Wastewater-based effective reproduction number and prediction under the absence of shedding information

Estimating effective reproduction number (R_e) and predicting disease incidences are essential to formulate effective strategies for disease control. Although recent studies developed models for inferring R_e from wastewater-based data, they require information on shedding dynamics. Here, we proposed a framework of R_e estimation and prediction without shedding information. The framework consists of a space-state model for smoothing wastewater-based data and a renewal equation modified for wastewater-based data. The applicability of the framework was tested with simulated data and real-world data on Influenza A virus (IAV) and SARS-CoV-2 concentration in wastewater in 2022/2023 season in the USA. We confirmed the state-space model effectively fits various simulated epidemic curves and real-world data. In simulations, we found wastewater-based R_e (R_e^ww) closely aligns with instantaneous clinical R_e when shedding dynamics are rapid. For more prolonged shedding, R_e^ww approximates a smoothed R_e over time. We also observed the necessary sampling frequency to trace dynamics of wastewater concentration and R_e^ww accurately in the framework varies depending on the precision of detection methods, the epidemic status, the transmissibility of infectious diseases, and shedding dynamics. By applying our framework to real-world data, we found R_e^ww for SARS-CoV-2 showed similar trend and values to clinically-based R_e. R_e^ww for IAV ranged from 0.66 to 1.52 with a clear peak in the winter season, which agrees with previously reported R_e. We also succeeded in predicting wastewater concentration in a few weeks from available wastewater-based data. These results indicate that our framework potentially enables near real-time monitoring of approximated R_e and prediction of infectious disease dynamics through wastewater surveillance, which limits the delay between infection and reporting. Our framework is useful especially for regions where reliable clinical surveillance is not available and notifiable surveillance is abolished, and can be expanded to multiple infectious diseases that have been detected from wastewater.