A mobility-adjusted framework for regional R_t estimation: enhancing spatial interpretation of transmission dynamics

Estimating the effective reproduction number ([Formula: see text]) is essential for monitoring and responding to infectious disease outbreaks. However, conventional methods such as the Wallinga-Teunis (WT) estimator assume intra-regional transmission and do not explicitly account for spatial connectivity. This underscores the need for approaches that explicitly incorporate spatial connectivity, such as inter-regional mobility, into transmission dynamics.

We propose a mobility-adjusted framework for regional [Formula: see text] estimation that incorporates inter-regional population movement data to reallocate transmission pressure across regions. This approach allows us to better account for the contribution of external transmission. We apply our method to real-world COVID-19 data from South Korea, using a daily mobility matrix derived from telecommunication records. The resulting [Formula: see text] estimates are compared with those obtained from the WT method. We also conduct sensitivity analysis on the size of the sliding window and comparative analysis based on the structure of the mobility matrix.

In high-mobility regions such as Seoul and Gyeonggi, both methods produced broadly similar trends, though the mobility-adjusted [Formula: see text] was more responsive during the early epidemic phase. In contrast, many low-incidence regions-including Jeonbuk, Jeonnam, and Ulsan-showed inflated WT [Formula: see text] estimates, which our framework mitigated by accounting for inter-regional transmission. Daegu, the epicenter of the initial outbreak, exhibited a sharp early peak in mobility-adjusted [Formula: see text] consistent with its role as a major source of onward transmission, while neighboring or closely connected regions such as Gyeongbuk and Busan showed largely consistent values across methods. Sensitivity analysis indicated that a 7-day sliding window provided stable and epidemiologically plausible estimates, and additional comparisons across alternative mobility matrix structures confirmed that incorporating temporally resolved, empirical movement data yields more robust and interpretable results than static or simplified assumptions.

This study presents a mobility-adjusted framework for estimating [Formula: see text] that incorporates inter-regional movement to better capture spatial transmission dynamics. The method mitigates inflated estimates in low-incidence areas and identifies mobility-driven risks in highly connected regions, offering context-aware insights beyond conventional approaches. While not universally superior, it complements existing methods and provides a practical tool for geographically targeted interventions, adaptable to diverse epidemiological settings where spatial connectivity shapes outbreaks.