2.1 Systematic review

The electronic search for available literature was conducted on 25 January 2021, following PRISMA guidelines [36]. The goal of the review was to identify and quantify major uncertainties for SARS-CoV-2 prevalence estimation through the WBE approach from the peer-reviewed literature. Databases (i.e., Web of Science core collection, Scopus, and PubMed) were searched using the strategy and terms in Table 1 . Two search scenarios were applied for uncertainties associated with SARS-CoV-2 excretion, and in-sewer transportations and detection. A total of 685 and 487 unique papers were identified after removing duplicates using the EndNote Reference Manager software for SARS-CoV-2 excretion and detection of SARS-CoV-2 in wastewater, respectively. Titles and abstracts of the retained articles were screened and assessed for eligibility following these criteria: 1) related to SARS-CoV-2 shedding from patients or SARS-CoV-2 in wastewater; 2) a review relevant to the study or contains quantitative data relevant to the study; 3) the article is in English and is peer-reviewed. Relevant articles were further assessed by full-text read and finally, 33 and 46 articles were included in this study for SARS-CoV-2 excretion, and SARS-CoV-2 in wastewater, respectively. Details of the review process are provided in the Supplementary Information (SI).

Table 1

Summary of literature search process.

Target	Search terms	Number of unique papers identified through databases	Number of papers identified from references of review or other papers	Number of papers identified as relevant	Number of papers subjected to full text review	Number of papers included
SARS-CoV-2 excretion	“SARS-CoV-2” AND (“Stool” OR “Feces” OR “Urine”)	685	0	57	54	33
SARS-CoV-2 in wastewater	“SARS-CoV-2” AND (“Wastewater” OR “Water”)	487	2	93	93	46

2.2 Bayesian simulation of shedding probability and magnitude

Monte Carlo simulation and Bayesian inference model have been applied in WBE for estimating the uncertainty of various factors including population, consumption of tobacco, alcohol, and drugs [4], [37]. This approach showed a promising outcome by a close-agreement to the estimated drug sales data globally [8], [38], [39]. The Bayesian approach is based on the idea that the posterior probability can be calculated by updating the prior probability and the final uncertainty of the unknown model parameter can be described by a probability distribution [40]. Thus, Bayesian statistics provides a more accurate approach to calculate and define the propagation of a parameter and its uncertainty derived from experimental and analytical procedures, especially for the experiment with a small scale and limited data point. Markov Chain Monte Carlo (MCMC) method is used to numerically calculate the modeling parameters, which ultimately provides the estimate for each modeling parameter with the associated credible intervals.

Through the systematic review, currently available data regarding SARS-CoV-2 RNA detection in stool and urine samples from more than 1,500 patients were summarized with all the gender, age, and pathological conditions (Table S1) and used as inputs for MCMC models using OpenBUGS (version 3.2.3), with details included as S2 and S3 in the SI. To estimate the shedding probability of SARS-CoV-2 RNA from COVID-19 infected patients in urine and stools, the number of patients with SARS-CoV-2 positive stool or urine (r_i) in a total number of patients (n_i) from each study (i), was modeled as a binary response variable with ‘true’ shedding probability (p_i) (Eq. (1)).

The shedding magnitude (m_i) of patients in each study (i) was defined as a normal distribution with mean as µ and variance as τ (Eq. (2)).

Models were built separately for the virus shedding magnitude and probability for urine and stool samples as described in SI. To provide stable distributions of results, 3000 runs were simulated for p _i and m_i.

2.3 Quantification of the uncertainties

To enhance the reliability of the back estimation for SARS-CoV-2 prevalence, the uncertainties in the estimation approach needs to be assessed. Gaussian error propagation was applied in this study to calculate the total uncertainty (for multiplications and divisions of independent uncertainties, the squared relative standard deviation (RSD) can be summed) [38]. Here we present a set of equations (Table 2 ) to consequently assess the uncertainties associated with each step in a transparent way. Two potential ways for estimating the COVID-19 prevalence through the WBE approach were included: 1) estimating the prevalence using the wastewater treatment plant (WWTP) influent flow rate and inhabitant population of the catchment area (Eq. B4.1, Table 2); 2) estimating the prevalence using the average water consumption data among the inhabitant population (Eq. B4.2, Table 2).

Table 2

Equations used to back-calculate SARS-CoV-2 prevalence and assess effects of uncertainties.

WBE processes	No.	WBE equations	Uncertainty equations
Viral load in sewers	B1	$$ L_{\mathit{Sewer}}=C_t\times F$$	$$ U_{L_{\mathit{Sewer}}}=\sqrt{U_S^2+U_A^2+U_F^2}$$
Decay of SARS-CoV-2	B2	$$ D=1-\frac{C_t}{C_0}=1-e^{-kt}$$	$$ U_D=\sqrt{{U_k}^2+{U_t}^2}$$
Excretion	B3	$$ E=Pop\times Q_s\times M$$	$$ U_E=\sqrt{U_{\mathit{Pop}}^2+U_Q^2+U_M^2}$$
Back-estimation	B4.1	$$ P_{\mathit{catchment}}=\frac{C_t\times F}{(1-D)\times P\times E}$$	$$ U_{P_{\mathit{catchment}}}=\sqrt{U_S^2+U_A^2+U_F^2+U_D^2+U_P^2+{(\frac{U_E}{\sqrt{n}})}^2}$$
	B4.2	$$ P_{\mathit{catchment}}=\frac{C_t\times Q_w}{(1-D)\times E}$$	$$ U_{P_{\mathit{catchment}}}=\sqrt{U_S^2+U_A^2+U_{Q_w}^2+U_D^2+{\left(\frac{U_E}{\sqrt{n}}\right)}^2}$$

Note: Eq. B1: L_sewer: the load of SARS-CoV-2 RNA detected in a sewer; C_t is the concentration of SARS-CoV-2 RNA detected in wastewater samples; F is the total wastewater flow during the sampling period; U_Lsewer, U_S and U_F are the uncertainty of L_sewer, sampling and flow measurement, respectively; U_A is the uncertainty of wastewater analysis, including concentration, RNA extraction, and detection. Eq. B2: D is the decay ratio of SARS-CoV-2 RNA in wastewater; C₀ is the concentration of SARS-CoV-2 RNA excreted in wastewater before transportation in sewers; t is the traveling time of SARS-CoV-2 genome in wastewater, and k is the decay rate constant; U_D, U_k, and U_t are the uncertainties of D, k and t. Detailed explanation was included in Section 3.2. Eq. (B3): E is the excretion rate of SARS-CoV-2 RNA from infected people; Pop is the shedding probability of SARS-CoV-2 RNA in stools or urine of infected person; Q_s is the shedding mass quantity of stools or urine among the population; M is the virus shedding magnitude in stools or urine from infected person; U_P, U_Qs, and U_M are the uncertainty of shedding probability, quantity and magnitude, respectively. Eq. B4.1: P_catchment is the COVID-19 prevalence in the catchment area, P is the population size in the catchment area; U_Pcatchment is the uncertainty of P_catchment. Eq. B4.2: Q_w is the daily amount of water usage, and U_Qw is its uncertainty.

3.1 Excretion factor determination

The excretion factor is commonly used in the WBE approach to convert the mass load of a certain biomarker in wastewater to the amount of substance consumed by the people [4]. Similarly, for the SARS-CoV-2 prevalence estimation, the excretion factor of SARS-CoV-2 RNA from an infected person is critical for the prevalence estimation. Currently, the excretion factors used in WBE for SARS-CoV-2 prevalence are calculated from the average or median values of SARS-CoV-2 RNA concentrations in stool samples [23]. However, to date, SARS-CoV-2 RNA has been detected in various clinical samples from infection-positive patients including feces, urine, blood, saliva, serum, sputum, etc. [41], [42], [43]. Moreover, the RNA shedding concentration, the probability of virus shedding among patients and the virus shedding sources are largely impacted by physiological factors such as gender, age and pathological conditions [44]. Considering the quantity and frequency, feces and urine are regarded as the main source of virus shedding in the WBE approach.

It is evident that the ratio of positive samples among patients in different studies varied greatly from 0 to 100% and 0 to 50% in stool and urine samples, respectively (Table S1). The presence of SARS-CoV-2 in stool and urine samples could be related to the swallowing of respiratory secretions from the upper respiratory tract or residues of infected antigen-presenting immune cells, or, more likely, due to virus replication in gastrointestinal epithelial cells or tubular epithelium [45], [46], [47]. Furthermore, the shedding magnitude detected in urine and stool samples varied from 10-10⁴ copies/mL in urine samples and 10–10⁸ copies/g in stool samples (Table S1). Monte-Carlo simulation was further applied to define the distribution and confidence interval for the shedding probability of patients in urine and stools (Fig. S2, Table 3 ). The mean probability of shedding in stools (0.545) was about 20 times higher than that of urines (0.0263), suggesting a negligible contribution of urine to the SARS-CoV-2 excretion (Table 3). Although the decay of SARS-CoV-2 by 99–99.9% could occur within several hours to 5 days in stool samples, considering the short time of toilet use, the decay of SARS-CoV-2 RNA concentrations during toilet use is regarded as negligible [48]. Thus, the distribution of shedding magnitude in stools was further defined (Fig. S2, Table 3). From pooled stool samples, the mean shedding magnitude was about 10^4.52 copies/g with a 95% confident interval (CI) ranged from 10^4.26 to 10^4.78 copies/g. Thereby the excretion rate E can be calculated based on the shedding probability, the magnitude of SARS-CoV-2 RNA in the stools of an infected person, and average daily stool amount for the population (Eq. (B3) in Table 2). For the daily average stool amount, 10% RSD is commonly applied based on previous observations [49]. Thus, U_E was further determined as 20% using Eq. (B3) in Table 2.

Table 3

Statistics of the shedding probability and magnitude.

	Urine shedding probability	Stool shedding probability	Stool shedding magnitude (log10 copies/g)
Mean	0.026	0.545	4.523
Standard deviation	0.030	0.093	0.133
Median	0.018	0.544	4.523
95% CI	6.3 × 10-4- 0.10	0.37–0.73	4.26–4.78

In addition, prolonged fecal shedding has been observed in patients for up to four to ten weeks after the first symptom onset and even after the patients' respiratory samples tested negative for SARS-CoV-2 RNA [50], [51], [52], [53], [54], [55]. Due to the limited clinical reports and difficulty in identifying the exact date of infection and cure, the prolonged shedding was not assessed in this study, which requires further investigations.

3.2 Determination of SARS-CoV-2 RNA decay in sewers

After shedding, SARS-CoV-2 virus in stools or urines enters the sewer system. With a broad range of pollutants and abundant microbial presence, sewers function as ‘microbial reactors’ where substances are transformed and degraded based on their chemical and biological reactivity [56]. Generally, for most viruses, the water matrix plays an important role in their inactivation and decay [57]. Without active human cells as hosts in wastewater, the infectivity of SARS-CoV-2 was reported to be reduced by 90% in several minutes to 2.1 days in wastewater environment, however, its RNA was significantly more persistent, reaching 3–33 days [58]. The relatively persistent RNA allows the detection of SARS-CoV-2 RNA from wastewater for estimating COVID-19 prevalence. As WBE estimates the prevalence of COVID-19 using downstream wastewater samples, which is transported through a sewer system to the sampling location, the accuracy of WBE is impacted by the uncertainty of SARS-CoV-2 RNA persistence in sewers.

The decay of SARS-CoV-2 RNA have been investigated in bulk wastewater at 20 °C [58], and 4–37 °C [59]. Currently available studies suggest that SARS-CoV-2 RNA decay in wastewater follows the first-order decay with the time as Eq. (3).

A higher decay rate of SARS-CoV-2 RNA has been observed in raw wastewater than autoclaved wastewater at 4–25 °C [64]. This could be related to the inactivation of RNases, and physicochemical characteristics change due to autoclaving or the presence and activity of microorganisms in raw wastewater [64], [65]. Furthermore, faster decay of SARS-CoV-2 RNA also occurred in raw wastewater than tap water, suggesting the potential impact of suspended solids, organic matters, chemical and biological compounds in wastewater [58], [64]. In addition, a physicochemical model was established to simulate the dynamic adsorption of SARS-CoV-2 RNA on suspended solids and also detectable SARS-CoV-2 concentrations in wastewater with several parameters (i.e., inlet flowrate, total suspended solids concentration, dissolved oxygen (DO), 5-days Biochemical Oxygen Demand (BOD₅), Chemical Oxygen Demand (COD), UV absorbance at 254 nm (UV254), Dissolved Organic Carbon (DOC), ammonium, nitrates, total organic nitrogen, total phosphorus and ortho-phosphates [66]. Through fitting the model with the data from real sewers and the COVID-19 prevalence in the catchment area, UV254/DOC and DO showed the highest correlation with the variation of viral concentration in wastewater, suggesting the strong impact on viral adsorption and decay in sewage caused by the presence of humic-like substances combined with DO. This could be potentially related to the oxidation of SARS-CoV-2 and increased metabolic activity of bacteria and bacterial enzymes [66]. To date, the detailed mechanism behind these above observations remains unclear and needs further investigations. Overall, these studies suggest that the first-order decay (Eq. (3)) can adequately describe the decay of SARS-CoV-2 RNA in wastewater, and the decay rate k was significantly affected by wastewater temperature. Variations of k could also be attributed to a variety of factors, including enzymatic activity, and the presence of solvents, detergents, DO concentration, grease, oil, fats and organic matter in wastewater, although there has yet to be specific evidence to definitively attribute these factors to virus decay [36].

Apart from the k value, the traveling time t also impacts the decay of SARS-CoV-2 RNA in wastewater (Eq. (3)). Most of the COVID-19 prevalence estimations were based on the SARS-CoV-2 concentration in the influent of WWTP, where wastewater traveling time occurred between shedding and sample collection. The traveling time of SARS-CoV-2 RNA in sewers, or more specifically hydraulic retention time (HRT) of sewers was found strongly correlated to the catchment size of a WWTP, ranging from several minutes to 6–10 h in small and large scale WWTPs, respectively [67]. Previously, extensive modeling and investigations for drug consumption estimations using WBE revealed that for most of the WWTP, the HRT within a catchment area follows a normal distribution with 4% RSD [67]. With currently available knowledge of SARS-CoV-2 in wastewater as discussed above sections, the uncertainty caused by decay (U_D) was thus calculated as Eq. (4).

3.3 Sampling and preservation of samples

Since SARS-CoV-2 was announced as a worldwide pandemic spread by WHO, researchers have been using WBE to detect and estimate the presence and community spread of this virus using water samples collected from mostly influent of WWTPs. Apart from WWTP samples, detection of the virus RNA in commercial passenger aircraft and cruise ship wastewater has also been reported [9]. Among these studies, sampling locations, sample collection techniques and preservation strategies vary greatly, which is another source of uncertainty for the prevalence estimation using WBE. Thus, the sampling location, technique and preservation conditions were systematically reviewed and summarized in Table 4 .

Table 4

Sampling practice and preservation techniques from current available publications.

Area/Country a	Sampling location	Sampling technique	Sample type	Results b	Preservation temperature, period	Reference
Queensland, Australia	WWTP and Pumping station	Grab and composite sampling (24 h)	Influent	2/9	4 °C, n.m. c	[8]
Queensland, Australia	WWTP	Grab and composite sampling (24 h)	Influent	19/63	4 °C, n.m.	[75]
Australia	Commercial passenger aircraft	Grab sampling	Treated aircraft wastewater	1/3	4 °C, within 6–24 h	[9]
	Cruise ship		Raw wastewater	1/1
			Effluent of membrane bioreactor	1/1
Niteroi, Brazil	WWTP	Composite sampling (10 h)	Influent	0/2	n.m.	[10]
	Hospital			3/8
	Sewer			2/2
Zhejiang, China	Hospital	n.m.	Influent of pre-processing disinfection pool in hospital	3/3	n.m.	[11]
			Effluent of hospital wastewater from pre-processing disinfection pool	1/1
			Final effluent of hospital wastewater	0/1
Wuhan, China	Hospital	n.m.	Influent of septic tank	7/9	4 °C, processed immediately	[12]
			Effluent of septic tank	0/4
Czech Republic	WWTP	Composite sampling (24 h)	Influent	13/112	5 ± 3 °C, within 48 h	[13]
Quito, Ecuador	River	Grab sampling	River water receiving raw wastewater	3/3	4 °C, less than 3 h	[14]
Montpellier, France	WWTP	Composite sampling (24 h)	Influent	3/12	−20 °C, n.m.	[16]
Thessaloniki, Greece	WWTP	Composite sampling (24 h)	Influent	16/29	4 °C, within 24 h	[66]
Gujarat, India	WWTP	Composite sampling (3 days)	Influent	6/6	4 °C, within 20 days	[17]
			Effluent	0/6
Gujarat, India	WWTP	Composite sampling (3 days)	Influent	4/6	4 °C, within 20 days	[18]
			Effluent	0/6
	A upflow anaerobic sludge blanket (UASB)		Influent of UASB	3/6
			Effluent of UASB	3/6
Jaipur, India	WWTP	Grab sampling	Influent	6/17	n.m.	[76]
			Effluent	0/8
Stockholm, Sweden	WWTP	n.m.	Influent	4/6	4 °C, within 24 h	[21]
North of Italy				1/4	Delivered to the laboratory on dry ice, stored at − 20 °C, n.m.
Italy	WWTP	Composite sampling (24 h)	Influent	6/12	−20 °C, n.m.	[20]
Italy	WWTP	Grab sampling	Influent	4/8	Under refrigeration, n.m.	[19]
			Effluent	0/4
	River		River water	3/4
Italy	WWTP	Composite sampling (24 h)	Influent	26/40	−20 °C, n.m.	[22]
Italy	WWTP and pumping stations	Grab sampling	Influent	4/9	4 °C, processed immediately and also after 24 h	[77]
			Effluent	2/2
Japan	WWTP	Grab sampling	Influent	0/5	On ice, processed within 6 h of collection	[23]
			Effluent from secondary treatment	1/5
	River		River water	0/3
Tokyo, Japan	WWTP	Grab sampling	Influent	4/12	−20 °C, n.m.	[78]
Japan	WWTP	Grab sampling	Influent	21/45	Four samples, −20 °C, n.m. 1 samples, on ice, within three days	[79]
Japan	Manholes and WWTP	Grab sampling	Supernatant of raw wastewater	6/32	−20 °C, within 10 days.	[73]
			Solids of raw wastewater	18/32
Slovenia	Pumping station of a hospital	Composite sampling (24 h)	Raw wastewater	10/15	−70 °C, n.m.	[27]
Sweden	WWTP	Composite sampling (24 h)	Influent	18/21	−20 °C, n.m.	[28]
			Effluent	13/21
	Sewer sampling station	0.5L wastewater per day for 4 days	Raw wastewater	15/20
Valencia, Spain	WWTP	Grab sampling	Influent	12/12	4 °C, n.m.	[24]
Murcia, Spain	WWTP	Grab sampling	Influent	35/42	4 °C, less than 24 h	[25]
			Effluent from secondary treatment	2/18
			Effluent from tertiary treatment	0/12
The Netherlands	WWTP	Composite sampling (24 h)	Influent	10/21	4 °C, processed on the day of sampling	[7]
South East England, UK	WWTP	Composite sampling (24 h)	Influent	3/5	−80 °C, n.m.	[26]
Louisiana, USA	WWTP	Composite sampling (24 h)	Influent	1/3	−80 °C, within 6 h	[31]
			Effluent from secondary treatment	0/3
			Effluent	0/3
		Grab sampling	Influent	1/4
			Effluent from secondary treatment	0/1
			Effluent	0/1
Virginia, USA	WWTP	Composite sampling (24 h) and grab sampling	Influent	98/198	On ice, within 6 h	[32]
Massachusetts, USA	WWTP	Composite sampling (24 h)	Influent	10/14	4 °C, n.m.	[35]
Montana, USA	WWTP	Grab and composite sampling (24 h)	Influent	7/7	4 °C, n.m.	[33]
New York, USA	WWTP	Composite sampling (24 h)	Influent	5/9	−20 °C, n.m.	[34]
Nevada, USA	WWTP	Grab and composite sampling (24 h)	Influent	46/46	n.m.	[80]
			Secondary effluent	0/4
			Finished effluent	0/2
	Natural lakes	Grab sampling	Lake water	0/22
	Drinking water	Grab sampling	Finished drinking water from a treatment plant	0/33
California, USA	WWTP	Composite sampling (24 h)	Influent	1/12	−20 °C, n.m.	[72]
		Composite sampling (24 h) and grab sampling	Settled solids samples from primary settler	9/17	−80 °C, n.m.
Seattle, USA	WWTP	Grab sampling	Primary composite sludge	12/17	4 °C, within one week	[74]
			Influent	22/45
Dubai, UAE	Pumping stations and WWTP	Grab sampling	Influent	829/2900	n.m.	[29]
	Commercial aircraft		Raw wastewater	27/198
UAE	Pumping stations, manholes	Grab samples	Raw wastewater	85%	Preserved on ice, and transported to a laboratory, n.m.	[30]
	WWTP	Composite sampling (24 h)	Influent
			Effluent	0%

Note:

^a: Sorted based on alphabetical order of countries.

^b: Results are presented as number of SARS-CoV-2 RNA positive samples/number of total samples tested.

^c: n.m. not mentioned.

3.4 SARS-CoV-2 detection in wastewater

For the detection of SARS-CoV-2 in the wastewater, a virus concentration and extraction step are usually employed prior to the subsequent detection, as the virus concentration in wastewater samples is fairly low. Electronegative membranes (EMB)-based filtration, ultrafiltration, polyethylene glycol (PEG) precipitation, ultracentrifugation, and aluminum hydroxide adsorption-precipitation have been applied for SARS-CoV-2 concentration in wastewater [7], [8], [9], [23], [25], [95]. Although the effectiveness of these concentration methods has been confirmed with successful detection of SARS-CoV-2 in wastewater, the recovery efficiencies largely varied between different concentration and extraction methods. Ahmed, et al. [96] compared 7 virus concentration methods for the RT-qPCR based recovery by using MHV from raw wastewater and found that the EMB-based filtration method with the addition of MgCl₂ had the highest recovery (65.7 ± 23.8%) of MHV. Similarly, a recent study used feline calicivirus (FCV) to investigate the efficiency of 11 concentration methods including EMB filtration followed by PEG precipitation, PEG precipitation, aluminum hydroxide adsorption-precipitation, ultrafiltration, skim milk flocculation and EMB filtration followed by ultrafiltration. Great variations between different methods were observed and PEG precipitation and aluminum hydroxide adsorption-precipitation were found as the most efficient methods as detailed in Table 5 [95]. The necessity of a secondary concentration step was investigated with ultrafiltration, PEG and ultracentrifugation in combination with hollow fiber ultrafiltration as a pretreatment for wastewater. The recovery efficiency decreased by about 50% for combined concentration methods in comparison to the single concentration method, suggesting that a secondary concentration may be detrimental for the detection and quantification of SARS-CoV-2 RNA [80]. Thus, the recovery efficiency with a single concentration step (i.e., ultrafiltration, PEG, and ultracentrifugation) of this study was included in Table 5. With currently available studies, great variations have been commonly observed for the same concentration methods, among different studies. For instance, with EMB, about 60% recovery of MHV was observed in one study [96], but less than 10% of MS2 was recovered in another [78]. Similarly, an interlaboratory assessment evaluated the reproducibility, sensitivity, and efficiency of 36 standard operating procedures (SOPs) including eight different concentration methods using the same wastewater sample, however, the concentration methods didn’t show a clear, systematic impact on the recovery efficiency [97]. This could be related to various factors, such as extraction methods, detection approaches, wastewater property and or the surrogate viruses used, which are further discussed in the following sections. With current limited understanding, the application and limitations of each concentration methods remain unclear, and require further investigations. Furthermore, although seven order of magnitude range of recovery efficiencies were observed with these 36 SOPs, 80% of the recovery-corrected results fell within a band of ± 1.15log₁₀ copies/L with high reproducibility, suggesting that a variety of methods could produce reproducible results with inclusion of surrogate viruses to quantify the recovery efficiency [97].

Table 5

Concentration methods and recovery efficiency in wastewater samples.

Concentration		Extraction methods	Detection method	Virus	Recovery efficiency	Uncertainty (RSD)	Reference
Methods	Consumables
Adsorption-elution method	Electronegative membrane (EMB)	RNeasy PowerMicrobiome Kit with glass beads replaced with garnet beads	RT-qPCR	MHV	60.5 ± 22.2%	0.37	[96]
	EMB/Acidification of sample to pH 4			MHV	26.7 ± 15.3%	0.57
	EMB/Addition of MgCl2			MHV	65.7 ± 23.8%	0.36
	EMB	NucliSENS easyMag (bioMerieux, Inc., Durham, NC, USA)	RT-ddPCR	BCoV	4.8 ± 2.8%	0.58	[32]
				BRSV	6.6 ± 3.8%	0.58
		QIAamp Viral RNA Mini Kit	RT-qPCR	MS2	1.0%-9.5%	N/Aa	[78]
				φ6	1.6%-21.0%
		Acid guanidinium thiocyanate–phenol–chloroform extraction using TRIzol reagent (TRIzol)		MS2	0.3% − 4.6%
				φ6	0.5% − 2.8%
Ultrafiltration	Amicon® Ultra-15 (30 K) Centrifugal Filter Devices	RNeasy PowerMicrobiome Kit with glass beads replaced with garnet beads	RT-qPCR	MHV	56.0 ± 32.3%	0.58	[96]
	Centricon Plus-70 centrifugal filter with a molecular weight cut-off of 10 kDa			MHV	28.0 ± 9.10%	0.33
		RNeasy PowerMicrobiome Kit	RT-qPCR	F-specific RNA phages	73 ± 50%	0.68	[7]
	Centricon Plus-70 centrifugal device with a molecular weight cutoff of 30 kDa	QIAamp Viral RNA Mini Kit	RT-qPCR	MS2	16.5% − 27.6%	N/A	[78]
				φ6	6.4% − 35.8%
		TRIzol		MS2	5.2% − 8.4%
				φ6	13.8% − 30%
	Hollow fiber ultrafiltration	Purelink Viral RNA/DNA Mini Kit	RT-qPCR	BCoV	54 ± 11%	0.20	[80]
				PMMoV	4.0 ± 2.2%	0.55
	Centricon Plus-70, 30 kDa or 100 kDa			BCoV	55 ± 38%	0.69
				PMMoV	1.3 ± 0.16%	0.12
	30 kDa AMICON® Ultra-15 Centrifugal Filters.	QIAamp® Viral RNA Mini Kit	RT-qPCR	SARS-CoV-2	51.4 ± 12.6%, 38.8 ± 11.6% b	0.25, 0.30b	[27]
	10 kDA AMICON® Ultra-15 Centrifugal Filters.				48.6 ± 41.6%, 49.5 ± 25.0% b	0.86, 0.51b
Precipitation	Aluminum hydroxide adsorption-precipitation	NucleoSpin RNA virus kit	RT-qPCR	PEDV	11 ± 3.5%	0.32	[25]
				MgV	11 ± 2.1%	0.19
					2.56%–18.78%	N/A	[24]
		Direct-zol RNA Miniprep (Zymo Research) Kit	RT-qPCR	FCV	45.0 ± 19.2%	0.43	[95]
		Maxwell® RSC 48 Extraction System (Promega)		SARS-CoV-2	7.4 ± 7.9% −9.4 ± 14.7%	1.07–1.56
		Maxwell® RSC Instrument	RT-qPCR	SARS-CoV-2	30.2 ± 17.7%	0.59	[98]
				MgV	6.8 ± 4.8%	0.71
	PEG/NaCl	NucliSENS® miniMAG® semi-automated extraction system	RT-qPCR	HCoV-229E	2.04 ± 0.7%	0.34	[22]
		RNeasy PowerMicrobiome Kit with glass beads replaced with garnet beads	RT-qPCR	MHV	44.0 ± 27.7%	0.63	[96]
		Direct-zol RNA Miniprep (Zymo Research) Kit	RT-qPCR	FCV	62.2 ± 30.8%	0.50	[95]
		Maxwell® RSC 48 Extraction System (Promega)		SARS-CoV-2	38.8 ± 46.5%	1.19
		QIAamp Viral RNA Mini Kit	RT-qPCR	MS2	27.0% − 51.4%	N/A	[78]
				φ6	1.4% − 3.0%
		TRIzol		MS2	27.5% − 77.6%
				φ6	29.8% − 49.8%
		Purelink Viral RNA/DNA Mini Kit	RT-qPCR	BCoV	11 ± 8.4%	0.76	[80]
				PMMoV	0.28 ± 0.10%	0.36
		Nucleospin RNA virus Kit	RT-qPCR	SARS-CoV-2	52.8 ± 18.2%	0.34	[98]
				MgV	11.1 ± 4.9%	0.44
	Beef extract solution	NucliSENS® miniMAG® system	RT-qPCR	TGEV	35.5 ± 13.0%	0.37	[13]
Ultracentrifugation	0.25 N glycine buffer (pH 9.5)	RNeasy PowerMicrobiome Kit with glass beads replaced with garnet beads	RT-qPCR analyses	MHV	33.5 ± 12.1%	0.36	[96]
Direct Extraction	Without concentration	NucliSENS® easyMag® system	RT-ddPCR	BCoV	59% ± 14%	0.24	[32]
				BRSV	75% ± 13%	0.17
InnovaPrep (with centrifugation)	0.05 μm PS Hollow Fiber concentrating pipette tip on the InnovaPrep Concentrating Pipette Select			BCoV	5.5% ±2.1%	0.38
				BRSV	7.6% ±3.0%	0.39

Note:

a: Not applicable.

b: Defined using two RT-qPCR assay targets.

PEG: Polyethylene glycol; MHV, Mouse hepatitis virus; BCoV, Bovine coronavirus; BRSV, Bovine respiratory syncytial virus; MS2, Bacteriophage MS2; φ6: Pseudomonas phage φ6; PEDV: Porcine epidemic diarrhea virus; MgV: Mengovirus; HCoV-229E, human coronavirus 229E; FCV, Feline calicivirus; PMMoV, Pepper mild mottle virus; TGEV, Transmissible gastroenteritis coronavirus; RT-ddPCR: Reverse transcription droplet digital PCR.

Aside from concentration methods, the extraction methods also affect the recovery efficiency. Using Pseudomonas phage φ6 (φ6) as a surrogate, the recovery efficiency was investigated with three concentration methods (i.e., EMB, PEG, and ultrafiltration) in combination with two extraction methods (i.e., QIAamp Viral RNA Mini Kit, and acid guanidinium thiocyanate–phenol–chloroform extraction with TRIzol reagent (TRIzol)). Among the tested combinations, PEG + TRIzol provided the highest φ6 recovery ratio of 29.8%–49.8%, while PEG + QIAamp provided only 1.4%-3.0% of φ6 recovery [78]. From currently available reports, even for the best recovery method, a considerable loss of virus RNA is commonly observed (Table 5). Furthermore, the wastewater matrix also played an important role on the recovery efficiency. Using wastewater collected from three different WWTPs, the recovery efficiency of a certain concentration and or extraction method differed [78]. This highlights the importance of adopting a suitable concentration and extraction method, and also the use of surrogate viruses as a control to minimize the recovery loss and calibrate the concentration of SARS-CoV-2 in wastewater.

Subsequently, after concentration and extraction, the detection of SARS-CoV-2 RNA is performed. Current detection techniques primarily rely on RT-qPCR or (nested) RT-PCR. With the recent development of detection methods, 13 available primer-probe sets, targeting regions and cycling parameters were further summarized (Table S2). Among these primer and probe sets, inconsistent performance between different primer-probe sets was commonly observed [27], [75], [77], [80], [98]. For instance, using the same wastewater samples, a higher positive ratio was detected with CDC N1 assays (19/63) than in E_Sarbeco assays (2/63) [75]. In addition, false positive results have been observed in some studies with E_Sarbeco assays, where amplifications were observed with a negative control [80]. This could be related to the detection limit of the assay, the linearity of the standard curve and the potential existence of PCR inhibitors. Wastewater is a complex matrix, components of which, such as calcium ions, urea, ethanol, sodium dodecyl sulfate and some proteins are normally regarded as PCR inhibitors [99]. These inhibitors are likely to impact the PCR efficiency of SARS-CoV-2 RNA. Moreover, considering that some the SARS-CoV-2 positive samples in these studies resulted in low detected concentrations (<1 copy/reaction), it is also possible that the target gene was occasionally absent in the reaction mixture, resulting in inconsistent results from different PCR assays [79].

Droplet digital PCR (ddPCR) has a higher precision compared to qPCR, as it can achieve absolute quantification without using a standard curve. A higher sensitivity of RT-ddPCR for SARS-CoV-2 detection in wastewater samples was reported [72], [100]. Similarly, slightly higher sensitivity was observed with RT-ddPCR than that of RT-qPCR in a study with 21 wastewater samples from airlines and a cruise ship [9]. Thus, RT-ddPCR could potentially increase the detection accuracy of SARS-CoV-2 in wastewater samples. In addition, molecular methods like digital PCR, sequencing, loop-mediated isothermal amplification (LAMP) and nucleic acid sequence-based amplification (NASBA) are also widely used in the study of environmental virology but have not been investigated for the detection of SARS-CoV-2 in wastewater samples. Their advantages and disadvantages have been summarized in Table S3, which could be further applied for SARS-CoV-2 detection in wastewater samples to improve the accuracy.

To quantify the recovery and detection efficiency of SARS-CoV-2 in wastewater, low-pathogenic surrogate viruses have been spiked into wastewater samples as external controls for the whole process including concentration, extraction, and detection. Bovine coronavirus (BCoV), MHV, the porcine epidemic diarrhea virus (PEDV), the mengovirus (MgV), bovine respiratory syncytial virus (BRSV), human coronavirus 229E (HCoV-229E), and transmissible gastroenteritis coronavirus (TGEV), were commonly applied as models of SARS-CoV-2 (Table 5). Variations in the recovery ratio with different surrogates using the same or similar concentration, RNA extraction and detection methods were observed in currently available studies (Table 5). For instance, using QIAamp Viral RNA Mini Kit, the recovery ratio reached 27.0%-51.4% for Bacteriophage MS2 (MS2) but only 1.4%-3.0% for φ6 [78]. Moreover, the actual detection efficiency of SARS-CoV-2 may differ from surrogate viruses. In studies using clinical positive or gamma-irradiated SARS-CoV-2 samples, different recovery and detection efficiencies were observed between SARS-CoV-2 and surrogate viruses (i.e., FCV and MgV) (Table 5). This might be related to the dissimilarity of surrogate viruses to SARS-CoV-2 in structure and morphology. To date, a detailed comparison between different surrogate viruses and SARS-CoV-2 in the concentration, extraction and detection from wastewater is still lacking, which requires further investigations. Apart from spiking surrogate virus, pepper mild mottle virus (PMMoV), an indicator for fecal contamination inherently in wastewater has also been applied to reduce the uncertainties, owing to its global distribution and its presence without substantial seasonal fluctuations [21], [35]. A recent study found that using PMMoV alone was sufficient to inform of relative recovery and to normalize between samples without adding external surrogate viruses in wastewater [21]. In addition, for WBE studies using sludge or solids from wastewater, PMMoV also showed superior performance in reducing background noise that possibly associated with the collection and transport of the samples along with the RNA concentration, extraction, and detection steps, over gut resident HF183 Bacteroides and 18S rRNA that is expressed in human cells [70]. CrAssphage, a human-specific gut-associated bacteriophage, was thought to be potentially a more specific biomarker due to its high detection sensitivity and abundance in wastewater [101]. Although the application of crAssphage as an internal standard for SARS-CoV-2 have not been reported in peer-reviewed articles, a recent preprint observed a close correlation between ratio of SARS-CoV-2 concentration to crAssphage concentration and cumulative COVID-19 cases [102]. This suggests the potential of using crAssphage as an internal standard, although further investigations are still in need.

With currently available data, depending on different processes, the recovery efficiency of these surrogate viruses varied from 1% to-75% for different wastewater samples (Table 5). Variations within batches using the same concentration and extraction methods have been observed with PMMoV, which is one of the major sources of uncertainty [35]. The RSD of each concentration and extraction process was thereby calculated based on the results in Table 5. Due to the highest recovery efficiency and lowest RSD, direct Extraction using NucliSENS® easyMag® system with RT-ddPCR as described by Gonzalez, et al. [32] and EMB/Addition of MgCl₂ RNeasy PowerMicrobiome Kit with RT-qPCR as described by Ahmed, et al. [96] are highly recommended (bolded in Table 5). For the systematic evaluation in this study, the U_A was determined as 17–36% assuming the best recovery procedures were taken by the WBE.