Epidemics Spreading on temporal networks with memory effects

Tuesday, May 21, 2019

2.30 p.m.

ISI seminar room 1st floor

Dr. Michele Tizzani - ISI Foundation

Activity Driven models are an interesting class of temporal networks. In this framework to each node is associated an activity ai, easily measured from extensive datasets, representing the number of activations per time of node i. Strong ties and rules for links formations in activity driven networks are encoded in a memory function pi(k) = (1 + ki/c)−β. This is the probability, for a node that has already been in contact with ki different nodes, to establish a new link (β is the parameter controlling the memory). We show that, memory effects lower the epidemic threshold, promoting infection spreading, and induce non ergodic effects in the dynamics: the value of the epidemic threshold strongly depends on the starting time t0 of the epidemic spreading, and on the average value ⟨ki⟩ of the degree of the time integrated network at time t0. We provide an analytic description of the epidemic thresholds for large t0. In this case, the creation of new connections becomes very unlikely so that the epidemics evolve on an effective static network, characterized by a large connectivity and suitable for a site dependent mean field approach. In Fig. 1 we compare numerical simulations with analytical predictions showing that for large ⟨ki⟩ a nice agreement is obtained for large enough β. For strong memory i.e. large β, the value of the threshold tends to the memoryless system (dashed lines), due to the vanishing of degree fluctuations. On the other hand, for β → 0 the static networks is maximally heterogeneous in the degree, providing a maximal difference between the analytic prediction for ⟨ki⟩ → ∞ and the threshold of the memoryless case. However for any finite value of ⟨ki⟩ the memoryless dynamics is recovered at small enough β.