If you look through horse ads in the United States, you'll see "negative Coggins" on a lot of them.
The "Coggins test" is an antibody test for Equine Infectious Anemia. This is an unpleasant disease that's sometimes called horse/equine malaria or swamp fever. It's transmitted by biting flies and is a viral infection. (It can also be transmitted by using contaminated needles or surgical equipment). It's called the Coggins test, after its inventor, Leroy Coggins. (There are also other tests, but they are more likely to result in false positives).
It's endemic in the Americas, some parts of Europe, the Middle and Far East, Russia, and South Africa. (It is not known in Australia or the United Kingdom).
EIA can be fatal in the acute form. Horses that have chronic EIA can recover, but remain infectious their entire lives. Many horses remain asymptomatic carriers or have infrequent "episodes" of illness. Coggins testing is conducted every twelve months (sometimes more often in horses that are at particularly high risk).
Positive horses are almost always euthanized, although pregnant mares may be kept alive long enough to deliver - although transmission through the placenta is known, it's rare). If the horse is kept alive, it can never be allowed within 200 yards of another horse as long as it lives - and most horsemen consider euthanasia a more humane option for these highly social animals. Also, in most of the United States, vets have the option of ordering euthanasia and not allowing the quarantine option.
Symptoms of acute EIA are fever, depression, anemia and loss of muscle tone and condition - but other diseases can present the same way, so an antibody test is normally performed.
All racetracks and most showing organizations in the United States require a negative Coggins test. Transporting a horse long distances (across state or country lines) except for slaughter also requires negative Coggins, as does sale by auction.
There's currently no EIA vaccine, but a lot of work is being done on it. And, of course, if you're operating in the past, the Coggins test was only developed in 1970 and approved in 1973. (In fact, Leroy Coggins only died in February of this year). So in your historical fiction or fantasy, "swamp fever" could be used if you need an equine epidemic - maybe to make somebody desperate to find healthy horses...
Depending on the level of knowledge, your characters might take anti-EIA precautions - which can be as simple as using a lot of fly spray.