Time-varying network topologies can deeply influence dynamical processes
mediated by them. Memory effects in the pattern of interactions among
individuals are also known to affect how diffusive and spreading phenomena take
place. In this paper we analyze the combined effect of these two ingredients on
epidemic dynamics on networks. We study the susceptible-infected-susceptible
(SIS) and the susceptible-infected-removed (SIR) models on the recently
introduced activity-driven networks with memory. By means of an activity-based
mean-field approach we derive, in the long time limit, analytical predictions
for the epidemic threshold as a function of the parameters describing the
distribution of activities and the strength of the memory effects. Our results
show that memory reduces the threshold, which is the same for SIS and SIR
dynamics, therefore favouring epidemic spreading. The theoretical approach
perfectly agrees with numerical simulations in the long time asymptotic regime.
Strong aging effects are present in the preasymptotic regime and the epidemic
threshold is deeply affected by the starting time of the epidemics. We discuss
in detail the origin of the model-dependent preasymptotic corrections, whose
understanding could potentially allow for epidemic control on correlated
temporal networks.Comment: 10 pages, 8 fogure
