Table 1.
Maximum likelihood parameter estimates for different models to UK commuting data at the district level of aggregation and for the MK, locally constrained model across different levels of aggregation.
Figure 1.
A) Comparison of observed node outflows with those generated by the globally-constrained MK model.
B) Distance distribution of synthetic connections generated by SK and MK locally constrained models.
Figure 2.
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).
Figure 3.
Estimates of time to infection from theory.
A) Time to infection against log resident population on the data network (initial seeding: Camden). B) Theoretical against simulated times to infection across whole network at county scale as predicted by quickest path (seeding: West Midlands). C) As B) but at District level (initial seeding: Birmingham). D) Sensitivity of time to infection to value or r (default r0 = 0.4) initial seeding: Birmingham.
Table 2.
Best fits for various models to US data at the county level of aggregation and the best fit for the MK model at the state level.
Figure 4.
Comparison of summary statistics between the best fit MK model and data.
A) Predicted inflow to nodes against actual inflow. B) Distribution of trip distances for matched kernel model and data.
Figure 5.
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.
Figure 6.
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.
Table 3.
Maximum likelihood estimators for parameters of the assortative model at the county level.
Figure 7.
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.