On a player's turn, he/she will take their actions, then draw player cards, and then play the role of the infector and draw cards from the infection pile equal to the infection rate. If you draw and Epidemic card from the player draw pile then you would increase the infection rate, draw the bottom card from the infection pile and place 3 cubes in it (if that disease is not eradicated) and place it in the discard, and shuffle the discard and place it on the top of the infection deck. You will also take the role of the infector to finish your turn as normal.
As in the rules, anytime an infection card is drawn for a city whose disease is currently eradicated the card is discarded with no effect -- no cubes are placed for an eradicated disease (even when it's drawn as part of an epidemic card).
That's what I thought, but thanks for the confirmation!