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Previous research on respiratory infection transmission among university students has primarily focused on influenza. In this study, we explore potential transmission events for multiple respiratory pathogens in a social contact network of university students. University students residing in on-campus housing (n = 590) were followed for the development of influenza-like illness for 10-weeks during the 2012–13 influenza season. A contact network was built using weekly self-reported contacts, class schedules, and housing information. We considered a transmission event to have occurred if students were positive for the same pathogen and had a network connection within a 14-day period. Transmitters were individuals who had onset date prior to their infected social contact. Throat and nasal samples were analysed for multiple viruses by RT-PCR. Five viruses were involved in 18 transmission events (influenza A, parainfluenza virus 3, rhinovirus, coronavirus NL63, respiratory syncytial virus). Transmitters had higher numbers of co-infections (67%). Identified transmission events had contacts reported in small classes (33%), dormitory common areas (22%) and dormitory rooms (17%). These results suggest that targeting person-to-person interactions, through measures such as isolation and quarantine, could reduce transmission of respiratory infections on campus.
We prove that any n-vertex graph whose complement is triangle-free contains n2/12 – o(n2) edge-disjoint triangles. This is tight for the disjoint union of two cliques of order n/2. We also prove a corresponding stability theorem, that all large graphs attaining the above bound are close to being bipartite. Our results answer a question of Alon and Linial, and make progress on a conjecture of Erdős.