Epidemics in adaptive social networks with temporary link deactivation

Disease spread in a society depends on the topology of the network of social contacts. Moreover, individuals may respond to the epidemic by adapting their contacts to reduce the risk of infection, thus changing the network structure and affecting future disease spread. We propose an adaptation mechanism where healthy individuals may choose to temporarily deactivate their contacts with sick individuals, allowing reactivation once both individuals are healthy. We develop a mean-field description of this system and find two distinct regimes: slow network dynamics, where the adaptation mechanism simply reduces the effective number of contacts per individual, and fast network dynamics, where more efficient adaptation reduces the spread of disease by targeting dangerous connections. Analysis of the bifurcation structure is supported by numerical simulations of disease spread on an adaptive network. The system displays a single parameter-dependent stable steady state and non-monotonic dependence of connectivity on link deactivation rate.