Most mathematical models for the spread of disease use differential equations based on uniform mixing assumptions or ad hoc models for the contact process. 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-like graph, and present provably-good algorithms and their empirical performance for outbreak detection by placing sensors. Within this large-scale simulation framework, we then analyze the relative merits of a number of proposed mitigation strategies for disease-spread.
The talk will mostly be based on the following two papers, and will also briefly touch upon ongoing work:
“Modelling Disease Outbreaks in Realistic Urban Social Networks”, by S. Eubank, H. Guclu, V. S. A. Kumar, M. V. Marathe, A. Srinivasan, Z. Toroczkai and N. Wang. Nature, Vol. 429, 180-184, May 2004;
“Structural and Algorithmic Aspects of Massive Social Networks”, by S. Eubank, V. S. A. Kumar, M. V. Marathe, A. Srinivasan, and N. Wang. Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA), 711-720, 2004.