Epidemic spreading on evolving signed networks

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.

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• Quartic Balance Theory: Global Minimum With Imbalanced Triangles
• Threshold cascade dynamics on signed random networks
• Heider Balance under Disordered Triadic Interactions
• Competitive Balance Theory: Modeling conflict of interest in a heterogeneous network
• Absorbing transition in a coevolution model with node and link states in an adaptive network: Network fragmentation transition at criticality
• Mean-Field Solution for Critical Behavior of Signed Networks in Competitive Balance Theory
• Heider and coevolutionary balance: From discrete to continuous phase transition
• Co-evolution of Viral Processes and Structural Stability in Signed Social Networks
• Hybrid balance theory: Heider balance under higher order interactions
• Modified Heider Balance on Sparse Random Networks
• Social Balance on Networks: Local Minima and Best Edge Dynamics
• Coevolutionary Dynamics of Group Interactions: Coevolving Nonlinear Voter Models
• Response of the competitive balance model to the external field
• Instability of social network dynamics with stubborn links
• The emergence of pseudo-stable states in network dynamics
• Dynamics of Social Balance on Networks: The Emergence of Multipolar Societies