"Epidemic" may be used to describe a disease which has spread and is/is not contagious.
I believe you are using epidemic as a noun, and with that in mind I suggest an example for comparison, for fun;
"Normally I would use forms of the words "stage" or "phase" for a period of time, but these would imply the period of time is finished. Are there any "nouns" for a period of time which has occurred but is not finished?"
I've ruled out "stage" as a possible answer for, in my opinion, the word "stage" implies the period of time is finished. As a matter of fact, I rule out all nouns which could be used to describe a period of time which is finished.