A novel disaster risk assessment framework based on Markov chain analysis of evacuation network structure and geometric coverage optimization

This study proposes a novel disaster risk assessment model for quantitatively evaluating structural vulnerabilities and evacuation difficulties in evacuation networks. First, we probabilistically model accessibility relationships between evacuation nodes using a gravity model based on the distribution of evacuees and shelters, formulating this as a discrete-time Markov chain. Subsequently, we extract equivalence classes based on strongly connected components and derive stationary distributions for the main equivalence class to visualize isolated areas and risk concentration within the evacuation network. For nodes not belonging to the main equivalence class, we calculate the number and locations of newly required evacuation support facilities using the minimum covering problem. Based on this structural information, we define a disaster risk score composed of the number of equivalence classes, covering circles, and the standard deviation of the stationary distribution. Through multiple simulations using virtual terrain, we confirm the consistency and reproducibility of the proposed method. Furthermore, through empirical analysis targeting 16 municipalities in Shizuoka Prefecture, Japan — a region characterized by coastal lowlands and mountainous terrain — we reveal elevation-dependent network disconnections and evacuation destination bias risks in coastal areas. The analysis demonstrates how topographical constraints significantly impact evacuation network connectivity, with coastal municipalities showing rapid risk score increases when elevation thresholds exceed 10 meters, while inland mountainous areas maintain relatively stable connectivity. This method serves as a novel disaster risk visualization approach that comprehensively evaluates spatial and structural factors, contributing to the assessment of evacuation shelter placement adequacy, proposals for complementary facilities, and prioritization of regional disaster prevention policies.