A Mathematical Framework for Assessing Disruptions in Maritime Logistics Operations

This study presents a novel mathematical framework to analyze operational disruptions in maritime logistics, using a compartmental model inspired by epidemiological systems. The model captures the dynamic transitions between Vulnerable, Disrupted, and Recovered operational states, providing a quantitative foundation for assessing resilience and disruption propagation. We define a threshold metric—the Maritime Resilience Number (MRN)—that determines whether disruptions are likely to escalate or be absorbed. Analytical results confirm the existence, uniqueness, and stability of equilibria under various conditions. Real-world data, including maritime traffic disruptions during the COVID-19 pandemic, are used to validate the model and estimate parameters. Numerical simulations demonstrate how varying disruption and recovery rates influence system outcomes. The framework can inform mitigation strategies, support policy-making, and be generalized to other forms of operational shocks such as cyberattacks, extreme weather events, or supply chain bottlenecks. This work contributes a rigorous and practical tool for enhancing resilience in global maritime systems.