Model for Interdependent Critical Flows: Addressing Cross-Sectoral Vulnerability

Societal well-being depends on the continuous operation of vital functions that critically depend on access to flows of essential commodities and services across sectors, i.e., Critical Flows. Understanding these cross-sectoral flow interdependencies requires modelling approaches capable of integrating both service and transfer interdependencies across different scales of analysis. Many existing modelling approaches typically either address the micro scale, capturing asset-specific vulnerabilities of critical infrastructures or supply chains, or the macroscale, dealing with a geopolitical view on security of supply and policy dynamics. Here, we propose a complementary meso-level modelling framework that enables the systematic representation of interdependency among critical functions through a flow perspective. Modelling these flows and their interdependencies is essential to capture cascading effects across vital societal functions. The model represents critical flows based on a modular system where critical infrastructure commodities, forms, and functions enable pathways from sources (productions, imports) to sinks (end-use, exports). Service and transfer interdependencies are explicitly represented in the formulation, allowing cross-sectoral effects to be captured within a unified modelling structure. The model integrates structural elements (nodes, links, spatial) with functional ones (capacities, dependencies, flows) and can be extended with temporal dynamics to account for disruption, buffer, restoration, and policy interventions. It employs a modular and incremental modelling approach, enabling continuous refinement from static flow representations to dynamic case-specific scenario simulations. This modelling development provides a foundation to study and understand cross-sectoral functionality and interdependency, quantify potential systemwide vulnerabilities, and support the strengthening of systemic resilience against diverse disruptions and hazards across sectors. Further, the underlying framework is also useful for researchers, practitioners, and policymakers to integrate resilience management, prioritize resources, and support resilience planning in complex interdependent socio-technical systems and critical entities.

Keywords: Critical flows, Vital societal functions, Critical entities, Interdependency, Cross-sectoral vulnerability, Meso-level modelling, Systemic resilience.