could not handle what she termed an “invasion.”

“We have diseases spreading across the country that are causing polio-like paralysis of our children,” she said.

That fact-free assertion was too much even for Dobbs.

“You can’t very well blame that disease on illegal immigrants,” he said. “We don’t know the cause of it. I don’t know that’s fair.”

But Powell remained undaunted.

“That is part of the problem,” she responded. “We don’t know where the diseases are coming from.”

Conservatives have used fear-mongering about disease in the past. In 2014, they launched a campaign to portray Latino immigrants as Ebola carriers, even though there have been no reported cases of Ebola among migrants or people of Latin American origin entering the United States.

At the time, Sen. Thom Tillis (R-NC) said in a debate that the U.S. risked being exposed to Ebola without a secure border with Mexico. Sen. Rand Paul (R-KY) echoed these false concerns in 2016.