A wastewater-based epidemic model for SARS-CoV-2 with application to three Canadian cities

Abstract

The COVID-19 pandemic has stimulated wastewater-based surveillance, allowing public health to track the epidemic by monitoring the concentration of the genetic fingerprints of SARS-CoV-2 shed in wastewater by infected individuals. Wastewater-based surveillance for COVID-19 is still in its infancy. In particular, the quantitative link between clinical cases observed through traditional surveillance and the signals from viral concentrations in wastewater is still developing and hampers interpretation of the data and actionable public-health decisions. We present a modelling framework that includes both SARS-CoV-2 transmission at the population level and the fate of SARS-CoV-2 RNA particles in the sewage system after faecal shedding by infected persons in the population. Using our mechanistic representation of the combined clinical/wastewater system, we perform exploratory simulations to quantify the effect of surveillance effectiveness, public-health interventions and vaccination on the discordance between clinical and wastewater signals. We also apply our model to surveillance data from three Canadian cities to provide wastewater-informed estimates for the actual prevalence, the effective reproduction number and incidence forecasts. We find that wastewater-based surveillance, paired with this model, can complement clinical surveillance by supporting the estimation of key epidemiological metrics and hence better triangulate the state of an epidemic using this alternative data source.

Keywords: Environmental surveillance; Epidemic model; SARS-CoV-2/COVID-19; Wastewater.

Fig. 1

Diagram of compartmental model. See main text for a description of the epidemiological states. The notation 1: n_• indicates a modelling using n_• sub-compartments to obtain a gamma-distributed sojourn time in the associated epidemiological state.

Fig. 2

Data sets used in this study for Edmonton, Ottawa and Toronto. Each horizontal panel is a city and colors represent the type of data (reported cases, hospital admissions and SARS-CoV-2 RNA concentration in wastewater). All curves were normalized to 1 (dividing by their respective maximum value) to plot them in one single panel to facilitate visual comparison. All data sets used in this study are available in Supplementary File S1.

Fig. 3

SARS-CoV-2 prevalence estimates. Each quadrant block represents one of the four selected locations. The left panel of each quadrant block shows the estimates of SARS-CoV-2 prevalence in time series. The lines show the mean estimate of prevalence. The right panel of each quadrant block compares the cumulative incidence estimated by the model fitted on the “Combined” data set to seroprevalence levels reported by the Canadian Blood Services for each city (grey point indicates the mean, the vertical grey bars show the 95% confidence intervals).

Fig. 4

Effective reproduction number. Each panel represents a wastewater treatment plant. For wastewater-based ${\mathcal{R}}_t$(blue curve), only estimates after 2020-Nov-15 are shown for Edmonton and Toronto to avoid the initial assay setup period. The ${\mathcal{R}}_t$estimates from our model are spline-smoothed, see Appendix A-7 for details.

Fig. 5

Forecast examples for Edmonton (left panel), Toronto/Highland Creek (middle panel) and Ottawa (right panel). Filled points represent past data of reported clinical cases. Circles represent reported clinical cases not yet observed at the time of forecast. Colour represents the type of data the model was fitted to: blue, SARS-CoV-2 concentrations in wastewater only (past observations not shown here, for legibility); red, clinical cases only. Dashed coloured lines indicate the fitted mean for reported cases. The thick solid line shows the 1-month-ahead mean forecast, and the shaded areas their respective 95%CrI. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6

Simulations were run varying selected parameters to show their impact on the reported detection time differential (Δ). Panel A: effect of the limit of detection of the quantification assay performed on wastewater. Values below the 0-intercept horizontal dashed line indicate a leading signal from wastewater concentrations than from clinical reports. Panel B: effect of the SARS-CoV-2 RNA decay rate in wastewater for different transit times between the shedding and sampling site. The colour of the curves represents the proportion of clinical cases reported (ρ) out of the total symptomatic incidence.

Fig. 7

Detectability of a sharp transmission reduction. Panel A: example of how the post-peak relative changes are calculated. The colour-coded dashed lines represent the time series of reported clinical cases and SARS-CoV-2 RNA concentration in wastewater. The grey shaded area indicates when the transmission rate decreases (here, T_interv = 10 days). The segment illustrates the relative change between the peak value and 7 days later (s_ww and s_cl),i.e., how we would typically assess the efficacy to reduce transmission. Panel B: the horizontal axis represents the time (since the start of the epidemic) when transmission begins to reduce to a third of its value. The vertical axis represents the post-peak relative changes from clinical reports (s_cl, red lines) or wastewater (s_ww, blue lines). Each subpanel indicates a different value (3, 10 and 20 days) for T_interv, the time it takes to reduces the transmission rate to a third of its initial value. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 8

Infection-permissive vaccination. Panel A shows the trajectories of reported clinical cases and SARS-CoV-2 concentration in wastewater under a scenario using an infection-permissive vaccine (“Vaccination”), or not (“Baseline”). In the vaccination scenario, the reported clinical cases decrease more rapidly than the level of SARS-CoV-2 in wastewater because sub-clinical infections tend to be less reported whereas faecal shedding continues. Panel B highlights this difference showing W(t)∕C(t), the ratio of reported wastewater concentration over reported cases, for the baseline / no-vaccination (pink) and the vaccination (green) scenarios. The ratio is normalized to have a starting value at 1 to make it easier to quantify the increase visually. The vertical dotted line indicates when vaccination starts (at time 70). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)