Estimating Wastewater Dilution Using Chemical Markers and Incomplete Flow Measurements: Application to Normalisation of SARS-CoV-2 Measurements

We construct a Bayesian estimator for the dilution of a wastewater sample, and use it to estimate the prevalence of SARS-CoV-2 in Wales using data from the Welsh Government Wastewater Monitoring Programme. In Wales wastewater is diluted by rainwater so an estimate of the level of dilution is required if we are to normalise sample measurements of disease markers such as SARS-CoV-2 RNA. We consider the situation where flow measurements are available, but will regularly be unreliable because of the action of combined sewer outflows (CSOs) and wastewater storage tanks, which divert wastewater away from treatment plants when the flow is excessive. However, we also have proxies for the flow from various chemical markers (e.g.\ phosphate, ammonium, electrical conductivity), whose level per unit of population is fixed. The new flow estimator has multiple advantages compared to existing procedures: credible intervals for the estimates; optimal weighting of the chemical markers; systematic handling of missing and censored values; and model based smoothing without lags.