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First 5000 Characters:Epidemics of infectious diseases are frequently characterized by multiple waves of infection [1-3]. Notably, the 1918 influenza pandemic spread through several US and European cities in multiple waves with local variation in the frequency and timing of individual epidemic peaks [4-8]. Predicting when and where disease will resurge is critical to effective prevention and control. However, the drivers and dynamics of multiwave epidemics are unclear. For influenza pandemics, possible explanations include antigenic drift [8-12], waning immunity , changing environmental conditions [12,14,15], and social distancing behavior [15-17].
Community structure—aggregation into highly intraconnected but loosely interconnected groups—is a common feature of social contact networks  that can potentially drive multiwave epidemics as a disease spreads through one group before emerging in another. However, community structure has been neglected as a possible explanation for multiwave influenza pandemics, in part because it is difficult to detect and estimate . Most studies describing routine human contact patterns have relied on diary- or questionnaire-based surveys  or specially deployed wireless sensors  and, thus, rarely yield data sufficient for inferring large-scale aggregations. Social networks estimated from electronic "contacts" (ie, cell phones, social networking websites) have been shown to exhibit community structure at larger scales [22-26], but do not capture the physical interactions through which diseases spread. However, the ubiquity of community structure across these networks suggests that it may be a general hallmark of social networks.
Here, we address the hypothesis that contact patterns in a large, empirical, urban contact network are sufficient to generate multiwave epidemics for pandemic influenza-like diseases in the absence of any temporal changes in the hosts, pathogen, or environment. We find that the fate of an epidemic in such a network—whether and when multiple waves occur—depends not only on community structure but also, critically, the presence or absence of bridge superspreaders who forge connections between communities. Direct links between the popular members of different communities synchronize outbreaks; the occasional absence of such bridges provides the epidemiological separation underlying multiwave epidemics.
Interactions between strangers can serve as critical transmission routes for respiratory diseases such as influenza, yet they are difficult to capture in traditional sociological surveys. Using data indicating the physical proximity of more than 100,000 Wi-Fi hotspots users, we characterize the structure of an urban extrasocial interaction network and assess its epidemiological implications.
Île Sans Fil (ÎSF) is a not-for-profit organization established in 2004 in Montreal, Canada, that operates a system of public Internet hotspots. Hotspots are located in cafes, community and recreation centers, salons, markets, and other small businesses and public places. They are maintained by ÎSF staff and volunteers with the Internet connection provided by the establishment. We analyzed the database of all connections to the system of 352 hotspots between August 2004 and March 2010. Raw data from the ÎSF database consisted of 2.18 million connection records. Each record included an anonymized user ID, latitude and longitude coordinates for each ÎSF hotspot location, connection and disconnection times, and the unique media access control address for the user's wireless device. The data reported in this paper are available from the Community Resource for Archiving Wireless Data at Dartmouth (CRAWDAD) archive .
We built a contact network by interpreting each individual user as a node and concurrent ÎSF usage at the same hotspot as an edge. This preliminary network contained 114,810 nodes and 1.2 million edges. It contained both self-loops (users connecting multiple devices at once) and parallel edges (pairs of users with multiple overlapping hotspot visits) that we removed to produce a nonredundant network with 637,430 edges. We analyzed the largest connected component of this network, which consisted of 103,425 nodes and 630,893 edges.
Modularity (Q) quantifies the extent of community structure in a network relative to a comparable random network. Given a network and a particular partitioning of the nodes into communities, Q is defined as the number of edges contained within communities minus the number of edges expected to fall within communities if the edges were distributed randomly (preserving the degrees of all nodes), normalized for network size. Q ranges from zero for randomly connected networks to greater than 0.3 for networks with substantial community structure . We used a heuristic method to divide the Montreal network into a set of communities that maximized Q using an algorithm  that initially assigned each node to its own community and then iterati