I'm Troubled by Vermin since various days ago, my value was around 19 now 11, using the normal ways ("A bad case of rattus faber:*") is taking me hours to reduce them to 0. Is there a way to do it more efficiently?
Buy a Talkative Rattus Faber from the Bazaar, in the Nassos Zoologicals shop, for 80 pence. It will open up a new storylet to complete the entire Troubled by Vermin storyline in an action or two in your Lodgings.
Of course, this means that you'll be bypassing a fair chunk of content. Personally, I regret having taken this course of action; I did it around Troubled by Vermin 17 or so, which means I missed quite a bit. Keep in mind that you can ignore this storyline for as long as you want, and it will have no ill consequences. If you're bored of it, come back later.