Impact of Non-Poissonian Activity Patterns on Spreading Processes

Abstract

Halting a computer or biological virus outbreak requires a detailed understanding of the timing of the interactions between susceptible and infected individuals. While current spreading models assume that users interact uniformly in time, following a Poisson process, a series of recent measurements indicates that the intercontact time distribution is heavy tailed, corresponding to a temporally inhomogeneous bursty contact process. Here we show that the non-Poisson nature of the contact dynamics results in prevalence decay times significantly larger than predicted by the standard Poisson process based models. Our predictions are in agreement with the detailed time resolved prevalence data of computer viruses, which, according to virus bulletins, show a decay time close to a year, in contrast with the 1 day decay predicted by the standard Poisson process based models.

Multiscale analysis of spreading in a large communication network

“…Thus, the slowing-down effect can be explained by characterizing the timings of the call sequences of links. For this, we have used the concept of relay times [4,6], and showed how the burstiness and the slow spreading speed compared to the Poisson process are equivalent concepts: the slowing down is due to the bursty nature of the event sequences. We also found that there is a lot of heterogeneity in the relay times of links even when normalizing by weight; thus not only the broad distribution of link weights but also the distribution of relay times affects the speed of spreading.…”

“…In this approximation, the relay times τ R of a link are determined purely by the inter-event time distribution of events on that link, P (τ ), where the inter-event time τ is defined as the time difference between two consecutive events. On the basis of the inter-event time distribution, the probability distribution of the relay times can be written as [4]. Further, assuming that the tail of the distribution is not too broad (lim x→∞ x 2 P (τ > x) = 0), the average relay time τ R can be calculated analytically for any inter-event time distribution:…”

“…Such empirical distributions have been fitted with power laws [24,25] or power laws with an exponential cutoff [4,26]. In Table 2 we present analytical formulas for τ R and τ R * for these distributions and illustrate their dependence on the distribution parameters.…”

“…However, in reality the timings of such contact sequences are heterogeneous and display several kinds of temporal correlations. This is the case, e.g., in sexual contact networks [16,17,18] and human communication networks [19,4,6,20,5]. For both cases, it has been shown that the spreading dynamics are considerably affected by the temporal features of the contact sequences.…”

“…It is relevant for a number of fields and applications ranging from epidemiology of biological viruses to the dynamics of social processes, such as opinion dynamics or information transmission [3]. While certain static characteristics of complex networks work to enhance spreading, such as the small world property, it has been shown that the temporal characteristics of links may slow it down [4,5,6]. These results indicate that dynamic processes cannot necessarily take advantage of topologically shortest paths [7].…”