The traps catch a certain number of rats a day, and the poison lowers the rate of increase of rats. The number of traps and poison you placed is shown at the bottom of the screen, to the right of the bar showing how many total rats are in the city.
Eventually, poison maxes out after a certain number of those are placed, and the rate of rat increase is down to zero (but there are still existing rats there), so if your strategy was using only poison it won't decrease the rats even though they stop increasing.
I hope that clears up any confusion, if there are still any questions please let me know, I'm happy to help



