Limits...
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.

Show MeSH

Related in: MedlinePlus

Times to infection for locally constrained MK model at A) district level and B) county level from initial seeding in Camden.C) Times to infection for smooth kernel model and data network against distance from seeding event. D) Matched kernel model times from least populous node in UK (Stewarty).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3475681&req=5

pcbi-1002699-g002: Times to infection for locally constrained MK model at A) district level and B) county level from initial seeding in Camden.C) Times to infection for smooth kernel model and data network against distance from seeding event. D) Matched kernel model times from least populous node in UK (Stewarty).

Mentions: Figure 2 compares the behaviour of epidemics on synthetic networks derived from these model fits with epidemic dynamics on the network constructed using the data. Times to first infection for each node are shown, calculated as the mean time (over 100 realisations) to the first infection of a resident of the node. Figure 2A and B show the results for the MK model for epidemics started in Camden, London, at the district and county level of aggregation. The fit is quite accurate across all nodes for both aggregations, with a root mean square error of 1.6 and 1.9 days for the district and county levels respectively. In contrast, the use of the SK model has a pronounced and characteristic effect on the progress of an epidemic (Figure 2C). Times to infection match well up to approximately 15 days, at which point the infection of subsequent nodes is delayed by up to 2 weeks. This is because the SK model underestimates the degree of contact over longer distances. Figure 2C therefore indicates that the later infected nodes are infected across long distances, from some of the initially infected nodes, rather than along longer chains of short range transmissions. The good agreement of times to infection between the data and synthetic networks is generally maintained across different initial nodes. The exception is for initial nodes with very small populations. In these cases, the times to infection for other nodes is uniformly faster for the MK modelled network than the data network (see Figure 2D). The faster transmission from the smallest nodes is matched by the faster transmission to the smallest nodes (points under the line with times>20 days in Figure 2A and B) and appears to be a general feature of these models.


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 locally constrained MK model at A) district level and B) county level from initial seeding in Camden.C) Times to infection for smooth kernel model and data network against distance from seeding event. D) Matched kernel model times from least populous node in UK (Stewarty).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002699-g002: Times to infection for locally constrained MK model at A) district level and B) county level from initial seeding in Camden.C) Times to infection for smooth kernel model and data network against distance from seeding event. D) Matched kernel model times from least populous node in UK (Stewarty).
Mentions: Figure 2 compares the behaviour of epidemics on synthetic networks derived from these model fits with epidemic dynamics on the network constructed using the data. Times to first infection for each node are shown, calculated as the mean time (over 100 realisations) to the first infection of a resident of the node. Figure 2A and B show the results for the MK model for epidemics started in Camden, London, at the district and county level of aggregation. The fit is quite accurate across all nodes for both aggregations, with a root mean square error of 1.6 and 1.9 days for the district and county levels respectively. In contrast, the use of the SK model has a pronounced and characteristic effect on the progress of an epidemic (Figure 2C). Times to infection match well up to approximately 15 days, at which point the infection of subsequent nodes is delayed by up to 2 weeks. This is because the SK model underestimates the degree of contact over longer distances. Figure 2C therefore indicates that the later infected nodes are infected across long distances, from some of the initially infected nodes, rather than along longer chains of short range transmissions. The good agreement of times to infection between the data and synthetic networks is generally maintained across different initial nodes. The exception is for initial nodes with very small populations. In these cases, the times to infection for other nodes is uniformly faster for the MK modelled network than the data network (see Figure 2D). The faster transmission from the smallest nodes is matched by the faster transmission to the smallest nodes (points under the line with times>20 days in Figure 2A and B) and appears to be a general feature of these models.

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