A plague of locusts as "cause of death" Is an epidemic, but is not an infectious disease ....
I think that' s the crux of the difference. I don't think you can have an epidemic of locusts?
So plagues of locusts (and so forth) would go under "natural disasters."
Epidemics are infectious diseases, although of course, not all infectious diseases reach epidemic proportions.
Glad the CDC & WHO do the definitions. :)