Epidemic spreading on evolving signed networks.

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.