In the wake of the revelation that the Dallas man infected with Ebola flew on United Airlines flights from Liberia, more than a few people have seized on a blunt response: Ban flights from West Africa. Rep. Ted Poe, R.-Texas, has written to the Centers for Disease Control asking it to recommend travel restrictions. Rep. Alan Grayson, D.-Fla., has called for a 90-day ban on travel from Ebola-touched countries to the U.S.

The White House is resisting those calls, and that’s the right thing to do. Restricting travel to and from the affected region will have little impact on the already minimal risk to Americans from the Ebola virus while further worsening the situation in West Africa. And the history of the global fight against infection has demonstrated that we shouldn’t raise the drawbridge or run away, but fight disease wherever we find it.

Travel restrictions have a long history as a tool against spreading infections. Quarantine was first used against the plague bacillus in 14th-century Europe. The case for plague quarantine was a lot stronger 600 years ago: It was pretty much the only potentially effective public health strategy at the time (neither prayer nor pogroms had the desired impact). The Black Death still exists — there were four cases of human infection in the U.S. in 2012 — but we now have a vaccine against the disease. It can be treated with antibiotics, and sanitary and housing conditions in the 21st century are considerably higher than in Europe in the 1300s. The plague bacillus led to the deaths of tens of millions in the 14th century; it kills a few hundred people worldwide each year today.

We don’t have a vaccine against Ebola, nor a fully developed cure. But, like the plague, the disease is an unlikely candidate for epidemic status in the U.S. or elsewhere in the developed world. The only way to get Ebola is for the bodily fluids of someone who’s exhibiting symptoms to come into contact with your soft tissues — the eyes or mouth, for example. In the worst of circumstances, the average Ebola victim infects from one to two other people, compared with 10 or more who can be infected by someone with measles.

Even partially effective isolation of people with symptoms is enough to stop an epidemic — and that’s why all previous Ebola outbreaks have sputtered, leaving the world with no reported cases in 2010, for example. The U.S. has top-notch isolation facilities, and health authorities have considerable experience of “contact tracing,” or finding all the people the victim has spent time with since they began exhibiting symptoms and checking that they don’t have the disease. All of which is why CDC Director Dr. Tom Frieden has expressed confidence that Ebola will be stopped in its tracks in America.

Controlling illness by quarantine of an entire country or region involves trade-offs. It’s always theoretically possible to avoid risk by completely cutting yourself off from contact, but then you’ll be alone. We take some risk of infection through contact because the benefits of that contact outweigh the risks. Trade is worth one-quarter of U.S. gross domestic product. People want to travel to see family and friends, visit new places, work or invest. We think all that is worth the price of somewhat increased risks of illness.

Other global diseases pose a far greater threat to the U.S. than Ebola: In an average year, more than 23,000 deaths in America are associated with influenza. Staff at the CDC have estimated the potential economic cost of an influenza pandemic in the U.S. at about $100 billion. But this toll isn’t enough for us to shut the borders in an attempt to keep influenza at bay. And, realistically, the idea that we could completely seal off the U.S. from the rest of the world is laughable — at best we might delay a disease from arriving by a few days or weeks. We’re not even willing to take considerably more targeted and effective measures, such as banning kids from school if they haven’t taken the flu vaccine or providing shots for free at pharmacies.

Even without a formal travel ban, most of the economic harm from epidemics comes from reduced commerce. A 2006 World Bank staff estimate of the global costs of a flu pandemic suggested it could reduce global GDP by $1.5 trillion. One-third of that sum was accounted for by death, illness and absenteeism. But two-thirds was due to the cost of efforts, including reduced travel, to keep away from infection. The bank has estimated the cost to Liberia of the Ebola outbreak in 2014 to be equal to more than 3 percent of the country’s GDP.  Add in a formal travel ban, and the impact on some of the world’s poorest economies could be catastrophic.

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

But with greater support, the three countries bearing the brunt of the epidemic can fight back against Ebola. Neighboring Nigeria and Senegal have shown that Ebola can be detected, victims isolated, their contacts traced and the disease shut down. And while Liberia, Guinea and Sierra Leone have desperately fragile and underfunded health systems made worse by Ebola’s toll on medical staff, their programs aren’t completely dysfunctional. All three countries have completely wiped out major infections: smallpox, polio and guinea worm. Liberia and Sierra Leone regularly vaccinate nine out of 10 children against diphtheria, whooping cough and tetanus, while Guinea vaccinates nearly two-thirds of children against the three diseases.

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. It wasn’t until the third decade of our knowledge about AIDS that the world made a significant global effort to respond, notably through George W. Bush’s 2003 announcement of the President’s Emergency Plan for AIDS Relief, or PEPFAR. By that time, the disease had killed millions and spread globally.

But for all the late start, the initiative currently supports treatments for 6.7 million people with HIV worldwide, and the number of new infections worldwide dropped by one-quarter from 2001 to 2011.

We’ve also seen incredible progress against a range of infectious diseases over the past 20 years because of the rollout of vaccinations and other interventions in even the poorest countries: From 1990 to 2010, according to the Global Burden of Disease Study, the number of tuberculosis deaths worldwide each year dropped by 276,000. Deaths from cholera and whooping cough each more than halved, saving more than 120,000 lives a year. And the number of deaths each year from tetanus and measles combined tumbled from 900,000 to 187,000. Just these five diseases kill more than 1 million fewer people each year than they did 20 years ago.

This global progress is the most powerful weapon we have in permanently reducing the risk and cost of infectious disease in the U.S. The eradication of smallpox has saved somewhere more than 40 million lives, but it also saves about $2 billion a year in vaccination and hospital expenditures in the U.S. alone — an impressive return for a global program that cost about $300 million.

Continued global progress against infection involves more financing for institutions that support the fight against contagion worldwide, such as PEPFAR and the Global Alliance for Vaccines and Immunizations. And, critically, it also means providing financial, human and moral support for national health systems worldwide to ensure they can better respond to outbreaks. And that’s impossible if we simply close our doors and cut the people of West Africa off from the rest of the world.

We live in a global disease pool. In the end, once a disease begins to spread, there’s no escaping an infection, whether it first appears in Africa, Asia or the U.S. Travel bans are less effective than hiding under a rock and considerably more costly. To battle continuing epidemics and any future potential pandemics, we need strong health and surveillance systems in every country and research and development not just for the diseases of the rich but for the infections of the poor. Hitting emerging disease threats early and where they emerge is far less costly in terms of lives and financing than trying to play catch-up once they have spread.

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This article originally published at Businessweek here