"Supplementary Materials for Resilience of Distributed Reproduction Numbers"

"The Distributed Reproduction Number (DRN) has recently been introduced as a decentralized framework for monitoring epidemic spread in metapopulation networks. While the DRN offers significant advantages for localized control and resource allocation, its practical utility depends on its resilience to inherent observation and modeling uncertainties. This paper presents a rigorous sensitivity analysis of the DRN estimator under non-ideal conditions, specifically focusing on its robustness to sensing noise and topological error. Using stochastic simulations on a heterogeneous network, we evaluate the estimator's performance when subjected to reporting delays, underreporting of incidence data, and missing connections in the underlying network model. Our results demonstrate that the DRN framework maintains numerical stability and structural reliability across a spectrum of practical perturbations. The resulting estimation error remains bounded under realistic levels of observation and modeling uncertainty, confirming that the DRN provides a resilient and decision-relevant metric for real-time epidemic monitoring in practical environments."