Most mathematical models for the spread of disease use differential equations based on uniform mixing assumptions or ad hoc models for the contact process. In this project, we developed 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 found that the contact network among people is a strongly connected small-world-like graph with a well-defined scale for the degree distribution. However, the locations graph is scale-free, which allows highly efficient outbreak detection by placing sensors in the hubs of the locations network. Within this large-scale simulation framework, we also analyzed the relative merits of several proposed mitigation strategies for smallpox spread. Our results suggested that outbreaks can be contained by a strategy of targeted vaccination combined with early detection without resorting to mass vaccination of a population. The results have been published in Nature in 2004 [7].

Disease spread in most biological populations requires the proximity of agents. In populations where the individuals have spatial mobility, the contact graph is generated by the collision dynamics of the agents, and thus the evolution of epidemics couples directly to the spatial dynamics of the population. Using the data generated by EPISIM project, we introduced the notion of dynamic proximity networks which takes into account the relevant time-scales for disease spread: contact duration, infectivity period, and rate of contact creation. This approach promises to be a good candidate for a unified treatment of epidemic types that are driven by agent collision dynamics. In particular, using a simple model, we showed that it can account for the observed qualitative differences between the degree distributions of contact graphs of diseases with short infectivity period (such as air-transmitted diseases) or long infectivity periods (such as HIV) [12].

We are currently working on an SIS (susceptible-infected-susceptible) scenario on scale-free networks with degrees bounded from above by a hard cutoff with one of my students. Preliminary results show that the hard cutoff on the degree has an effect similar to finite size which helps us to contain the disease for small values of infection probability [17].

* For references see my CV.