the words "protest demanding"
Ebola sparks fear, and protests demanding stronger and smarter government actions.
What is "protests demanding"?

Question

Answer

I agree with Mojave.  The sentence becomes easier if we split it into its component parts:

Ebola sparks fear.

Ebola sparks protests.

What do the protesters demand?

Answer

"demanding stronger and smarter government actions" is a phrase that is modifying the noun "protests".

Another way to say it is "protests that demand ... action"

"protests demanding" by itself doesn't make sense. You need the complete phrase "demanding stronger... actions".

I hope that helps.