Modelling disease outbreaks in realistic urban social networks

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Most mathematical models for the spread of disease use differential equations based on uniform mixing assumptions1 or ad hoc models for the contact process2,3,4. Here we explore the use of dynamic bipartite graphs to model the physical contact patterns that result from movements of individuals between specific locations. The graphs are generated by large-scale individual-based urban traffic simulations built on actual census, land-use and population-mobility data. We find that the contact network among people is a strongly connected small-world-like5 graph with a well-defined scale for the degree distribution. However, the locations graph is scale-free6, which allows highly efficient outbreak detection by placing sensors in the hubs of the locations network. Within this large-scale simulation framework, we then analyse the relative merits of several proposed mitigation strategies for smallpox spread. Our results suggest that outbreaks can be contained by a strategy of targeted vaccination combined with early detection without resorting to mass vaccination of a population.

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Figure 1: An example of a small social contact network.
Figure 2: Degree distributions for the estimated Portland social network.
Figure 3: Shattering and covering the people–contact graph.
Figure 4


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We thank G. Korniss, G. Istrate and the Fogarty International Center at the National Institutes of Health for useful discussions, and acknowledge the work of all the members of the TRANSIMS and EpiSims team. The EpiSims project is funded by the National Infrastructure Simulation and Analysis Program (NISAC) at the Department of Homeland Security. The TRANSIMS project was funded by the Department of Transportation. H.G. was supported in part by the National Science Foundation (Division of Materials Research) and Z.T. by the Department of Energy. We thank the anonymous referees for their helpful suggestions.

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Correspondence to Stephen Eubank.

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