Fluctuating epidemics on adaptive networks.

A model for epidemics on an adaptive network is considered. Nodes follow a susceptible-infective-recovered-susceptible pattern. Connections are rewired to break links from noninfected nodes to infected nodes and are reformed to connect to other noninfected nodes, as the nodes that are not infected try to avoid the infection. Monte Carlo simulation and numerical solution of a mean field model are employed. The introduction of rewiring affects both the network structure and the epidemic dynamics. Degree distributions are altered, and the average distance from a node to the nearest infective increases. The rewiring leads to regions of bistability where either an endemic or a disease-free steady state can exist. Fluctuations around the endemic state and the lifetime of the endemic state are considered. The fluctuations are found to exhibit power law behavior.