Ebola is on the move, with confirmed cases in the United States last week and in Spain this week. “The ability of people who are infected who could carry that across borders is something that we have to take extremely seriously,” President Obama said Monday after meeting with top advisers to discuss the Ebola epidemic. In response, Obama said his administration would increase passenger screenings at airports in the United States and Africa.

The president did not go into detail about the new screening possibilities, though the White House said Tuesday new measures would be announced in “the coming days.” An official familiar with the options being considered said they include everything from taking the temperature of travelers arriving at U.S. airports from Ebola-stricken countries to doing more to track the travel histories of international travelers arriving in the country. Sen. Charles E. Schumer (D-N.Y.) told The Washington Post on Tuesday that there will be “tougher types of screening” at U.S. airports. [UPDATE: The new screening measures announced Wednesday include taking temperatures of people who traveled from West Africa. More here.]

These plans could theoretically prevent some people who are infected with the Ebola virus from entering the country. They also cannot possibly stop every person with Ebola who may arrive in the country. This is because of the simple realities of the disease ravaging West Africa, whose symptoms take time to manifest, as well as the nature of air travel in the 21st century.

Public health officials are realistic about this point, openly stating that the danger of additional Ebola cases in the United States will remain real as long as the outbreak is raging in West Africa, where the disease has killed more than 3,400 people and infected double that number.

“The plain truth is, we can’t make the risk zero until the outbreak is controlled in West Africa,” Thomas Frieden, director of the Centers for Disease Control and Prevention, said during a conference call with reporters last week. “What we can do is minimize that risk.”

One way the U.S. government has tried to minimize that risk: Increased exit screenings at airports in the afflicted countries. Since August, the CDC has been working on strengthening efforts to screen passengers leaving West Africa. That screening involves taking temperatures (checking for a fever greater than 101.5 degrees Fahrenheit), keeping an eye out for any other symptoms and having travelers fill out a questionnaire. These methods have stopped 77 people from boarding planes out of the affected countries, including 17 last month, according to Frieden.

Of course, these methods cannot stop everyone, as you can tell from the fact that a person who went through such a screening is currently being treated for Ebola in a Dallas hospital.

Thomas Eric Duncan, the first person diagnosed with Ebola in the United States, left Liberia on Sept. 19. He filled out an airport questionnaire asking whether he had touched anyone who had died from Ebola or whether he had cared for an Ebola patient. A person trained by the CDC took his temperature, using a thermometer approved by the U.S. Food and Drug Administration, but he had no fever. And he did not exhibit any symptoms for five more days. When people arrive in the United States, Customs and Border Protection personnel are supposed to look at travelers for “overt signs of illnesses,” but, again, a person who is not symptomatic would not display any signs.

Duncan’s example illustrates the gaps in the system, which can be knowingly or unknowingly exploited. A person filling out the questionnaire may not want to answer honestly, because that could prevent them from being able to leave Liberia. But a person filling it out may simply just not realizethat  they had contact with someone infected with Ebola. (The Liberian government plans to prosecute Duncan on suspicion of lying on the questionnaire.)

But there are myriad hypotheticals that illustrate why travel restrictions based on taking temperatures and closely monitoring travel histories would not be foolproof. A person could fly from Liberia to Brussels, spend a few days there and book a separate ticket to the United States. (Tracking by U.S. Customs and Border Protection would show that a traveler who booked the entire trip on one ticket started in Liberia, but a passenger who buys multiple tickets wouldn’t show up the same way.) A person could fly from Liberia to London, begin exhibiting symptoms and inadvertently pass the illness on to another person who is flying to the United States and who has never been to West Africa. A person could be transported from an Ebola-riddled country and treated in another country before infecting a person there who thought they were following the necessary protocols and traveled elsewhere. The list goes on and on.

In addition, it takes time for the Ebola symptoms to emerge. The peak period is about eight to 10 days after infection, but it can take as long as 21 days for the symptoms to appear. So a person may be infected with the virus but have no fever or exhibit no other signs, which means the thermometer and visual check would not work, and they would be able to travel weeks after being infected.

There are also the realities of the epidemic raging in West Africa. The World Health Organization has reported more than 7,400 confirmed or likely cases of Ebola, with each infected person infecting about two additional people. So there was no way to avoid any cases of Ebola in the United States.

“It was inevitable once the outbreak exploded,” said Thomas Geisbert, a professor at the University of Texas Medical Branch at Galveston, who has researched the Ebola virus for decades. “Unless you were going to shut down airports and keep people from leaving [West Africa], it’s hard to stop somebody from getting on a plane.”

And that raises a question that has been broached by politicians and other people: Why not just ban travelers from these countries? (Some airlines have reduced air travel in the region.) Public health officials have pushed back against such a move, saying that it would result in economic damage and keep doctors, nurses, humanitarian workers and needed supplies from reaching the region.

“Although we might wish we could seal ourselves off from the world, there are Americans who have the right of return,” Frieden said during a briefing Saturday. “There are many other people who have the right to enter into this country.”

Authorities in the United States continue to sa ythat they do not plan to ban travelers from West African countries. The White House said Monday that such a ban was not being considered. The Federal Aviation Administration, which has the ability to revoke the rights of certain foreign carriers from landing in the United States, said in a statement Monday that the World Health Organization and the CDC have not recommended tighter travel restrictions.

Obama on Monday reiterated what various officials and experts have been saying, emphasizing that the United States is prepared to contain Ebola. He also pointed to the fact that despite months of travel since the Ebola outbreak and more than a dozen people being tested for Ebola in the United States, Duncan is an outlier.

“In recent months, we’ve had thousands of travelers arriving here from West Africa,” he said, “and so far only one case of Ebola has been diagnosed in the United States, and that’s the patient in Dallas.”

Ashley Halsey III, Sean Sullivan and Brady Dennis contributed to this report.

[This report has been updated to note the White House’s comment that the new measures would be released in the coming days.]