The word centre does not.
the central point of something, typically a difficult
or unpleasant situation: the patient was at the
epicenter of concern.I've read many articles declaring that NYC was an "epicenter" of the COVID outbreak in spring of 2020, when "center" seems simpler and more appropriate.
Honestly, it's not a big deal, but I feel like those two syllables ("epi") are added to "center" without much thought and perhaps with some vague feeling that they give some high-tech oomph to the word "center."
edit: for earthquakes "epicenter" makes sense. For the distribution of an infectious agent, less so.