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An endemic disease is one that is present all the time in the population or area1. There is a more or less constant low level of occurrence of the disease in the population. For example, malaria is endemic to many of the tropical areas of the world where certain mosquitoes are common.
This is contrasted to an epidemic disease, which occurs in widespread outbreaks affecting many individuals, and then essentially disappears2.
Note that while one might properly refer to "an epidemic" of a disease, one does not ordinarily say "an endemic" of something3. A disease "is endemic to the region," or it is not. Also, you might wonder what an outbreak of a particular disease in animals might be properly called.
1. It is "in the people" (Greek: demos)
2. It is "among the people"
3. But note:
Fear, which is an endemic latent in every human heart, sometimes rises into an epidemic. --J. B. Heard.