To be precise, some parasites can be eradicated, such as fish louse.
But Ich, which include several different species, some can be managed but not eradicated, some can be eradicated, such as by tank transfer method.
It depends on the methods of reproduction. Some ich such as Brook, multiply by dividing, some ich go through a life cycle that form cysts and fall off the fish.
It is reported that some ich can be alive even without fish, they can use soft coral as host, or other marine life form.
The bottom line is that in this hobby, many infections frequently lumped together and treated as such.
Also in general hobbyists do not have access to labs that can correctly identify the illness.
So keep the fish’s immune system up is the way to long term success.
By the way, fish can carry parasites, one form or the others, without showing symptoms. When it is stress, it’s immune system will be compromised that lead to infections.
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