How should deadly diseases be kept out of a free society?

A free society is supposed to have open borders, yet wouldn't that make preventing the entry of foreign diseases impossible? A society that opens it borders inevitably puts itself at risk for foreign diseases simply because people aren't being screened and excluded, as they are now. These diseases can be very dangerous, particularly when the domestic population has never been, or rarely is, exposed to them. So shouldn't the borders be closed to certain countries that might spread Ebola and other dangerous diseases.