Identifying the epidemiological key-stone communities in a metapopulation network is primarily important in designing efficient control against an infectious disease. Various network centrality measures commonly utilized for this purpose haven’t directly focused on the most important measure in epidemiology: the basic reproductive number, $R_0$, of epidemiological dynamics on the network, which determines whether or not the infectious disease spreads over the whole network. We here introduce a new centrality measure, $R_0$-centrality, which quantifies how sensitive is the control in each local community to the reduction in $R_0$ of the whole network. Our perturbation analysis then reveals that the largest local population in the network should have extremely large $R_0$ centrality than the others, indicating that all the effort in control should be directed to the largest community. For example, when applied to the commuter network of the Tokyo metropolitan area, we found that the impact of control at the largest daytime-population, that around Shinjuku station, is more than 1,000 times stronger than that at the second largest daytime-population, that around Tokyo station, even though the difference between population sizes are only 1.5 times between them.
Once an infectious disease has already spread over the network, we found that the opposite extreme control becomes optimum: indeed, to reduce the total number hosts that have ever exposed to the infectious disease after it has already penetrated in the network, the optimal policy is to spreading controls shallowly and widely over the network. We also discuss the conditions under which “treating-only-the-biggest” control becomes the optimum, and the key-stone community for the emergence is virulent or resistant pathogens.