Many real contact networks are characterized by a mutual interplay between the spreading of a disease and the state of their nodes. A meaningful example is the individual's perception of the risk of infection when meeting infected people. Here we describe a two-parameters SIS model that investigates how the perception of the infection risk leads to behavioral changes that alters the network dynamics. We show that for finite average network connectivity, there is always a value of perception that stops the epidemics. For scale-free networks with diverging input connectivity, a linear perception cannot stop the epidemics; however we show that a non-linear parameterization of the perception's risk may lead to the extinction of the disease. Our results indicate that the interplay between dynamics and topology can have important consequences for the spreading of infectious diseases and related applications.