You’ve heard the warnings. Supporters of President Donald Trump’s strict immigration policies are spreading alarm about a caravan of Spanish-speaking migrants bringing deadly diseases to our borders. There are even claims that some of them are carrying smallpox.

If that were true, it wouldn’t be the first time. Caravans of disease-carrying migrants have reached our borders before, and the devastating effects for public health are well known. They spread measles, typhus, cholera and a host of other lethal infectious conditions in addition to smallpox, causing misery and death for countless native-born Americans.

The first caravan, this one composed of ships, arrived in 1492 from Spain. Its successful voyage led many others to follow from England, France and other countries in Europe, bringing waves of disease-carrying migrants. Within a few decades, the illnesses they carried had sickened or killed thousands of people.

The early migrants didn’t know they harbored deadly germs. Most of them had developed immunity from early exposure at home. However, they were highly infectious to those who had never been exposed, like the people who lived in America before they arrived.

But, there is a big difference between the public health consequences of the migrant caravans of past centuries and the one that recently arrived at the Mexican border. We know with near certainty that none of the newcomers has smallpox, because that disease was completely eradicated almost 40 years ago. And there is no evidence that they present any serious disease risk. We also have tools for screening and treating them, if they do.

Border controls today are, of course, essential for protection against countless risks that open borders could present. But debates over immigration policy should focus on real risks and benefits of immigration, not imaginary ones. The health threats from today’s migrants are nothing compared to those brought by the early European newcomers, some of whom are the forebears of those warning about the risks of immigration today.