Modeling infection from SARS-CoV-2 wastewater concentrations: promise, limitations, and future directions

SARS-CoV-2, the virus that causes COVID-19 infections, primarily causes respiratory illness (CDC 2021a). However, the RNA from this virus is also present in feces of infected symptomatic, pre-symptomatic, post-symptomatic, and asymptomatic individuals (Cheung et al. 2020; Foladori et al. 2020; WHO 2020a; Wolfel et al. 2020; Zhang et al. 2020; Zheng et al. 2020). Environmental surveillance through the testing of wastewater for evidence of pathogens has a long history of use in public health, particularly for poliovirus and more recently antimicrobial resistance (Asghar et al. 2014; WHO 2020b, 2020c). SARS-CoV-2 RNA has been reported in untreated wastewater and settled solids (e.g., sludge) in a number of countries (WHO 2020a), and wastewater SARS-CoV-2 RNA monitoring data have proven useful as an indicator of community illness in conjunction with traditional case reporting and surveillance methods (Medema et al. 2020; Peccia et al. 2020; D'Aoust et al. 2021; Fernandez-Cassi et al. 2021; Saguti et al. 2021; Weidhaas et al. 2021; Hewitt et al. 2022). Because of this, wastewater surveillance systems are being implemented for the COVID-19 response to provide data on overall infection trends and variant tracking within specific populations as a complement to clinical- and individual-based surveillance data for public health decision-making (Bivins et al. 2020; Medema et al. 2020; Peccia et al. 2020; Betancourt et al. 2021; Graham et al. 2021; Zhu et al. 2021; Kirby et al. 2022).

In addition to community infection trends, wastewater-based surveillance data have been proposed as a tool for estimating absolute community-level COVID-19 infections (Ahmed et al. 2020; Bivins et al. 2020; Hart & Halden 2020; Gerrity et al. 2021; Wurtzer et al. 2021). Estimating absolute infection levels (reported and unreported) is important for understanding disease transmission and designing effective mitigation strategies but has proven difficult to achieve using traditional surveillance indicators due to the large and variable relative burden of unreported cases (Bivins et al. 2020; Medema et al. 2020). To date, methods for estimating wastewater-based SARS-CoV-2 infections have included mechanistic-, statistical-, and epidemiological-based numerical modeling approaches (Baud et al. 2020; Ceylan 2020; Medema et al. 2020; Paul et al. 2020; Turk et al. 2020; Gerrity et al. 2021; Huisman et al. 2022; Kaplan et al. 2022; Weidhaas et al. 2021). For a mechanistic example, Ahmed et al. (2020) proposed an approach for COVID-19 wastewater surveillance in Australia based on the concentration of SARS-CoV-2 RNA in wastewater, the volume wastewater generated daily in a catchment, the number of SARS-CoV-2 RNA copies shed in stool by an infected individual each day, and the concentration of SARS-CoV-2 RNA in feces, each of which is represented by a combination of point estimate values and statistical distribution estimates in a Monte Carlo-based numerical simulation. Kaplan et al. (2022) proposed an epidemiologically- and statistically-calibrated scaling model to estimate incidence in a community from sludge RNA, a transmission dynamics model that aligns lagged epidemic indicators, and a site-specific scaling factor.

Mechanistic wastewater models are based on the processes that generate SARS-CoV-2 RNA signals in wastewater without additional statistical calibration against reported cases. Although wastewater-based disease research is rapidly advancing, the previously proposed mechanistic models fail to account for salient attributes of the wastewater processes, such as target decay within the system, and to account for variability in available data to estimate human contribution to the wastewater stream. In addition, the proposed statistical and epidemiological wastewater-infection-based models are either site-specific, using statistical correction factors dependent on reported cases, or are dependent on other clinical surveillance data; both limit the ability of wastewater to provide estimates independent of the variability in these clinical surveillance data (Li et al. 2020; Wu et al. 2020; Fernandez-Cassi et al. 2021). Moreover, epidemiologic compartmental models anchored to hospitalization or death rates are limited in their ability to provide near real-time infection estimates due to delayed nature of these indicators (Kaplan et al. 2021).

In this study, we derive three mechanistic models for estimating community infection levels from wastewater measurements that are agnostic to location. Each model uses a distinct approach to account for the human fecal content of wastewater, including endogenous microbial markers, wastewater flow measurements, and population-level estimates of per-capita wastewater generation. A numerical method is used to simulate the models, which are illustrated through two case studies of wastewater data and COVID-19 case data collected over several months in 2020–2021 (Virginia Beach, VA, and Santa Clara County, CA). We also propose a mathematical approach for connecting wastewater-based infection estimates to clinical surveillance data for public health interpretation. Finally, we describe the uncertainty associated with each modeling approach and the critical data needed to effectively use wastewater pathogen measurements to estimate community infections for public health decision-making.

Our model formulations were developed to estimate the fraction of infected individuals in a community that could be shedding SARS-CoV-2 RNA either through respiratory or fecal secretions, or both, regardless of symptoms (referred to hereafter as ‘infected’). Some of these individuals may not be considered ‘infected’ from a clinical perspective because the fecal shedding of viral RNA does not necessarily correspond with respiratory symptoms or shedding (Wolfel et al. 2020; Zheng et al. 2020). We use a stochastic, Monte Carlo numerical simulation-based mechanistic modeling approach (Soller & Eisenberg 2008) encompassing the following three related formulations: (1) a flow generation formulation based on per-capita domestic potable water use adjusted for wastewater generation from non-domestic sources; (2) a fecal strength formulation that is a modified flow generation formulation to include an endogenous human fecal control as a proxy for dilution and loss of human feces and associated pathogens during the sewer transport and testing processes; and (3) a flow receipt formulation based on collection site daily flow measurements and wastewater utility provided sewershed population estimates. The inputs of the models are microbial wastewater influent concentrations (i.e., SARS-CoV-2 RNA and endogenous control when applicable), where influent is defined as the untreated wastewater entering a treatment plant containing both solids and liquids.

The three formulations are summarized below, and detailed mathematical specifications are provided in Supplementary Material (SI) Section A. The model formulations, as applicable, incorporate the following: variability in each model parameter using data from the peer reviewed scientific literature; differences between disease presentation that exhibit gastrointestinal (GI) symptoms and those that do not (i.e., account for differences in total fecal matter shed for those with and without GI symptoms); per-capita water use; the decay of viral RNA during transport within the wastewater collection system, and finally, the fraction of wastewater that results from human fecal waste (versus commercial, industrial, run-off, etc.) (refer to Supplementary Material, Table A1 for a comparison of the three formulations). All three modeling approaches are fundamentally dependent on the levels of SARS-CoV-2 RNA in the feces of infected individuals and are related as shown mathematically in Supplementary Material, Section A.

The defining attribute of this formulation is a variable that defines the fraction of daily municipal wastewater that could be contributing SARS-CoV-2 RNA into the waste stream (F_cont). F_cont represents a variable, but time-invariant, estimate of the ‘human fecal strength’ (FS) of the wastewater. The salient assumption for this formulation is that it is feasible (e.g., for a wastewater treatment plant manager at the site monitored) to estimate with reasonable accuracy.

The flow generation formulation is limited when F_cont cannot be estimated accurately or when temporal variation of fecal strength is important. Such temporal variation could occur because of increased flows due to wet weather or variable wastewater composition due to dynamic water usage and human behavioral patterns (e.g., governmental restricted water usage or communities with large population influxes such as tourist locations). To address this, we reconfigured the flow generation model to define FS-based on an endogenous microbial control – a wastewater constituent that is present in relatively stable, high, and measurable concentrations in human excreta – rather than an expert judgement point estimate. We used Pepper Mild Mottle Virus (PMMoV) as the example human fecal-specific endogenous control (Zhang et al. 2006; Hamza et al. 2011).

Comparison of Equations (2) and (4a) indicates that two additional pieces of information are needed for this formulation compared to the flow generation formulation: (1) the concentration of the endogenous control in stool (D_{stool_endog}), which does not distinguish concentrations between diarrheal and non-diarrheal stool and (2) the corresponding decay coefficient (k_endog).

This fecal strength formulation (Equation (4a) and (4b)) has both advantages and disadvantages compared to the flow generation formulation (Equation (2)). The advantages are that the endogenous control (e.g., PMMoV RNA) measurements can theoretically serve as a normalizing control in that they can reflect the strength of human feces in the wastewater, the viral losses and dilution that occur as stool is transported from excreta through the sewage collection system to the sampling location, and the viral losses that occur during laboratory processing and testing. The primary disadvantage of this formulation is that it relies on measurements of the endogenous control concentrations in human feces, of which data are limited, and that endogenous control measurements must be made in each sample. This disadvantage is further complicated by the fact that wastewater processing and testing methods are not standardized, meaning that absolute concentrations generally cannot be compared across laboratories (without first conducting inter-lab comparisons).

Similar to the derivations provided above, this flow receipt formulation is equivalent to the fecal strength formulation under specific, realistic conditions (mathematical details are provided in the Supplementary Material, refer to formulas A3.6–A3.11). This formulation also assumes that the SARS-CoV-2 RNA wastewater measurement multiplied by the average daily flow rate reasonably represents the average SARS-CoV-2 RNA load over one day. A primary advantage of this formulation is that, for samples collected at treatment plants, flow measurements and population estimates are commonly available. Therefore, the flow receipt formulation reduces the requisite number of laboratory measurements compared to the other two formulations. Moreover, flow measurements and population estimates may have lower relative error and/or variability than microbial endogenous control measurements, which vary on a log-scale basis. The disadvantages of the flow receipt formulation are that it does not reflect SARS-CoV-2 RNA losses that occur during laboratory processing or unpredictable SARS-CoV-2 RNA losses in the sewage system that are attributable to processes other than the modeled gene target decay. This formulation also requires a static wastewater contributing population estimate, total daily flow measurements, and an aggregated average value for D_stool (used to account for variability in influent over the course of a day into a treatment facility).

The characteristics of the wastewater case studies are summarized in Table 1, including information on geographic area and population represented, sampling and testing methodologies, and clinical case data. For both case studies, viral wastewater concentration data (SARS-CoV-2 and PMMoV RNA) were measured by reverse transcriptase quantitative polymerase chain reaction (RT-qPCR) using digital droplet PCR technology (ddPCR). Note that the SARS-CoV-2 RNA and PMMoV RNA data were collected from primary settled solids rather than wastewater influent for the San Jose, CA case study (SJ). For the purposes of numerical modeling, the observed settled solids concentrations of SARS-CoV-2 RNA and PMMoV RNA were converted to estimated wastewater influent concentrations using a solid-to-liquid partitioning coefficient (K_d) following methods described in Kim et al. (2022) and Graham et al. (2021). Use of a fixed K_d assumes the viral RNA remains at a consistent level of equilibrium between water and solids through the sample collection period.

To parameterize the model for SARS-CoV-2, we used SARS-CoV-2 data from the scientific literature, other surrogate pathogen data when not available for SARS-CoV-2, and professional judgement as needed – details are provided in Supplementary Material, Section B. The model variables, corresponding statistical distributions, and distribution parameters used in the model formulations are shown in Table 2.

For each formulation, we ran simulations using Eqns 2, 4a and 5 (for the flow generation, fecal strength, and flow receipt formulations, respectively) using case study SARS-CoV-2 influent concentration data to estimate F_active. For the flow generation and fecal strength formulations, the measured daily average SARS-CoV-2 RNA concentration (via 24-h composite sampling) was converted to an estimated median SARS-CoV-2 RNA concentration. This conversion is necessary so that subsequent calculations are not biased by the measured SARS-CoV-2 RNA concentrations, which are inherently mean values and right skewed rather than the median values that are required for the subsequent calculations. For each observation, this conversion was accomplished by running an initial set of simulations to solve for an F_active.value in which the simulated mean concentration equaled the observed mean. The median value of the simulated distribution was then used in the subsequent calculations as indicated above. For the flow receipt formulation, we computed an average value of D_stool through simulation for use in Eqn 5c for consistency with the conceptual model of flow receipt at a treatment plant rather than variation in D_stool from individuals. During each iteration of the numerical simulation, values for the parameters were drawn from their respective statistical distributions to estimate F_active, and each Monte Carlo simulation comprised of 100,000 iterations for each case study and model formulation.

We conducted a series of in-depth analyses to determine the extent to which selected parameter value choices in the three model formulations affected the output (see Supplementary Material, Section D for further detail). The parameters evaluated include the following: (1) the concentration of SARS-CoV-2 RNA in feces of infected individuals, (2) the duration of SARS-CoV-2 RNA shedding in feces, and (3) the partitioning coefficients for SARS-CoV-2 and PMMoV (for the San Jose, CA case study where primary sludge was sampled). Not all model parameters were evaluated in this way and other potentially important considerations related to sensitivity include, but are not limited to (1) the gene target used to quantify SARS-CoV-2 RNA in sewage; (2) uncertainty or variability of sewage concentration measurements including the approach to handling SARS-CoV-2 RNA values reported below quantifiable limits; and (3) relative contributions of non-fecal (mucosal) SARS-CoV-2 RNA shedding to the wastewater stream. Consideration of those additional factors could serve as a guide for future study.

Detailed results from the sensitivity evaluations are presented in Supplementary Material, Sections C and D. Section C includes the fecal shedding distribution evaluation, and Section D includes evaluation of the uncertainty in the simulation results (D1), variability/uncertainty in computed influent concentrations for the San Jose case study based on the range of partitioning coefficients (D2), fecal shedding duration (D3), and model formulation sensitivity from inter-site variability (D4). The sensitivity evaluations indicate that: (1) there is substantial variability/uncertainty in the model output from individual simulations (Supplementary Material, Figure D1). These results are likely driven primarily by the highly uncertain fecal shedding data (Supplementary Material, Section C); (2) computed influent concentrations are strongly influenced by the selected values for the partitioning coefficients for conditions using sludge data as input (Supplementary Material, Figure D2); and (3) the general trends observed within any given site were not dependent on the specific fecal shedding duration used (Supplementary Material, Figure D3). Further details are presented in Supplementary Material, Sections C and D.

This study describes a modeling framework for estimating community-level COVID-19 infection based on wastewater monitoring data that are independent of individual and clinical surveillance data. However, the case studies presented highlight the limited available data to parameterize key model inputs, resulting in high outcome variability and presumed uncertainty, in turn, limiting model application to support public health decision-making for the COVID-19 response. The mechanistic modeling framework described encompasses three complementary formulations, each of which requires a unique set of inputs for estimating human contribution to wastewater (referred to as fecal strength) and size of population represented by a wastewater sample. A principal benefit of the mechanistic modeling approach is that it provides the conversion of wastewater (or sludge) levels into estimated total cases for direct comparison and interpretation against clinical surveillance data for public health decision-making. For example, this wastewater modeling approach can aid in understanding the variable effective reproductive number through the epidemic by estimating a total community infection burden that includes unreported and sub-clinical infections (Huisman et al. 2022). An additional benefit of the mechanistic modeling approach is that it can be updated to aid in understanding relative differences in community infection as the underlying drivers of transmission change temporally, such as changing variants and increasing vaccination levels. It can also be useful to provide insights about relative infection levels during time periods where community-level testing is changing (increasing or decreasing) or reporting of testing results is delayed or aggregated (such as holidays or some weekends).

Available wastewater-related data, and public health decision-making needs will determine which of these three wastewater-based infection model formulations would be most suitable for a community. For example, if it is reasonable to estimate the fraction of wastewater that derives from industrial and/or other sources that are unlikely to contain viral contributions and to assume those estimates are stable over the modeled period; or if endogenous control data are not available or feasible to collect, the flow generation formulation may be most applicable. Conversely, if a community is generating paired SARS-CoV-2 RNA and endogenous control wastewater surveillance data, the fecal strength formulation may be desirable over the flow generation formulation to provide enhanced potential for inter-site comparability. Moreover, Figure 4 suggests that, when applying the model across lab methods, sample types, and locations, the FS model maybe more applicable because the fecal normalization incorporated into that model likely makes the ratio of SARS-CoV-2 to reported cases more consistent across sites and sample types.

Differences between wastewater characteristics in communities may also influence which formulation is most appropriate. For example, in communities with substantial agricultural contributions to the community wastewater, the use of PMMoV RNA or another endogenous control may be more complicated as PMMoV may not be human fecal-specific in those settings (Zhang et al. 2006), and thus, make the flow generation or flow receipt formulation more appropriate. Another consideration is the population served by a treatment facility and whether the population is relatively static (i.e., are there large changes over short periods of time or does a large fraction of the population live in one sewershed and work in another). The FS formulation may be more representative of the true population contributing feces to wastewater, but it is also likely more vulnerable to outliers, as seen in Figure 2, because the formulation is dependent on two microbial measurements that can easily vary across orders of magnitude. Interpretation of the modeling results is complicated in cases where the population is more dynamic, and in such cases, careful consideration of these important factors is warranted.

Average modeled AR values ranged from 2 to 10 across the two case studies for the period of March 2020 to March 2021. While this range appears plausible given the reported levels of asymptomatic COVID-19 infections and estimates of unreported cases (Ma et al. 2021; Sah et al. 2021), the range of model results and sensitivity evaluations limit confidence in the model output for any specific data point. In particular, fecal shedding data for SARS-CoV-2 RNA and PMMoV RNA are presently limited, constraining the utility of the model. Moreover, multiple wastewater testing method evaluation studies have shown that absolute SARS-CoV-2 RNA wastewater measurements are not necessarily comparable across laboratory methods or wastewater sample types (Deng et al. 2021; Pecson et al. 2021; Foster et al. 2022; Kim et al. 2022). Therefore, it is unknown whether the differences in AR values between the two case studies reported here (mean AR values of 2–4 in VB compared to 6–10 in SJ) represent true differences in community infection levels captured by case reporting over the modeled period or are a function of differences in virus recovery, testing methods, and/or sample types (i.e., influent versus sludge). However, one interesting perspective from this modeling approach is the evaluation of the temporally varying nature of AR, which can vary due to many factors including community mitigation behavior (e.g., mask wearing, physical distancing), testing availability, circulating variants, and vaccination status. Few other analytical approaches have the ability to evaluate this characteristic on a time frame relevant for decision-making (Fernandez-Cassi et al. 2021; Huisman et al. 2022).

Although we conducted an extensive analysis of available data related to fecal shedding of SARS-CoV-2 RNA, there are limitations and uncertainties associated with those data. To mitigate potential bias associated with high levels of shedding, we selected best fitting distributions with an emphasis on the upper tails (refer to Supplementary Material, Section C for evaluation of this assumption on model estimates). However, future work is critically needed to characterize fecal shedding of SARS-CoV-2 RNA and human-specific microbial fecal targets, such as PMMoV RNA, to enhance the utility of this modeling framework. The model sensitivity evaluations showed that the mechanistic model was most sensitive to the fecal shedding parameter, which due to lack of available data was treated stochastically rather than temporally varying over the estimated shedding period. Temporal characterization of SARS-CoV-2 RNA fecal shedding over the full duration of infection, from exposure to recovery could allow for a time dependent model and in turn may reduce the uncertainty in community SARS-CoV-2 infection level estimates from wastewater. Similarly, inter-laboratory method evaluations that identify critical methodological impacts on measurement comparability would allow for model output comparability across sites. Finally, while shedding contributions via other bodily fluid types (e.g., mucous, urine, etc.) was found to be negligible compared to fecal contributions (Supplementary Material, Appendix B), these other shedding routes should be considered as variants emerge with potentially different clinical presentations.

Until more well characterized shedding data are available, site-specific relative ascertainment ratios (RAR) (relative to specific times of known infection and transmission profiles as described in the Supplementary Material, Section A for methods and Supplementary Material, Figures D3 and D4 for examples) are a present use for the described SARS-CoV-2 infection modeling framework given the uncertainties in the available input data. Relative AR values could provide insight into coverage of testing resources in relation to trends in total community cases relative to reported cases (Supplementary Material, Section D). This may become particularly useful to continue monitoring SARS-CoV-2 infection levels as mass screening of asymptomatic patients is no longer conducted due to elevated costs and increased vaccination coverage. Another possible approach that could help to minimize bias associated with the proposed mechanistic model uncertainty is the use of multiple formulations. This general approach has proven to be useful in other unrelated applications that need to account for substantial uncertainty in the modeling (i.e., long-range weather forecasting).

The described mechanistic modeling framework can be used for future wastewater surveillance targets, such as those diseases currently endemic in the United States, like norovirus, or other pathogens where sufficient high-quality input data are available. One potential complicating factor is the presence of pathogens that are also shed from non-human sources (i.e., parasitic protozoans such as Cryptosporidium spp.) as those other sources to the waste stream are not accounted for in the present framework. Antibiotic resistance genes (ARGs) are another promising target for wastewater surveillance, but in terms of modeling infection burden, ARGs have the added complication of being carried by multiple health relevant microorganisms. However, the current framework could be used for emerging pathogens whose characteristics are similar to currently well characterized pathogens – new SARS variants may fall into this category in the near term. In this case, the framework can be useful for complementing traditional epidemiological approaches (i.e., case counts, etc.) for broadly understanding pathogen spread within a community while the AR is unknown or changing.

Because of the public health utility of wastewater surveillance, the Centers for Disease Control and Prevention in the United States (CDC) launched the National Wastewater Surveillance System (NWSS) (CDC 2021b). NWSS provides novel national wastewater-based disease surveillance infrastructure to support public health action during and after the COVID-19 pandemic by providing coordination, laboratory and epidemiology capacity, and technical guidance for wastewater surveillance programs implemented by state, tribal, local, and territorial health departments (Kirby et al. 2021). NWSS runs a centralized data system that standardizes wastewater data submission, analysis, visualization, and sharing between jurisdictions and with the public. If the uncertainty in wastewater-infection modeling is sufficiently reduced, NWSS is positioned to rapidly integrate this analytic capacity into the data dashboard for public health use, which may become more relevant as CDC adds new targets, including emerging pathogens and antimicrobial resistance genes (CDC 2021b).

The interpretation of wastewater SARS-CoV-2 RNA data will continue to be multi-faceted and complicated as vaccination and variant emergence evolve. Understanding the extent to which these emerging factors will affect SARS-CoV-2 RNA fecal shedding will be critical to understand the utility of this modeling framework. Nevertheless, interpretation of wastewater SARS-CoV-2 RNA data will continue to be important to complement traditional surveillance data and the modeling framework presented can be useful for researchers and public health decision-makers.

We thank the participating wastewater utilities, Hampton Roads Sanitation District and San José-Santa Clara Regional Wastewater Facility, for the use of their data and dedication to protecting public health during the COVID-19 response. We also thank Santa Clara County and Virginia Beach Health Department for gathering and publicly sharing their data used in this study, as well as their dedication to the COVID-19 response. Finally, we acknowledge Daniel Gerrity, Nasa Armstrong, and Zach Marsh for their intellectual feedback and discussion regarding model development. Use of trade names and commercial sources is for identification only and does not imply endorsement by the Centers for Disease Control and Prevention (CDC). The findings and conclusions in this report are those of the authors and do not necessarily represent those of the CDC.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.