There is no apocalyptic disaster that could eradicate coyotes and rats. Not a meteor the size of Ohio. Nor a volcano with the diameter of Australia. A tidal wave the height of the space station wouldn't deplete the population of coyotes or rats in the least.
Dangerous? Well, never thought of a coyote as dangerous. Could be to a small child, I'm sure. Hell on small pets. Although, and with coyotes living all around me, I do not recall any of my neighbors losing a pet to a coyote... which is NOT to say it couldn't happen, it definitely could. - JamesJM