It parses fine to me, but then I'm a native English speaker (and I don't claim to know whether its content is actually true). Strictly speaking, there should be a comma after "case", which may have helped you but is unusual unless you're writing something really formal.

Here's the sentence restructured:

... vaccine refers to anything that induces an immune response against a pathogen or disease. Here is how that definition applies in this case: the vaccine causes the immune system to produce anti-EGFR antibodies.