Rat-catching, Mumbai, India

Another, more recent appearance of a rat-catcher in fiction is the children's novel The Twinkie Squad by Gordon Korman. As a result of a student prank which leaves the entire school smelling like dead fish, the principal hires several "professionals" to find and remove the cause of the stench, including a sewer gas expert, an x-ray technician, and a man calling himself the "District of Columbia Ratcatcher". All three "experts" fail to find anything, with the rat-catcher concluding that there is a dead animal in the walls which can only be found and removed by means of demolition.
However, the story has a modern setting, not a Victorian one, and therefore the rat-catcher in the story is more of a general pest-control man, not strictly a specialist in rats alone.
In the DC Universe one of Batman's enemies is the Rat Catcher, formerly Otis Flannegan, who was employed as a real rat catcher for Gotham City. He occasionally orchestrates rat plagues using his uncanny ability to control rats.
British author Roald Dahl wrote a short story with the title "The Ratcatcher."