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

Mean time to infection difference matrix for the US.For each network, the time to infection between 2 nodes is averaged across all connections within a square. Colours in the matrix represent the difference between mean times on the A) MK network B) Assortative network and the data network. Positive values represent slower transmission on the synthetic network. Times to infection are calculated from equation 5.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002699-g006: Mean time to infection difference matrix for the US.For each network, the time to infection between 2 nodes is averaged across all connections within a square. Colours in the matrix represent the difference between mean times on the A) MK network B) Assortative network and the data network. Positive values represent slower transmission on the synthetic network. Times to infection are calculated from equation 5.

Mentions: There is considerable variation in the goodness of fit among epidemics started from different nodes between the MK and data US networks. This suggests that the model is failing to capture accurately some subset of the work flows in the dataset. We can use the expression for the time to infection (Equation 5) to calculate the theoretical mean time to infection for all connections in both the data network and the synthetic MK-based network to try to identify what the essential discrepancies are. The two networks differ not only in the work flows between nodes, but also in which connections are present, so it's necessary to aggregate the time to infection information to allow comparison. In Figure 6, average times to infection between pairs of nodes are shown aggregated into bins by source and destination log population size. Use of log population size is suggested both by the form of equation 5 and the strong correlation it has with infection times.


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

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

Mean time to infection difference matrix for the US.For each network, the time to infection between 2 nodes is averaged across all connections within a square. Colours in the matrix represent the difference between mean times on the A) MK network B) Assortative network and the data network. Positive values represent slower transmission on the synthetic network. Times to infection are calculated from equation 5.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002699-g006: Mean time to infection difference matrix for the US.For each network, the time to infection between 2 nodes is averaged across all connections within a square. Colours in the matrix represent the difference between mean times on the A) MK network B) Assortative network and the data network. Positive values represent slower transmission on the synthetic network. Times to infection are calculated from equation 5.
Mentions: There is considerable variation in the goodness of fit among epidemics started from different nodes between the MK and data US networks. This suggests that the model is failing to capture accurately some subset of the work flows in the dataset. We can use the expression for the time to infection (Equation 5) to calculate the theoretical mean time to infection for all connections in both the data network and the synthetic MK-based network to try to identify what the essential discrepancies are. The two networks differ not only in the work flows between nodes, but also in which connections are present, so it's necessary to aggregate the time to infection information to allow comparison. In Figure 6, average times to infection between pairs of nodes are shown aggregated into bins by source and destination log population size. Use of log population size is suggested both by the form of equation 5 and the strong correlation it has with infection times.

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