  We study an SIS epidemic process over a static contact network where the
nodes have partial information about the epidemic state. They react by limiting
their interactions with their neighbors when they believe the epidemic is
currently prevalent. A node's awareness is weighted by the fraction of infected
neighbors in their social network, and a global broadcast of the fraction of
infected nodes in the entire network. The dynamics of the benchmark (no
awareness) and awareness models are described by discrete-time Markov chains,
from which mean-field approximations (MFA) are derived. The states of the MFA
are interpreted as the nodes' probabilities of being infected. We show a
sufficient condition for existence of a "metastable", or endemic, state of the
awareness model coincides with that of the benchmark model. Furthermore, we use
a coupling technique to give a full stochastic comparison analysis between the
two chains, which serves as a probabilistic analogue to the MFA analysis. In
particular, we show that adding awareness reduces the expectation of any
epidemic metric on the space of sample paths, e.g. eradication time or total
infections. We characterize the reduction in expectations in terms of the
coupling distribution. In simulations, we evaluate the effect social distancing
has on contact networks from different random graph families (geometric,
Erd\H{o}s-Renyi, and scale-free random networks).
