Contagion-induced risk: An application to the global export network

In many systems, the state of each of their components can itself be a source of risk affecting the other components, and it is not easy to aggregate these individual values together with the interconnecting structural elements of the network. There are simulation models in the literature that establish propagation curves for the population as a whole, especially in the epidemiological case, but these models do not provide a clear analytical expression of the risk borne by each of the network nodes. Moreover, classical models, such as the generalized cascade model, are not necessarily convergent. Neither can the individual values of each node be aggregated on the same scale as they were measured. This paper proposes a mathematical model that makes it possible to analyze the propagation of risk in the face of a given adverse event that may reach all the elements of a network and precisely calculate the risk borne by each node according to its own vulnerability and the relationships with the other nodes, which may be more or less vulnerable and constitute additional sources of risk. It is shown that the new model ensures convergence and that the aggregated results can be interpreted in terms of the risk measurement scale previously given for each node. In addition, the global import–export network is used to illustrate how political or economic instability in one state can generate crises in other states.