The talk of travel bans and the panic over the two infected nurses in Dallas reflects a huge mistake that Americans are making about the Ebola virus. The key to stopping the disease in the United States isn't stopping it in Texas; it's stopping it in West Africa.

Here's the scariest sentence yet in the entire Ebola outbreak: "The current assumption is that for every four known Ebola cases, about six more go unreported." That comes from an October 9th Washington Post report, and it's based on estimates from the Centers for Disease Control and Prevention. Hidden in that sentence is the pathway by which Ebola becomes an outbreak that threatens not just America, but the entire world.

We know how to stop Ebola: it's called "contact tracing," and health professionals have been using it to stamp out Ebola outbreaks for decades now. It's almost ludicrously simple: you quarantine the patient infected with Ebola, then you find every single person who had contact with the infected patient and watch them for signs of Ebola. It's as low-tech as medicine gets; it's almost more like being a door-to-door salesman than a surgeon. Here's how it works:

But contact tracing requires manpower. Lots and lots of manpower. You need health-care workers to track down the contacts, health-care workers to monitor their temperatures, health-care workers to follow up on new cases, health-care workers to treat the infected. And as the number of Ebola patients grows, the number of contacts that need to be traced grows exponentially.

This is the horrifying math of Ebola's spread. One patient might require you to watch 50 people. Three patients could mean tracking down 150 people. A hundred patients could mean 5,000 contacts to watch. A thousand patients could mean monitoring 50,000 contacts.

And now imagine that you don't even know where half of the cases — or more than half the cases — actually are.

This is how Ebola overwhelms health-care systems: it creates more contacts than can be traced, and it creates carriers that can't be traced. That's been happening in Guinea and Sierra Leone and Liberia. As Dr. Thomas Frieden, the director of the Centers for Disease Control and Prevention, told me, "We're increasing our efforts arithmetically, and the virus is increasing exponentially." And that's when Ebola gets dangerous: when we lose track of its spread.

The nightmare scenario for Ebola isn't a handful of high-profile transmissions in America. It's the outbreak's continued exponential growth in West Africa, where more than half of all cases go unreported. It's those shadow cases — people either unaware that they're sick, mistrustful of health authorities, or fleeing the threat of quarantine — spreading the disease back to Nigeria, or giving it a footing in India. It's 100,000 more cases emerging, and spreading the disease into yet more countries, more quickly, through more contacts than we can possibly trace.

And it's once that happens — once the rest of the world is overwhelmed, and once contact tracing can't keep up — that America will truly be threatened, because that's when cases we can't track begin coming into the country from disease clusters we didn't know about. And that's when Ebola will have the possible scale to begin overwhelming our defenses.

The US outbreak centered around Thomas Duncan in Dallas isn't going to infect 10 people. It probably won't even infect five. Contact tracing is pretty easy when you know exactly who the infected patients are, and where they went, and who they saw. The long-term threat to the US comes from the Ebola outbreak attaining the critical mass it needs to overwhelm West Africa, and then jumping to India, and then jumping everywhere else. And that critical mass will either emerge or be stopped in West Africa.

"The lesson of the world's efforts to stop other deadly diseases is that if we want to reduce our exposure to dangerous pathogens, we have to fight them where they are and when they emerge," writes Charles Kenny, a fellow at the Center for Global Development.

This is why a travel ban would be such a bad idea. As Kenny writes:

A travel ban would also be counterproductive for the U.S., making the likely global impact of the epidemic far worse. The three West African countries affected need outside support, including the hundreds of medical volunteers who have stepped forward from countries as disparate as the U.K. and Cuba. Banning flights into West Africa will delay the arrival of help when every day is critical in preventing an explosion of cases. Banning commercial flights out of the countries will deter people from volunteering to work in the region.

So that's one problem with a travel ban: it complicates the medical community's ability to quickly and flexibly mobilize against Ebola in West Africa, which is key to stopping the outbreak.

The second problem is that travel bans don't stop diseases from traveling. As Julia Belluz notes in a round-up of the evidence, we've tried travel bans before, and they haven't worked. But what a travel ban might do is convince the banned that if they want to escape Ebola, or even just to see family, they need to travel quietly, carefully, in ways that can't be easily tracked. To paraphrase the old saying, outlaw travel, and only outlaws will travel. And if the people trying to evade the ban turn out to be infected by Ebola but asymptomatic, then they'll bring those hard-to-trace infections to our shores.

You can't find a disease if you pass laws encouraging people to hide the disease. To stop the Ebola outbreak, you need a culture where people feel it's safe to come forward if they've been exposed. And you need to do that before the disease has infected so many people that health officials don't have the resources to track them all.

Which is all to say that America's focus needs to be making contact tracing work in West Africa. Ebola expert Richard Preston told Belluz that one reason America's initial response to Ebola was lackluster was that "all of the people who really know about Ebola are all over in Africa fighting it there. The CDC sent more than 50 Ebola experts and disease detectives over to Africa. Every expert was over there, and the people left [in the United States] didn't have that much experience with Ebola." Viewed one way, that's a problem: America's Ebola experts should be here, protecting us! But viewed correctly, that's great news: America's Ebola experts are there, protecting us!