Epidemic criticality in temporal networks

Analytical studies of network epidemiology almost exclusively focus on the extreme situations where the timescales of network dynamics are well separated (longer or shorter) from that of epidemic propagation. In realistic scenarios, however, these timescales could be similar, which has profound implications for epidemic modeling (e.g., one can no longer reduce the dimensionality of epidemic models). Combining Monte Carlo simulations and mean-field theory, we analyze the critical behavior of susceptible-infected-susceptible epidemics in the vicinity of the critical threshold on the activity-driven model of temporal networks. We find that the persistence of links in the network causes the threshold to decrease as the recovery rate increases. Dynamic correlations (coming from being close to infected nodes increases the likelihood of infection) drive the threshold in the opposite direction. These two counteracting effects make epidemic criticality in temporal networks a remarkably complex phenomenon.