Explosive Contagion in Networks

Abstract

The spread of social phenomena such as behaviors, ideas or products is an ubiquitous but remarkably complex phenomenon. A successful avenue to study the spread of social phenomena relies on epidemic models by establishing analogies between the transmission of social phenomena and infectious diseases. Such models typically assume simple social interactions restricted to pairs of individuals; effects of the context are often neglected. Here we show that local synergistic effects associated with acquaintances of pairs of individuals can have striking consequences on the spread of social phenomena at large scales. The most interesting predictions are found for a scenario in which the contagion ability of a spreader decreases with the number of ignorant individuals surrounding the target ignorant. This mechanism mimics ubiquitous situations in which the willingness of individuals to adopt a new product depends not only on the intrinsic value of the product but also on whether his acquaintances will adopt this product or not. In these situations, we show that the typically smooth (second order) transitions towards large social contagion become explosive (first order). The proposed synergistic mechanisms therefore explain why ideas, rumours or products can suddenly and sometimes unexpectedly catch on.

Memory-induced complex contagion in epidemic spreading

“…• In edge-centric approaches, one still considers the transmission channel from infected nodei to susceptible nodej. Now, however, the transmission rate w  i j is affected by the neighborhoods ofi and/orj (for specific examples, see [28,29,44]). Considering only nearest-neighbors, the transmission rate from nodei to nodej at timet, w  ( | ( ) ( )) t z t z t ,…”

“…Conversely, a plethora of complex contagion schemes has been proposed to mediate the assumption of independent transmissions. Examples include correlated, nonlinear transmission channels [26,27], extended neighborhood effects [28,29], and deterministic threshold models [30,31]. So far, not much research has focused on tackling both assumptions simultaneously, and little is know about how these two features interact.…”

Spreading to localized targets in complex networks

“…Results are fruitful. For instance, the spreading on complex networks is found to undergo a second-order phase transition in most cases but could be explosive in synergistic epidemics89, and the critical infection probability can be estimated by the mean-field theory10. The networks with heterogeneous degree distribution in general have a lower critical infection probability than those with homogeneous degree distribution11.…”

Effects of local and global network connectivity on synergistic epidemics

“…A recently developed model [29] provides a flexible framework to study any degree of constructive or interfering synergy in any type of network. With this model, it was shown that synergy affects the size, duration and foraging strategy of spreaders [29,32] and can even result in explosive invasions [37] of epidemics with and without node removal and for the Maki-Thompson model [38] describing social phenomena. For regular lattice models, it was found that synergistic effects on invasion are enhanced by increasing local connectivity [32].…”