  Prediction and control of spreading processes in social networks (SNs) are
closely tied to the underlying connectivity patterns. Contrary to most existing
efforts that exclusively focus on positive social user interactions, the impact
of contagion processes on the temporal evolution of signed SNs (SSNs) with
distinctive friendly (positive) and hostile (negative) relationships yet,
remains largely unexplored. In this paper, we study the interplay between
social link polarity and propagation of viral phenomena coupled with user
alertness. In particular, we propose a novel energy model built on Heider's
balance theory that relates the stochastic
susceptible-alert-infected-susceptible epidemic dynamical model with the
structural balance of SSNs to substantiate the trade-off between social tension
and epidemic spread. Moreover, the role of hostile social links in the
formation of disjoint friendly clusters of alerted and infected users is
analyzed. Using three real-world SSN datasets, we further present a
time-efficient algorithm to expedite the energy computation in our Monte-Carlo
simulation method and show compelling insights on the effectiveness and
rationality of user awareness and initial network settings in reaching
structurally balanced local and global network energy states.
