Endemic and epidemic are both words that diseases love, but something endemic is found in a certain placeand is ongoing, and epidemic describes a disease that's widespread.
A disease that is endemic is found in a certain geographic region or in a specific race of people. Malaria is endemic to parts of Africa because it's hot and skeeters love it. Tay-Sachs is a genetic disease endemic to Jews and French Canadians. On the brighter side, a plant or animal can also be described as endemic to a region. If it's in the system, it's endemic:
Many relief workers who came to Haiti lived in South Asia, where cholera was endemic. (New York Times)
Catalina endemic plants are species that occur naturally on Catalina Island and nowhere else in the world. (Catalina Island Conservancy)
Epidemic describes a disease that is widespread, affecting an "atypically large number of individuals within a population, community, or region at the same time," according to the Merriam-Webster Medical Dictionary. The disease, however eventually subsides. Here are some epidemics:
The Sunshine Coast is in the midst of a whooping cough epidemic with an average of three new cases presenting every day this year. (Sunshine Coast Daily)
But we're still talking about a huge epidemic in this country where more than half a million babies are born each year preterm. (Time)
An endemic disease is restricted to a place, as with malaria, or a people, as with Tay-Sachs. An epidemic disease may happen in a specific place, but it can spread beyond that place, as with asthma or AIDS.