title: Multi-stage complex contagions.
abstract: The spread of ideas across a social network can be studied using complex contagion models, in which agents are activated by contact with multiple activated neighbors. The investigation of complex contagions can provide crucial insights into social influence and behavior-adoption cascades on networks. In this paper, we introduce a model of a multi-stage complex contagion on networks. Agents at different stages-which could, for example, represent differing levels of support for a social movement or differing levels of commitment to a certain product or idea-exert different amounts of influence on their neighbors. We demonstrate that the presence of even one additional stage introduces novel dynamical behavior, including interplay between multiple cascades, which cannot occur in single-stage contagion models. We find that cascades-and hence collective action-can be driven not only by high-stage influencers but also by low-stage influencers.
authors.affiliation: Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX1 3LB, United Kingdom.
authors.forename: Sergey
authors.initials: S
authors.lastname: Melnik
authors.forename: Jonathan A
authors.initials: JA
authors.lastname: Ward
authors.forename: James P
authors.initials: JP
authors.lastname: Gleeson
authors.forename: Mason A
authors.initials: MA
authors.lastname: Porter
mesh_terms: D033181:Information Dissemination; D007398:Interpersonal Relations; D007857:Leadership; D008962:Models, Theoretical; D010379:Peer Group; D012919:Social Behavior; D060756:Social Networking; D012944:Social Support; D013598:Systems Theory; D013997:Time Factors