Before revision:  We also show that a reduction in the fraction of unaware individuals does not always imply a decrease of the prevalence, as the relative time scale between disease and awareness spreadings plays a crucial role in the systems' dynamics  .
After revision:  We also show that a reduction in the fraction of unaware individuals does not always imply a decrease of the prevalence, as the relative time scale between disease and awareness spreadings plays a crucial role in the systems' dynamics . This result is shown to be independent of the network topology. We finally calculate the epidemic threshold of our model, and show that it does not depend on the relative timescale .