  Most studies of disease spreading consider the underlying social network as
obtained without the contagion, though epidemic influences people's willingness
to contact others: A "friendly" contact may be turned to "unfriendly" to avoid
infection. We study the susceptible-infected disease-spreading model on signed
networks, in which each edge is associated with a positive or negative sign
representing the friendly or unfriendly relation between its end nodes. In a
signed network, according to Heider's theory, edge signs evolve such that
finally a state of structural balance is achieved, corresponding to no
frustration in physics terms. However, the danger of infection affects the
evolution of its edge signs. To describe the coupled problem of the sign
evolution and disease spreading, we generalize the notion of structural balance
by taking into account the state of the nodes. We introduce an energy function
and carry out Monte Carlo simulations on complete networks to test the energy
landscape, where we find local minima corresponding to the so-called jammed
states. We study the effect of the ratio of initial friendly to unfriendly
connections on the propagation of disease. The steady state can be balanced or
a jammed state such that a coexistence occurs between susceptible and infected
nodes in the system.
