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How can we identify the epidemiologically high-risk communities in a metapopulation network? The network centrality measure, which quantifies the relative importance of each location, is commonly utilized for this purpose. As the disease invasion condition is given from the basic reproductive ratio  R  0 , we have introduced a novel centrality measure based on the sensitivity analysis of this  R  0  and shown its capability of revealing the characteristics that has been overlooked by the conventional centrality measures. The epidemic dynamics over the commute network of the Tokyo metropolitan area is theoretically analyzed by using this centrality measure. We found that, the impact of countermeasures at the largest station is more than 1,000 times stronger compare to that at the second largest station, even though the population sizes are only around 1.5 times larger. Furthermore, the effect of countermeasures at every station is strongly dependent on the existence and the number of commuters to this largest station. It is well known that the hubs are the most influential nodes, however, our analysis shows that only the largest among the network plays an extraordinary role. Lastly, we also found that, the location that is important for the prevention of disease invasion does not necessarily match the location that is important for reducing the number of infected.

Spotting Epidemic Keystones by R0 Sensitivity Analysis: High-Risk Stations in the Tokyo Metropolitan Area