A model for epidemics on an adaptive network is considered. Nodes follow an
SIRS (susceptible-infective-recovered-susceptible) pattern. Connections are
rewired to break links from non-infected nodes to infected nodes and are
reformed to connect to other non-infected 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.Comment: Submitted to Phys Rev
