Critical infrastructure preparedness: cascading of disruptions considering vulnerability and dependency

Critical Infrastructures’ disruptions may result in crises of unacceptable outcomes in modern societies. Thus, it is important to develop models that allow describing CIs’ disruptions and their propagation characteristics. CI disruptions depend on both the type of the threat and on the nature of the CIs’ mutual dependencies. A model describing the cascade of disruptions should, then, be able to consider the CI-threat vulnerability and the CI-CI dependency. The paper presents a model where cascades are exactly described using an integral equation. The integral equation admits an analytical solution if the occurrence probability distribution functions (pdf) of the disruptions obey Stochastic Poisson Processes (SPP). The introduction of the “vulnerability to the threat” and the “CIs’ (inter)dependencies” is carried out with the help of time constant factors called: “vulnerability strain factor” and “disruption strain factor”, respectively. An academic case is presented in order to demonstrate the applicability of the model and illustrate some interesting features of the model. A complete set of numerical applications will be published separately.