A simple SEIR-V model to estimate COVID-19 prevalence and predict SARS-CoV-2 transmission using wastewater-based surveillance data

Abstract

Wastewater-based surveillance (WBS) has been widely used as a public health tool to monitor SARS-CoV-2 transmission. However, epidemiological inference from WBS data remains understudied and limits its application. In this study, we have established a quantitative framework to estimate COVID-19 prevalence and predict SARS-CoV-2 transmission through integrating WBS data into an SEIR-V model. We conceptually divide the individual-level viral shedding course into exposed, infectious, and recovery phases as an analogy to the compartments in a population-level SEIR model. We demonstrated that the effect of temperature on viral losses in the sewer can be straightforwardly incorporated in our framework. Using WBS data from the second wave of the pandemic (Oct 02, 2020-Jan 25, 2021) in the Greater Boston area, we showed that the SEIR-V model successfully recapitulates the temporal dynamics of viral load in wastewater and predicts the true number of cases peaked earlier and higher than the number of reported cases by 6-16 days and 8.3-10.2 folds (R = 0.93). This work showcases a simple yet effective method to bridge WBS and quantitative epidemiological modeling to estimate the prevalence and transmission of SARS-CoV-2 in the sewershed, which could facilitate the application of wastewater surveillance of infectious diseases for epidemiological inference and inform public health actions.

Keywords: Epidemic model; SARS-CoV-2; SEIR-V model; Temperature; Wastewater-based epidemiology.

Graphical abstract

Fig. 1

Illustration and fitting fecal viral shedding dynamics. (A) Illustration of the fecal viral shedding dynamics based on the infection progression. The viral shedding profile is divided into three periods shaded: Exposed (E), Infectious (I), and Recovered (R). The red-shaded region is the period of infectiousness I, which is corresponding to the compartment I in the SEIR model. (B) Fitting of the proposed viral shedding function to viral shedding in hospitalized patients' stool data from (Wolfel et al. 2020). While aggregated data seem to show a viral shedding peak at around day 13–14, declining trends were found in the 9 individual cases. The average viral shedding rate in stool during the infectious period (from day 3 to day 11) is 4.49 × 10⁷ viral RNA per g. The horizontal dashed line is the average fecal viral shedding rate for infectious individuals inferred from the model. The viral shedding peak is set at the 4th day post infection.

Fig. 2

Model fit and prediction to wastewater data covering the second wave of pandemic. (A) Best fit to virus concentration data in wastewater from October 2 to December 18, 2020 (dashed grey line), and model prediction to January 25, 2021. Red dots are the measured viral load in wastewater and blue curve is the modeling result. (B) Model estimation of the true number of COVID-19 cases (blue curve) and clinically reported cases (red curve). The blue and red dashed lines are dates when the two curves peak, and ΔT_lead is the time difference between the two peaks. (C) Correlation between simulation cases and reported cases. Best fit parameters: λ = 9.66 × 10⁻⁸ day⁻¹ person⁻¹, α = 249 g, γ = 0.08, and E(0) = 11 people.

Fig. 3

Incorporating the effect of temporal variation of wastewater temperature in the SEIR-V model. (A) Best fit to viral concentration data in wastewater from October 2 to December 18, 2020 (dashed grey line), and model prediction to January 25, 2021. Red dots are the measured viral load in wastewater and blue curve is the modeling result. (B) Comparison of the SEIR-V models with and without incorporating temperature effect. Top left: corrected Akaike information criterion (AICc) values, the statistically significant AICc difference is 9.2; Top right: initial populations exposed to SARS-CoV-2; Bottom left: wastewater lead time difference at peak; Bottom right: fold of difference between the number of predicted cases and clinically reported cases. The AIC/AICc are calculated assuming normal distribution of residuals with mean zero using the formulas$\mathit{AIC}=nlog\left(\frac{\mathit{sse}}{n}\right)+2k$ and$\mathit{AICc}=\mathit{AIC}+\frac{2k\left(k+1\right)}{n-k-1}$, where n is the number of data used for fitting, k is the number of fitting parameter and the SSE is calculated based on the data used for fitting. Light blue represents the model without including temperate effect, while blue represents the model with temperature effect. Best fit parameters when incorporating temperature: λ = 9.06 × 10⁻⁸ day⁻¹ person⁻¹, α = 360 g,and E(0) = 1182 people.