Most mathematical models for the spread of disease use differential equations based on uniform mixing assumptions or ad hoc models for the contact process. 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-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 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.

In a parallel discrete-event simulation (PDES) scheme, tasks are distributed among processing elements (PEs) whose progress is controlled by a synchronization scheme. For lattice systems with short-range interactions, the progress of the conservative PDES scheme is governed by the Kardar-Parisi-Zhang equation from the theory of nonequilibrium surface growth. Although the simulated (virtual) times of the PEs progress at a nonzero rate, their standard deviation (spread) diverges with the number of PEs, hindering efficient data collection. We show that weak random interactions among the PEs can make this spread nondivergent. The PEs then progress at a nonzero, near-uniform rate without requiring global synchronizations.

Background: Mathematical and computational models provide valuable tools that help public health planners to evaluate competing health interventions, especially for novel circumstances that cannot be examined through observational or controlled studies, such as pandemic influenza. The spread of diseases like influenza depends on the mixing patterns within the population, and these mixing patterns depend in part on local factors including the spatial distribution and age structure of the population, the distribution of size and composition of households, employment status and commuting patterns of adults, and the size and age structure of schools. Finally, public health planners must take into account the health behavior patterns of the population, patterns that often vary according to socioeconomic factors such as race, household income, and education levels.

Worldwide, food supplies often contain unavoidable contaminants, many of which adversely affect health and hence are subject to regulations of maximum tolerable levels in food. These regulations differ from nation to nation, and may affect patterns of food trade. We soughtto determine whether there is an association between nations' food safety regulations and global food trade patterns, with implications for public health and policymaking. We developed a network model of maize trade around the world. From maize import/export data for 217 nations from 2000–2009, we calculated basic statistics on volumes of trade; then examined how regulations of aflatoxin, a common contaminant of maize, are similar or different between pairs of nations engaging in significant amounts of maize trade. Globally, market segregation appears to occur among clusters of nations. The United States is at the center of one cluster; European countries make up another cluster with hardly any maize trade with the US; and Argentina, Brazil, and China export maize all over the world. Pairs of nations trading large amounts of maize have very similar aflatoxin regulations: nations with strict standards tend to trade maize with each other, while nations with more relaxed standards tend to trade maize with each other. Rarely among the top pairs of maize-trading nations do total aflatoxin standards (standards based on the sum of the levels of aflatoxins B1, B2, G1, and G2) differ by more than 5 µg/kg. These results suggest that, globally, separate maize trading communities emerge; and nations tend to trade with other nations that have very similar food safety standards.