Epidemic spreading on evolving signed networks

TL;DR

This paper investigates how disease spreading influences and is influenced by the evolution of social relationships in signed networks, revealing complex steady states including balanced and jammed configurations.

Contribution

It introduces a coupled model of disease spread and edge sign evolution, incorporating node states into structural balance theory and analyzing energy landscapes via Monte Carlo simulations.

Findings

Steady states can be balanced or jammed.

Initial friendly/unfriendly ratio affects disease propagation.

Coexistence of susceptible and infected nodes observed.

Abstract

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.