epidemio

The seam is real, but it is Greek, not Esperanto. Nothing in epidemio decomposes with the affixes you have learned: there is no epi- prefix and no -demi- root in the language. Treat it as one indivisible borrowing and stop looking. What is worth knowing is what the Greek pieces meant, because they are a small free lesson: epi is upon and demos is the people. An epidemic is a thing that comes down upon a population. Once you see that, demokratio (rule by the people) and epidemio stop looking unrelated, and the word becomes almost impossible to forget.

The medical family around it. Viruso at rank 2,057 and bakterio are the causes; infekti at 1,783 is what they do; gripo at 2,791 is the everyday example this course reached only a hundred ranks ago. When an epidemic goes global, Esperanto says pandemio, formed on the same Greek root with pan- (all) instead of epi-. The adjective is epidemia, and the verb epidemiiĝi exists but is rare and clumsy; ordinary prose prefers disvastiĝi, to spread.

A register note. This is a newspaper and public-health word, not a conversational one. In speech about being unwell you want malsana at 456 or the specific illness. Reserve epidemio for the scale it names: a whole town, a whole winter, a whole lernejo shut.