The most lore-consistent way i think for a trap to be set up as Edogawa's Rubbing Treatment next victim patient is simply to introduce a gay variant of Monderella, which conveniently the trap had contracted.
I mean, the early chapters actually gives the impression that the "strange" modern-time diseases is actually many and not just Monderella Syndrome and i thought this manga gonna revolve around this many fictional diseases at first. Heck, to be honest i thought the harem aspect is going to be from the many girls contracting said varied diseases and how the MC managed to take up the role of a emergency first-aid helper/reliever for all of those diseases.