In the next phrase:
Only a few doctors assess their patients about the type and frequency of the tests they should be doing to detect opportunely and prevent such diseases, but we will help you solve this problem.
What makes more sense "detect opportunely" or "opportunely detect" and why? Is there a rule?
I would strongly recommend against putting "opportunely" or any other adverb inside that clause.
Only a few doctors assess their patients about the type and frequency of the tests they should be doing to detect and prevent such diseases, but we will help you solve this problem.
(As to the rule itself, writers disagree, but in general both orders are possible. See split infinitive.)
You didn't ask about the sentence in general, but it could definitely be shorter and clearer. Ralph M. has one good suggestion. Here's mine, a bit closer to the original:
Too few doctors assess the type and frequency of tests needed to detect and prevent such diseases, but we will help you solve this problem.
Neither works, actually. It would be better to rephrase the whole thing. Something like this might work:
Relatively few doctors work proactively to prevent [these] diseases by testing and monitoring their patients.
I assume both the detection and prevention are opportune, and hence, I would recommend using 'opportunely' before the verb. I honestly cannot quote a rule or convention, but this page has a few examples, along with a few rules of placement.
I would have used 'detect opportunely and prevent', only if the detection is opportune, and not the prevention.
I would use "opportunely detect" as it focuses attention on the word "opportunely" which is the focus of the passage - i.e. all doctors are in the business of detection and prevention but most doctors give insufficient attention to how to catch things in time.
In detect opportunely and prevent you can make a case that the placement of opportunely is intentional and serves to exclude a reading of opportunely detect and prevent where it applies to both nouns.
Detecting a disease when it has already caused symptoms isn't ideal. We'd rather detect it with tests (e.g. genetic), much early, when we might even prevent it from manifesting itself—hence the opportunely.
If you prevent a disease, however, does it matter if you do so opportunely? What does that entail? Preventing it 10 years prior to when it would have manifest itself rather than 5 years?
I read the OP's phrase as opportunely detect so as to prevent.
