This sentence isn't quite right in my grammar. It ought to be "Those with mild symptoms only require monitoring."
I would only put an infinitive after require if there's also an object.
*Bringing up children often requires to put their needs first.
The word you is missing there.
The object can be missing if the sentence is passive, as often occurs:
You are required to do your homework.
But your sentence is not passive.
However, I see examples on the internet of require+infinite:
one does not require to be a specialist — Elizabeth Bowen