You're right, it is a modern day problem, mostly caused the toxins that are in almost everything we eat and breath. If your body didn't have this environmental damage we wouldn't have the problem that some people have with parasites. One of thing you have to do actually, if you want to permanently get rid of parasites, is to remove toxins from your tissues. This is where fasting can really help.
Unfortunately, once parasites get a foothold in your body though, you're not getting rid of them with just fasting.