My answer is
(D). It took me 01:15.
(A) Can we say "an animal’s immune system" is "like a police officer"? In the context of this sentence, we can argue the two parties are similar.
The issue with (A) lies mainly in the use of "when police dogs are deployed". The relationship between tracking a criminal and deploying dogs is not clear and certainly not in parallel with the main clause.
We can keep it for now, hoping for a better choice.
(B) Can we say "an animal’s immune system" is "like the tracking of a criminal"? No. (B) is out.
(C) Very much like (A). There are two differences from (A)
(1) "a fleeing criminal" or "fleeing criminals"? Not necessarily a deal breaker, but plural form is better aligned with "antigens".
(2) “when police dogs are deployed” or "while deploying police dogs"? Again, they should be considered interchangeable. But an active voice in (C) might be better.
To ask test takers to pick between (A) and (C) is rather unfair. So it is possible that neither is correct.
(D) This is so much better!
"By deploying" clearly illustrates the relationship between deploying and tracking.
What's more, this as- clause is written in perfect parallel with the main clause.
Choose (D) as the best choice.
(E) Now "who tracks fleeing criminals by deploying police dogs" is a relative clause that modifies "a police office".
When "as" is used as a preposition, it means "in the capacity / role of".
Does "an animal’s immune system" serve in a position as a police officer? Hardly so.
In a realistic setting, only a person can serve as a police officer.
For example: As a police officer who tracks fleeing criminals, Mr. Johnson has trained 20 police dogs.