Efficient reporting delay calibration in spatial metapopulation models for reconstructing cross-regional epidemic dynamics

Reconstructing the early spatiotemporal dynamics of emerging infectious diseases (EIDs) is essential for effective public health response but remains difficult due to reporting delays, heterogeneous surveillance systems, and cryptic transmission chains. This study proposes a systems-oriented computational framework that tackles these challenges through three key innovations. First, we develop a stochastic infectious disease model tailored to limited early-stage case counts, grounded in a simplified metapopulation structure that enables accurate reconstruction of initial outbreak conditions while maintaining computational efficiency comparable to existing methods. Second, we introduce a matrix-based algorithm for calibrating reporting delays in spatial metapopulation models. By leveraging matrix operations to synchronize case-report updates across multiple regions, the method eliminates the need for traditional iterative traversal, thereby achieving substantial gains in computational efficiency and improving its practical utility in engineering applications. Third, leveraging complex network theory, we develop a parameter estimation framework using open-source algorithm libraries from the Medical Research Council Centre for Global Infectious Disease Analysis (MRC GIDA), achieving more than a tenfold increase in estimation efficiency for individual cities with populations exceeding one million. Validation using both simulated networks and empirical Chinese urban mobility networks covering early coronavirus disease 2019 (COVID-19) transmission scenarios demonstrates that the proposed approach substantially improves parameter estimation efficiency while ensuring robustness and accuracy. This framework provides a powerful tool for rapid, high-fidelity reconstruction of epidemic dynamics, enabling more informed responses to future public health emergencies.