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An outstanding problem of interdisciplinary interest is to understandquantitatively the role of social contacts in contagion dynamics. In general,there are two types of contacts: close ones among friends, colleagues andfamily members, etc., and ordinary contacts from encounters with strangers.Typically, social reinforcement occurs for close contacts. Taking into accountboth types of contacts, we develop a contact-based model for social contagion.We find that, associated with the spreading dynamics, for random networks thereis coexistence of continuous and discontinuous phase transitions, but forheterogeneous networks the transition is continuous. We also find that ordinarycontacts play a crucial role in promoting large scale spreading, and the numberof close contacts determines not only the nature of the phase transitions butalso the value of the outbreak threshold in random networks. For heterogeneousnetworks from the real world, the abundance of close contacts affects theepidemic threshold, while its role in facilitating the spreading depends on theadoption threshold assigned to it. We uncover two striking phenomena. First, astrong interplay between ordinary and close contacts is necessary forgenerating prevalent spreading. In fact, only when there are propagation pathsof reasonable length which involve both close and ordinary contacts are largescale outbreaks of social contagions possible. Second, abundant close contactsin heterogeneous networks promote both outbreak and spreading of the contagionthrough the transmission channels among the hubs, when both values of thethreshold and transmission rate among ordinary contacts are small. We develop atheoretical framework to obtain an analytic understanding of the main findingson random networks, with support from extensive numerical computations.

Close and ordinary social contacts: how important are they in promoting large-scale contagion?