Risk propagation in heterogeneous supply-chain networks using a SEIS-based multi-state disruption model

Abstract

Introduction Transport and supply chain systems are composed of interconnected components, making them susceptible to disruptions that affect system stability and resilience. Most existing models rely on SIS-type dynamics, where exposed nodes become infected immediately, neglecting phased degradation, stress accumulation, activation delays, and transient vulnerabilities observed in real systems. Methodology This research develops a SEIS-based risk propagation framework with three node states (susceptible, exposed, infectious), where the exposed state represents a degradation phase before active disruption. Degree-dependent transition mechanisms capture structural heterogeneity, allowing different node behaviours while preserving global transition intensities. The framework is analysed using stochastic simulation to study the effects of activation delays and structural heterogeneity on disruption dynamics. Results Including an exposed phase alters disruption dynamics. In homogeneous networks, it smooths the evolution of disruptions, while in heterogeneous and hierarchical networks, stress accumulates structurally and may lead to rapid system-wide escalation when central nodes become infected. Discussion These findings provide a more realistic representation of disruption propagation by accounting for capacity deterioration before failure. They also show that focusing only on active disruptions may underestimate systemic risk, highlighting the importance of modelling latent degradation in heterogeneous transport and supply chain networks.