Fig. 3: Estimated daily distributed lag parameters describing the association between viral RNA in sludge and COVID-19 epidemiological parameters.

a, Daily lags of 0–2 d and leads of 1 d are associated with the number of positive tests based on specimen collection date. b, Cumulative relationship between viral RNA in sludge and the number of positive tests based on specimen collection date. c, Daily lags of 0–2 d and leads of 1 d are associated with the percentage of positive tests based on specimen collection date. d, Cumulative relationship between viral RNA in sludge and the percentage of positive tests based on specimen collection date. e, Daily lags of 1–4 d are associated with hospitalization. f, Cumulative relationship between viral RNA in sludge and hospital admissions. g, Daily lags of sludge virus RNA data at longer time lags (6–8 d in the past) best correlate with the time series of publicly reported positive tests. h, Cumulative beta relationship between viral RNA in sludge and reported number of positive tests. Posterior means at the center of each data point and 90% credible intervals for error bars are displayed. For each lag, n = 75 daily values for positive tests by date of specimen collection (a,b), 75 daily values for percentage of positive tests by date of specimen collection (c,d), 75 daily values for hospital admission (e,f) and 75 daily values for publicly reported positive tests (g,h).