Network theory and SARS: predicting outbreak diversity

Abstract

Many infectious diseases spread through populations via the networks formed by physical contacts among individuals. The patterns of these contacts tend to be highly heterogeneous. Traditional "compartmental" modeling in epidemiology, however, assumes that population groups are fully mixed, that is, every individual has an equal chance of spreading the disease to every other. Applications of compartmental models to Severe Acute Respiratory Syndrome (SARS) resulted in estimates of the fundamental quantity called the basic reproductive number R0--the number of new cases of SARS resulting from a single initial case--above one, implying that, without public health intervention, most outbreaks should spark large-scale epidemics. Here we compare these predictions to the early epidemiology of SARS. We apply the methods of contact network epidemiology to illustrate that for a single value of R0, any two outbreaks, even in the same setting, may have very different epidemiological outcomes. We offer quantitative insight into the heterogeneity of SARS outbreaks worldwide, and illustrate the utility of this approach for assessing public health strategies.

Predicting epidemics on directed contact networks

“…Using the degree distribution from a contact network model containing 10,000 households (~25,000 individuals), we predict the fate of an outbreak for a spectrum of respiratory-borne diseases for which hospitalization is likely. As reported in [22], the undirected-degree distribution is roughly exponential. The in-degree and out-degree distributions are solely determined by the flow of infected people into health care facilities.…”

“…The contact networks We have previously developed a method to simulate urban contact networks based on demographic data for the city of Vancouver, British Columbia [20][21][22][23][24][25]. Using the degree distribution from a contact network model containing 10,000 households (~25,000 individuals), we predict the fate of an outbreak for a spectrum of respiratory-borne diseases for which hospitalization is likely.…”

Analysis of a stochastic SIR epidemic on a random network incorporating household structure

“…Models where an epidemic spreads over a random network with a prescribed degree distribution have also received significant attention (see, for example, Andersson [4], Newman [5], Kenah and Robins [6] and Myers et al [7]). These network models have also been extended by treating the random graph as a local contact structure and introducing casual, homogeneously mixing contacts (Kiss et al [8] and Ball and Neal [9]).…”

Mathematical modeling of the malignancy of cancer using graph evolution

“…Real-world graphs [1] have been extensively studied to model different phenomena in manmade [2][3][4], social [5][6][7][8][9], and biological systems [10][11][12][13]. The graphs of man-made systems include the Internet router graph with routers being the nodes and fiber connections being the edges [2], the World Wide Web graph with web pages being the nodes and URLs being the edges [3], and the USA power grid network with generators, transformers, and substations being the nodes and high-voltage transmission lines being the edges [1].…”

“…The graphs of man-made systems include the Internet router graph with routers being the nodes and fiber connections being the edges [2], the World Wide Web graph with web pages being the nodes and URLs being the edges [3], and the USA power grid network with generators, transformers, and substations being the nodes and high-voltage transmission lines being the edges [1]. The graphs of social systems include the Hollywood movie star network with actors being the nodes and co-starring in the same movie being the edges [1], scientific collaboration network with scientists being the nodes and co-authoring in the same publication being the edges [5], and the SARS disease spreading network with people being the nodes and contacts between any two people being the edges [6]. The graphs of biological systems include the neural network of the worm Caenorhabditis elegans with neurons being the nodes and neural connections being the edges [1], the protein-protein interaction graph of the bacteria Saccharomyces cerevisiae with proteins being the nodes and direct physical interactions being the edges [10], and metabolic graphs of different organisms with substrates being the nodes and actual metabolic reactions being the edges [11].…”