What's a word for a non-communicable (non-contagious) disease that has still spread throughout a population?

Solution 1:

Epidemic means only that the disease has spread more than expected; pandemic that it has spread to other countries. It doesn't have to be contagious — Bradd Szonye is correct in that — but it could be, so if you really want "words that mean a disease has spread but is not contagious" epidemic doesn't specifically say that.

You could try outbreak:

a sudden, violent, or spontaneous occurrence, esp of disease or strife

Solution 2:

In medical/veterinary fields, the word prevalence means:

the total number of cases of a specific disease in existence in a given population at a certain time

(Saunders Comprehensive Veterinary Dictionary, p 920; Dorland's Illustrated Medical Dictionary 31st Ed., p 1536)

And the word prevalent means:

widespread occurrence (Saunders Comprehensive Veterinary Dictionary, p 920)

I think you could say that a disease is prevalent in a community without necessarily implying that it was spread by contagion. You are just stating that it is now widespread.