Table 1.
Factors influencing temporal variation in the observed RNA count in wastewater samples.
Fig 1.
RNA fragments shown as red circles. The amount from each household may vary across time and depend on severity of outcomes. When samples are taken, this variability is expected to affect the outcome of taking a sample. Composite sampling may reduce variability but the quantity of viral RNA detected may still be dominated by RNA originating from a single infection.
Fig 2.
The model is fitted to the data by iteratively adding data points and optimizing the parameters using hill-climbing at each iteration. In each iteration a candidate change point (CP) is added. If there is an improvement in the likelihood resulting from the added exceeds some threshold value then the change point becomes part of the accepted model.
Fig 3.
Relationship between the sensitivity threshold and the number of trajectory changes.
(A) The top panel shows the raw data reporting the quantity of viral RNA in the collected samples. The panels below show the outcome of model fitting using maximum likelihood estimation for two values of the threshold hyperparameter. (B) The dependence of the number of change points on the threshold hyperparameter for the 10 largest WWTPs by catchment population. (C) Relationship between the number of change points and the index of dispersion. With fewer change points, variability around the mean must necessarily be larger in order to explain the distribution of observed quantities.
Fig 4.
Real-time growth rate estimates.
(A) Estimates for the Seafield WWTP at three threshold values. The solid line in these figures shows the estimated growth rate using the data available at each the given point in time. Higher thresholds are less responsive to high frequency variability in the data. Regions shaded red indicate periods uninterrupted positive growth. (B) The number of periods uninterrupted positive growth. Low threshold values produce a high frequency of “false alarms” - changes to the trajectory that are not sustained—higher threshold values are more stable but periods of positive growth tend to begin later.
Fig 5.
Comparison to admissions data.
(A) Model fitted to data from hospital admissions of individuals living in the catchment of the Seafield WWTP using identical methods to those applied to wastewater data in previous figures. (B) The real time growth rate estimated using samples from the Seafield WWTP and admissions for the corresponding catchment area. (C) Pearson’s r correlation between the time-series produced in panel B and for the 10 largest WWTP catchments (by population) in Scotland over a range of lags. Circles are added at the bottom of the figure to show the value of the lag that yields the maximum correlation. The mean correlation over the 10 sites is shown as a dashed line. Positive lag implies that wastewater growth rates respond faster than those obtained from hospital admissions data.