You still perform the normal draws from the infection deck, after increasing the infection rate, infecting a new city with 3 cubes, and increasing the intensity of the infection.
If a card is an Epidemic card, instead of taking the card in hand, refer to the rules for Epidemics, below. After drawing the required cards, take on the role of the Infector. See Playing the Infector on page 7.
Playing the Infector - Draw cards from the Infection Draw Pile equal to the current Infection Rate and add one cube to the pictured cities, using a cube of the same color as each card. (Page 7)