Hierarchical analysis of spreading dynamics in complex systems

Abstract

Modeling spreading dynamics on spatial networks is crucial to addressing challenges related to traffic congestion, epidemic outbreaks, efficient information dissemination, and technology adoption. Existing approaches include domainspecific agent-based simulations, which offer detailed dynamics but often involve extensive parameterization, and simplified differential equation models, which provide analytical tractability but may abstract away spatial heterogeneity in propagation patterns. As a step toward addressing this trade-off, this work presents a hierarchical multiscale framework that approximates spreading dynamics across different spatial scales under certain simplifying assumptions. Applied to the Susceptible-Infected-Recovered (SIR) model, the approach ensures consistency in dynamics across scales through multiscale regularization, linking parameters at finer scales to those obtained at coarser scales. This approach constrains the parameter search space, and enables faster convergence of the model fitting process compared to the non-regularized model. Using hierarchical modeling, the spatial dependencies critical for understanding system-level behavior are captured while mitigating the computational challenges posed by parameter proliferation at finer scales. Considering traffic congestion and COVID-19 spread as case studies, the calibrated fine-scale model is employed to analyze the effects of perturbations and to identify critical regions and connections that disproportionately influence system dynamics. This facilitates targeted intervention strategies and provides a tool for studying and managing spreading processes in spatially distributed sociotechnical systems.