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Analytical studies of network epidemiology almost exclusively focus on theextreme situations where the time scales of network dynamics are well separated(longer or shorter) from that of epidemic propagation. In realistic scenarios,however, these time scales could be similar, which has profound implicationsfor epidemic modeling (e.g., one can no longer reduce the dimensionality ofepidemic models). We build a theory for the critical behavior ofsusceptible-infected-susceptible (SIS) epidemics in the vicinity of thecritical threshold on the activity-driven model of temporal networks. We findthat the persistence of links in the network leads to increasing recovery ratesreducing the threshold. Dynamic correlations (coming from being close toinfected nodes increases the likelihood of infection) drive the threshold inthe opposite direction. These two counteracting effects make epidemiccriticality in temporal networks a remarkably complex phenomenon.

The nature of epidemic criticality in temporal networks