Health-care systems can be represented as complex, multi-layered networks. Demographic shifts, like population aging and urbanization, together with increasing financial pressures exert an ever-growing amount of stress on the system and its ability delivery of appropriate care. Given these tendencies, that often result in a reduction of the density of primary care providers in a specific region, how much can the stress increase before the health-care system loses its capacity to deliver adequate care to the population? How does one measure the systemic risk in health care? Here, for the first time, we show how recent methodological advances in our ability to anticipate system-wide failures of financial systems resulting from localized events, can be used to quantify the systemic risk in health care. We have therefore used a comprehensive, large-scale, and nation-wide dataset of the Austrian health-care system to model it in terms of patient-sharing networks, where nodes represent health-care providers and links indicate flows of patients between them. The removal of a provider in this network causes a cascading process of referrals between providers, as patients have to locate an alternative doctor. We observe that typically the removal of a few providers does not have a major impact but there is a regime where removals trigger system-spanning cascades and patients are not cared for anymore. We see that regions are particularly susceptible to cascading impacts if the topology of their underlying patient-sharing network shows high clustering coefficients and low betweenness centrality. This suggests that the network topology has a strong effect on the resilience of the system. Namely there is a “strength of weak ties” effect, whereby high betweenness centrality is important in order to spread the shock while a high clustering coefficient hinders the diffusion. We discuss the implications of these results for efficient design and management of health-care networks.
