Traditional epidemiological research has focused on rate-based differential-equation models with completely mixing populations. Although successful in explaining certain phenomena of disease spreading, the traditional approach is unable to deal with disease spreading in realistic massive social networks, where most people only mix locally with few other people. We have develop an approach based on a combination of network theory and discrete-event simulations to study epidemics in large urban areas, which do not assume complete mixing populations. Our results include (1) detailed structural and temporal analyses of the social contact networks produced by TRANSIMS, a simulator for detailed transportation/traffic studies; (2) realistic simulation of contagious diseases (e.g., smallpox) on the social contact networks through EpiSims, a simulation-based analytical tool to study the spread of infectious diseases in an urban environment; (3) identifying a number of new measures that are significant for understanding epidemics and for developing new strategies in policy planning; (4) introduction of random graph models for theoretical analysis of the structural and algorithmic aspects of the social networks; and (5) combinatorial formulations and approximation algorithms for performing quarantine, vaccination and sensor placement, as aids to decision-making.

The social network that we have mostly dealt with is for the city of Portland, Oregon, USA, developed as a part of the TRANSIMS/EpiSims project at the Los Alamos National Laboratory. The most expressive social contact network is a bipartite graph, representing people and locations; edges represent people visiting locations on a typical day. We also build random graph models to generate a family of social networks by taking as input some basic parameters of the Portland social network, and analyze social networks generated by these models.