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Evaluating the adequacy of gravity models as a description of human mobility for epidemic modelling.

Truscott J, Ferguson NM - PLoS Comput. Biol. (2012)

Bottom Line: On synthetic US networks, the match in epidemic behaviour is initially poor and sensitive to the initially infected node.Analysis of times to infection indicates a failure of models to capture infrequent long-range contact between large nodes.An assortative model based on node population size captures this heterogeneity, considerably improving the epidemiological match between synthetic and data networks.

View Article: PubMed Central - PubMed

Affiliation: MRC Centre for Outbreak Analysis and Modelling, Imperial College London, London, UK. j.truscott@imperial.ac.uk

ABSTRACT
Gravity models have a long history of use in describing and forecasting the movements of people as well as goods and services, making them a natural basis for disease transmission rates over distance. In agent-based micro-simulations, gravity models can be directly used to represent movement of individuals and hence disease. In this paper, we consider a range of gravity models as fits to movement data from the UK and the US. We examine the ability of synthetic networks generated from fitted models to match those from the data in terms of epidemic behaviour; in particular, times to first infection. For both datasets, best fits are obtained with a two-piece 'matched' power law distance distribution. Epidemics on synthetic UK networks match well those on data networks across all but the smallest nodes for a range of aggregation levels. We derive an expression for time to infection between nodes in terms of epidemiological and network parameters which illuminates the influence of network clustering in spread across networks and suggests an approximate relationship between the log-likelihood deviance of model fit and the match times to infection between synthetic and data networks. On synthetic US networks, the match in epidemic behaviour is initially poor and sensitive to the initially infected node. Analysis of times to infection indicates a failure of models to capture infrequent long-range contact between large nodes. An assortative model based on node population size captures this heterogeneity, considerably improving the epidemiological match between synthetic and data networks.

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Epidemic dynamics in the US.A) Mean times to infection on the data network for counties against log population. Mean times to infection on the MK model network vs. those on the data network for epidemics initialised in B) Los Angeles County and C) Clinton County, Iowa (small dots give 95% confidence intervals on the times to infection for the data network). D) RMS difference in time to infection between data and synthetic networks (see Results section) against mean deviance for the best fit MK model on different data sets and at various aggregation levels.
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pcbi-1002699-g005: Epidemic dynamics in the US.A) Mean times to infection on the data network for counties against log population. Mean times to infection on the MK model network vs. those on the data network for epidemics initialised in B) Los Angeles County and C) Clinton County, Iowa (small dots give 95% confidence intervals on the times to infection for the data network). D) RMS difference in time to infection between data and synthetic networks (see Results section) against mean deviance for the best fit MK model on different data sets and at various aggregation levels.

Mentions: Figure 5A shows mean times to infection on the data network for all counties in the continental US against the log of their populations. There is a strong linear correlation between node infection time and log population and this relationship is to a large extent independent of the initial point of infection. The effect matches that seen in the UK epidemics, but is more pronounced.


Evaluating the adequacy of gravity models as a description of human mobility for epidemic modelling.

Truscott J, Ferguson NM - PLoS Comput. Biol. (2012)

Epidemic dynamics in the US.A) Mean times to infection on the data network for counties against log population. Mean times to infection on the MK model network vs. those on the data network for epidemics initialised in B) Los Angeles County and C) Clinton County, Iowa (small dots give 95% confidence intervals on the times to infection for the data network). D) RMS difference in time to infection between data and synthetic networks (see Results section) against mean deviance for the best fit MK model on different data sets and at various aggregation levels.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3475681&req=5

pcbi-1002699-g005: Epidemic dynamics in the US.A) Mean times to infection on the data network for counties against log population. Mean times to infection on the MK model network vs. those on the data network for epidemics initialised in B) Los Angeles County and C) Clinton County, Iowa (small dots give 95% confidence intervals on the times to infection for the data network). D) RMS difference in time to infection between data and synthetic networks (see Results section) against mean deviance for the best fit MK model on different data sets and at various aggregation levels.
Mentions: Figure 5A shows mean times to infection on the data network for all counties in the continental US against the log of their populations. There is a strong linear correlation between node infection time and log population and this relationship is to a large extent independent of the initial point of infection. The effect matches that seen in the UK epidemics, but is more pronounced.

Bottom Line: On synthetic US networks, the match in epidemic behaviour is initially poor and sensitive to the initially infected node.Analysis of times to infection indicates a failure of models to capture infrequent long-range contact between large nodes.An assortative model based on node population size captures this heterogeneity, considerably improving the epidemiological match between synthetic and data networks.

View Article: PubMed Central - PubMed

Affiliation: MRC Centre for Outbreak Analysis and Modelling, Imperial College London, London, UK. j.truscott@imperial.ac.uk

ABSTRACT
Gravity models have a long history of use in describing and forecasting the movements of people as well as goods and services, making them a natural basis for disease transmission rates over distance. In agent-based micro-simulations, gravity models can be directly used to represent movement of individuals and hence disease. In this paper, we consider a range of gravity models as fits to movement data from the UK and the US. We examine the ability of synthetic networks generated from fitted models to match those from the data in terms of epidemic behaviour; in particular, times to first infection. For both datasets, best fits are obtained with a two-piece 'matched' power law distance distribution. Epidemics on synthetic UK networks match well those on data networks across all but the smallest nodes for a range of aggregation levels. We derive an expression for time to infection between nodes in terms of epidemiological and network parameters which illuminates the influence of network clustering in spread across networks and suggests an approximate relationship between the log-likelihood deviance of model fit and the match times to infection between synthetic and data networks. On synthetic US networks, the match in epidemic behaviour is initially poor and sensitive to the initially infected node. Analysis of times to infection indicates a failure of models to capture infrequent long-range contact between large nodes. An assortative model based on node population size captures this heterogeneity, considerably improving the epidemiological match between synthetic and data networks.

Show MeSH
Related in: MedlinePlus