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United States Department of Agriculture

Agricultural Research Service

Research Project: FRAMEWORKS FOR INFECTIOUS DISEASE DYNAMICS

Location: Plant-Microbe Interactions Research

Title: Epidemic fronts in complex networks with metapopulation structure

Authors
item Hindes, Jason -
item Singh, Sarabjeet -
item Myers, Christopher -
item Schneider, David

Submitted to: Physical Review E (PRE) - Statistical, Nonlinear, and Soft Matter Physics
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: June 25, 2013
Publication Date: July 15, 2013
Citation: Hindes, J., Singh, S., Myers, C.R., Schneider, D.J. 2013. Epidemic fronts in complex networks with metapopulation structure. Physical Review E (PRE) - Statistical, Nonlinear, and Soft Matter Physics. DOI: 10.1103/PhysRevE.88.012809.

Interpretive Summary: Many diseases spread only by direct contact between infectious and susceptible individuals. In practice, however, we live in a complicated hierarchical world where we come into contact with other people with widely varying frequencies depending on social and geographical structures such as households, schools and cities. One can model the patterns of contact as networks – mathematical structures where individuals are represented by points and potential contacts are represented by lines joining these points. Such networks are very complicated and display elements of both regularity (children routinely play with their classmates) and randomness (one might meet many strangers on a vacation). In this paper we use a variety of mathematical methods to describe the transmission of diseases in hierarchical networks that allows certain kinds of random connections within spatially distributed subpopulations.

Technical Abstract: Infection dynamics have been studied extensively on complex networks, yielding insight into the effects of heterogeneity in contact patterns on disease spread. Somewhat separately, metapopulations have provided a paradigm for modeling systems with spatially extended and “patchy” organization. In this paper we expand on the use of multitype networks for combining these paradigms, such that simple contagion models can include complexity in the agent interactions and multi-scale structure. We first present a generalization of the Volz-Miller mean-field approximation for Susceptible-Infected-Recovered (SIR) dynamics on multitype networks. We then use this technique to study the special case of epidemic fronts propagating on a one-dimensional lattice of interconnected networks – representing a simple chain of coupled population centers – as a necessary first step in understanding how macro-scale disease spread depends on micro-scale topology. Using the formalism of front propagation into unstable states, we derive the effective transport coefficients of the linear spreading: asymptotic speed, characteristic wavelength, and diffusion coefficient for the leading edge of the pulled fronts, and analyze their dependence on the underlying graph structure. We also derive the epidemic threshold for the system and study the front profile for various network configurations. To our knowledge, this is the first such application of front propagation concepts to random network models.

Last Modified: 9/10/2014
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