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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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Related in: MedlinePlus

Times to infection for different nodes for the assortative model in the US at the county level of aggregation with initial seeding A) Los Angeles County, B) Clinton County, Iowa.Grey dots represent 95% intervals across simulation realisations for the times to infection on the data network.
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pcbi-1002699-g007: Times to infection for different nodes for the assortative model in the US at the county level of aggregation with initial seeding A) Los Angeles County, B) Clinton County, Iowa.Grey dots represent 95% intervals across simulation realisations for the times to infection on the data network.

Mentions: The gain in likelihood of the assortative model over the simpler version is not large. However, the improvement in the ability to reproduce the epidemic timing seen for the data network is significant (See Figure 5D for the corresponding value). The improvement in the quality of the fit in terms of epidemic behaviour can be seen Figure 7. Figure 7A and B should be compared with Figure 5B and C respectively. The assortative structure has clearly lessened some of the bias towards transmission being too fast to smaller nodes and too slow to larger ones in the epidemic initiated in Los Angeles (Figure 7A). Equally, the epidemic started in Clinton County has ‘slowed down’, converging towards the behaviour seen for the data network (Figure 7B). These improvements in fit are reflected in the RMS time differences shown in Figure 5D.


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

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

Times to infection for different nodes for the assortative model in the US at the county level of aggregation with initial seeding A) Los Angeles County, B) Clinton County, Iowa.Grey dots represent 95% intervals across simulation realisations for the times to infection on the data network.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002699-g007: Times to infection for different nodes for the assortative model in the US at the county level of aggregation with initial seeding A) Los Angeles County, B) Clinton County, Iowa.Grey dots represent 95% intervals across simulation realisations for the times to infection on the data network.
Mentions: The gain in likelihood of the assortative model over the simpler version is not large. However, the improvement in the ability to reproduce the epidemic timing seen for the data network is significant (See Figure 5D for the corresponding value). The improvement in the quality of the fit in terms of epidemic behaviour can be seen Figure 7. Figure 7A and B should be compared with Figure 5B and C respectively. The assortative structure has clearly lessened some of the bias towards transmission being too fast to smaller nodes and too slow to larger ones in the epidemic initiated in Los Angeles (Figure 7A). Equally, the epidemic started in Clinton County has ‘slowed down’, converging towards the behaviour seen for the data network (Figure 7B). These improvements in fit are reflected in the RMS time differences shown in Figure 5D.

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