I wonder also, although I kind of doubt it. As predators, they maintain relatively low population densities and are typically the first to go extinct when things get weird.
Selection would favor pathogens that instead specialize for hosts that are hard to get rid of. Mice, cockroaches, prairie dogs...
>Lime disease
Ah yes, good old Lime Disease, named after the town it was invented in, "Lime, Connecticut", Abraham Lime 1898, former student of Koch's lab in Germany.
Lime disease has a similar relationship with predators that eat mice, so let's also keep an eye out for the owls and snakes.