The late-2000s …nancial crisis has stressed the need of understanding the world …nancial system as a network of countries, where cross-border …nancial linkages play a fundamental role in the spread of systemic risks. Financial network models, that take into account the complex interrelationships between countries, seem to be an appropriate tool in this context. In this paper we propose to enrich the topological perspective of network models with a more structured statistical framework, that of graphical Gaussian models, which can be employed to accurately estimate the adjacency matrix, the main input for the estimation of the interconnections between di¤erent countries. We consider di¤erent types of graphical models: besides classical ones, we introduce Bayesian graphical models, that can take model uncertainty into account, and dynamic Bayesian graphical models, that provide a convenient framework to model temporal cross-border data, decomposing the model into autoregressive and contemporaneous networks. The paper shows how the application of the proposed models to the Bank of International Settlements locational banking statistics allows the identi…cation of four distinct groups of countries, that can be considered central in systemic risk contagion.

www.nature.com/scientificreports/ process: geographical boundaries and age classes 9. Finally, we show how these dimensions can shape policy interventions aiming at containing the epidemic outbreak. This paper contributes to the extant literature on trade-offs between mitigation, i.e. slowing down the epidemic contagion, and suppression, i.e. temporarily compressing the risk of contagion 9,16-18. Notwithstanding micro data on individual profiles are not taken into account in our compartmental model, we show how the inclusion of geographical and age classes uncovers relevant features impacting on model results on virus diffusion, providing some guidance to policy makers. We show that an early lockdown shifts the epidemic in time and that beyond a critical threshold of the intensity of the lockdown, the epidemic would tend to fully recover its strength as soon as the lockdown is lifted. As a consequence, specific mitigation strategies for a second wave must be prepared during the lockdown phase. To provide some guidance on the relative importance of different general strategies, we first study how the heterogeneity of the intensity of mobility flows across Italian administrative Regions influences the observed delays of the contagion. The relative strength of intra-Regional mobility with respect to interRegional mobility flows implies that, once the epidemic has started, it then tends to develop independently within each Region, as also empirically observed in simulations of Covid-19 spread in China 19. Then, we study the impact of patterns of interaction within and between age classes, finding that the structure of the interactions is of primarily importance in estimating post-lockdown effects. According to our results, age-based mitigation strategies, which can affect local behaviours can represent a key ingredient to contain a second wave and to protect age-classes with higher incidence of severe cases.

The spread of SARS-COV-2 has affected many economic and social systems. This paper aims at estimating the impact on regional productive systems in Italy of the interplay between the epidemic and the mobility restriction measures put in place to contain the contagion. We focus then on the economic consequences of alternative lockdown lifting schemes. We leverage a massive dataset of human mobility which describes daily movements of over four million individuals in Italy and we model the epidemic spreading through a metapopulation SIR model, which provides the fraction of infected individuals in each Italian district. To quantify economic backslashes this information is combined with socio-economic data. We then carry out a scenario analysis to model the transition to a post-lockdown phase and analyze the economic outcomes derived from the interplay between (a) the timing and intensity of the release of mobility restrictions and (b) the corresponding scenarios on the severity of virus transmission rates. Using a simple model for the spreading disease and parsimonious assumptions on the relationship between the infection and the associated economic backlashes, we show how different policy schemes tend to induce heterogeneous distributions of losses at the regional level depending on mobility restrictions. Our work shed lights on how recovery policies need to balance the interplay between mobility flows of disposable workers and the diffusion of contagion.

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