The Use of Wastewater Surveillance to Estimate SARS-CoV-2 Fecal Viral Shedding Pattern and Identify Time Periods with Intensified Transmission

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Wastewater-based surveillance is an important tool for monitoring the COVID-19 12 pandemic. However, it remains challenging to translate wastewater SARS-CoV-2 viral load to 13 infection number, due to unclear shedding patterns in wastewater and potential differences 14 between variants. 15

We utilized comprehensive wastewater surveillance data and estimates of infection 16 prevalence (i.e., the source of the viral shedding) available for New York City (NYC) to 17 characterize SARS-CoV-2 fecal shedding pattern over multiple COVID-19 waves. 18

We collected SARS-CoV-2 viral wastewater measurements in NYC during August 31, 19 2020 – August 29, 2023 (N = 3794 samples). Combining with estimates of infection prevalence 20 (number of infectious individuals including those not detected as cases), we estimated the 21 time-lag, duration, and per-infection fecal shedding rate for the ancestral/Iota, Delta, and 22 Omicron variants, separately. We also developed a procedure to identify occasions with 23 intensified transmission. 24

Models suggested fecal viral shedding likely starts around the same time as and lasts 25 slightly longer than respiratory tract shedding. Estimated fecal viral shedding rate was highest 26 during the ancestral/Iota variant wave, at 1.44 (95% CI: 1.35 – 1.53) billion RNA copies in 27 wastewater per day per infection (measured by RT-qPCR), and decreased by ~20% and 50-60% 28 during the Delta wave and Omicron period, respectively. We identified around 200 occasions 29 during which the wastewater SARS-CoV-2 viral load exceeded the expected level in any of 14 30 sewersheds. These anomalies disproportionally occurred during late January, late April - early 31 May, early August, and from late-November to late-December, with frequencies exceeding the 32 expectation assuming random occurrence (P < 0.05; bootstrapping test). 33

These estimates may be useful in understanding changes in underlying infection 34 rate and help quantify changes in COVID-19 transmission and severity over time. We have also 35 demonstrated that wastewater surveillance data can support the identification of time periods 36 with potentially intensified transmission. 37 38 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. 2 39

40 Since the early phase of the COVID-19 pandemic, studies have reported that wastewater SARS-41 CoV-2 viral loads often closely track or lead case and/or hospitalization trajectories and, as 42 such, can serve as a cost-effective surveillance tool for monitoring the COVID-19 pandemic.1-5 43 Thus, wastewater-based surveillance systems have been built worldwide on local and national 44 scales. With decreasing clinical testing and genomic sequencing,6,7 there has been increased 45 interest in wastewater surveillance, given results are generated independently of clinical testing 46 practice. 47 48 Though there are advantages of SARS-CoV-2 wastewater surveillance, a large US national 49 survey of public health agencies completed in 2022 noted the results were often deemed 50 supplementary to surveillance involving clinical laboratory tests.8 One of the hurdles is that 51 while the trends could indicate changes in SARS-CoV-2 community circulation, it remains 52 challenging to directly translate wastewater SARS-CoV-2 viral loads to a specific number of 53 infections in the population, due to the unclear fecal viral shedding rate (after accounting for 54 the recovery rate of virus genomes) in wastewater samples. In addition, with the fast 55 emergence and turnover of new SARS-CoV-2 variants, it is unclear how fecal shedding of the 56 virus may have altered over time by variant. To address these questions, we utilize 57 comprehensive wastewater surveillance data and estimates of infection prevalence (i.e., the 58 source of the viral shedding) available for New York City (NYC) to characterize SARS-CoV-2 fecal 59 shedding over multiple COVID-19 pandemic and epidemic waves. 60 61 NYC experienced the earliest pandemic wave in the United States (US), and shortly after the 62 initial wave, established a wastewater surveillance program that covers all of its 14 sewersheds 63 which serve over 8 million residents.2 Since August 31, 2020, the program has continuously 64 measured SARS-CoV-2 viral load weekly. Independently, we have developed and used a 65 comprehensive model-inference system – calibrated to case, emergency department (ED) visit, 66 and mortality data – to reconstruct the underlying transmission dynamics and estimate key 67 epidemiological characteristics.9,10 In particular, the model-inference system estimates the 68 number of infectious individuals including those not detected as cases (i.e., infection 69 prevalence) in each of the city’s 42 neighborhoods during each week since March 1, 2020.9,10 70 Combining the wastewater SARS-CoV-2 viral load data and infection prevalence estimates over 71 a 3-year period (i.e., August 31, 2020 – August 29, 2023), we are able to characterize the viral 72 shedding pattern (i.e., time-lag, duration, and per-infection shedding rate) for the 73 ancestral/Iota, Delta, and Omicron variants, separately. We are also able to identify time 74 periods with greater transmission. 75 76 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 3

77 SARS-CoV-2 wastewater surveillance data. 78 The SARS-CoV-2 wastewater surveillance program in NYC started on August 31, 2020. 79 Wastewater samples were taken at each of the city’s 14 wastewater treatment plants, usually 80 twice per week on Sundays and Tuesdays (N = 3794 samples; see variations and details in Table 81 S1). SARS-CoV-2 RNA concentration was measured using quantitative reverse transcription 82 polymerase chain reaction (RT-qPCR) assays during August 31, 2020, through April 11, 2023, 83 and reverse transcription digital PCR (RT-dPCR) assays from November 1, 2022, through August 84 29, 2023. All measurements adjusted for sewershed-specific flow rate and service population 85 size. Specifically, per-capita SARS-CoV-2 viral load (RNA copies per day per population) was 86 computed as the viral concentration measure multiplied by the daily sewage flow rate and then 87 divided by the service population. 88 89 For weeks after April 11, 2023, when the samples were measured using RT-dPCR alone, we 90 converted the RT-dPCR measurements to RT-qPCR equivalents, to allow characterization of 91 SARS-CoV-2 viral shedding during the entire Omicron period. Specifically, we first computed the 92 conversion ratio using measurements from November 1, 2022, through April 11, 2023, when 93 both assays were conducted, simply as the mean of all RT-qPCR measurements dividing the 94 mean of all RT-dPCR measurements, during these weeks. We then multiplied the RT-dPCR 95 measurements by the conversion ratio to obtain the converted RT-qPCR equivalents. As an 96 alternative, we stratified the data by sewershed and performed the conversion using 97 sewershed-specific conversion ratios (see Sensitivity Analysis). In addition, the RT-qPCR and RT-98 dPCR measures differed substantially (by a factor of 16.7 based on the aforementioned 99 overlapping measurements), likely due to difference in methodology.11 To facilitate comparison 100 with studies primarily using RT-dPCR, we also converted all RT-qPCR measurements to RT-dPCR 101 equivalents when reporting the viral shedding rates. 102 103 SARS-CoV-2 infection prevalence estimates. 104 Estimated SARS-CoV-2 infection prevalence came from a model-inference system,12 105 independent of the wastewater surveillance data. Briefly, the model-inference system fit a 106 neighborhood-level Susceptible-Exposed-Infectious-(re)Susceptible-Vaccination (SEIRSV) model 107 to age-grouped, neighborhood-specific COVID-19 case, ED visit, and mortality data, accounting 108 for concurrent nonpharmaceutical interventions, vaccinations, under-detection of infection, 109 and seasonal changes. We used the SEIRSV model to explicitly simulate the number of 110 infectious individuals – i.e., anyone who can actively transmit SARS-CoV-2 and infect others 111 regardless of symptoms and test-seeking behaviors – present in the population and estimated 112 this infection prevalence during each week using the full model-inference system using COVID-113 19 case, ED visit, and mortality data.12 That is, similar to the wastewater SARS-CoV-2 viral loads 114 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 4 measuring the total population fecal shedding regardless of clinical testing, estimated infection 115 prevalence here included all individuals actively transmitting SARS-CoV-2 (primarily via 116 shedding from the respiratory tracts) regardless of whether they were detected as cases. 117 118 The infection prevalence estimates are United Hospital Fund neighborhood-13 and age group 119 specific, and available for each week starting March 1, 2020 (the pandemic onset in NYC) to the 120 week starting August 27, 2023. To match with the sewershed-level wastewater SARS-CoV-2 121 viral load data, we first mapped each neighborhood (42 in total vs. 14 sewersheds) to the 122 corresponding sewershed based on geolocation; if a neighborhood overlapped multiple 123 sewersheds, we assigned it to the one with the maximal overlap. For each sewershed and 124 week, we then aggregated all estimated infectious individuals from all related neighborhoods. 125 126 Estimating the fecal viral shedding time-lag, duration, and rate. 127 To analyze the fecal viral shedding pattern by variant, we defined three time periods based on 128 data availability and the predominant circulating variant14 (i.e., to be more variant-specific): i) 129 the 2nd wave (predominantly the ancestral and Iota variants), from August 31, 2020 (i.e., the 130 first day of wastewater surveillance) through June 26, 2021; ii) the Delta wave (predominantly 131 the Delta variant), from June 27, 2021 (i.e., the first week the share of Delta exceeding 50% 132 among the sequenced specimens) through December 4, 2021; and iii) the Omicron period 133 (predominantly Omicron subvariants and included multiple Omicron-subvariant waves), from 134 December 5, 2021 (i.e., the first week the share of Omicron BA.1 exceeding 25% among the 135 sequenced samples; note that we used a lower threshold here given the milder severity of 136 Omicron BA.115 and thus likely fewer infections detected and sequenced) though August 29, 137 2023 (i.e., the last wastewater sample during the study period). 138 139 SARS-CoV-2 viral load in wastewater represents the pooled fecal shedding of the virus by the 140 population, whereas the infection prevalence represents the proportion of population actively 141 infectious at a given time (i.e., the source of the viral shedding after a potential time-lag). Thus, 142 to estimate the viral shedding rate for each variant (per the time period defined above), we 143 used a linear regression model, accounting for circulating variants and spatial variations by 144 sewershed, per Eq. 1: 145 146 𝑉𝐿!∈{!}%& = 𝛽' + 𝛽(𝑆𝑒𝑤𝑒𝑟𝑠ℎ𝑒𝑑 + 𝛽)𝐼! + 𝛽*𝑃𝑒𝑟𝑖𝑜𝑑! + 𝛽+𝐼!𝑃𝑒𝑟𝑖𝑜𝑑! (Eq. 1) 147 148 where, 𝑉𝐿!∈{!}%& is the wastewater SARS-CoV-2 viral load measured during time-window {𝑡}, 149 adjusted by a time-lag or lead of 𝜏 days (see details below); Sewershed is a categorical variable 150 (Sewershed = one of the 14 sewersheds in the city) to account for spatial variation; 𝐼! is the 151 infection prevalence estimated for week-t; and 𝑃𝑒𝑟𝑖𝑜𝑑! represents three epidemic time 152 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 5 periods as defined above, included as a proxy for circulating variants during week-t (Period = 2nd 153 wave, Delta wave, or Omicron period, as defined above). The interaction term 𝐼!𝑃𝑒𝑟𝑖𝑜𝑑! is 154 included to account for potential nonadditive interaction of the two variables (here, in essence, 155 to allow different viral shedding rates by variant). Per Eq. 1, we computed the estimates of 156 fecal viral shedding rate for each variant using the coefficients 𝛽) and 𝛽+. 157 158 Given the different surveillance schedules and likely difference between fecal and respiratory 159 viral shedding, we tested three sliding time-windows (i.e., {𝑡} in Eq. 1) for matching the 160 wastewater measurements (twice per week, representing fecal shedding) with the infection 161 prevalence estimates (weekly estimates, representing respiratory shedding); specifically, we 162 averaged 2, 3, or 4 consecutive wastewater samples, corresponding to roughly a 1-, 1.5-, or 2-163 week window, respectively, depending on the wastewater sampling schedule and time-164 adjustment used. For each time-window {𝑡}, to identify a proper time-adjustment (𝜏 in Eq. 1), 165 we tested five settings to capture the time difference from becoming infectious via respiratory 166 shedding to fecal shedding per the population-level surveillance data: 167 i) a 6- to 7-day lead, i.e., the wastewater samples included in time-window {𝑡} started from 168 the 1st sample taken the week before the infection prevalence estimate; note the 1st 169 sample was taken on Sunday (corresponding to a maximum of 7-day lead) or Monday 170 (corresponding to a maximum of 6-day lead); 171 ii) a 4- to 5-day lead, i.e., the wastewater samples included in time-window {𝑡} started from 172 the 2nd sample taken the week before the infection prevalence estimate; note the 2nd 173 sample was taken on Tuesday (corresponding to a maximum of 5-day lead) or Wednesday 174 (corresponding to a maximum of 4-day lead); 175 iii) concurrent (no time-difference, 𝜏=0), i.e., the wastewater samples included in time-176 window {𝑡} started from the 1st sample taken the week of the infection prevalence 177 estimate; 178 iv) a 2- to 3-day lag, i.e., the wastewater samples included in time-window {𝑡} started from 179 the 2nd sample taken the week of the infection prevalence estimate (a Tuesday sample 180 corresponded to a 2-day lag and a Wednesday sample corresponded to a 3-day lag); and 181 v) a 7- to 8-day lag, i.e., the wastewater samples included in time-window {𝑡} started from 182 the 1st sample taken the week after the infection prevalence estimate (a Sunday sample 183 corresponded to a 7-day lag and a Monday sample corresponded to a 8-day lag). 184 185 In addition, we performed variant/period-specific analyses for each of the three time-periods 186 defined above, using a similar model form as Eq. 1 but without the terms related to time-period 187 (𝑃𝑒𝑟𝑖𝑜𝑑!). Since the Omicron period included multiple Omicron-subvariant waves, we also 188 performed stratified analyses for the Omicron BA.1 wave (December 5, 2021, through March 4, 189 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 6 2022, i.e., the last week the share of Omicron BA.1 exceeding 50%) and for weeks from March 190 5, 2022 onwards, separately. 191 192 Identifying timings with higher-than-expected transmission 193 Visual inspection of the wastewater data showed there were occasional spikes in SARS-CoV-2 194 viral load, potentially due to intensified transmission. Due to the temporal dynamics and 195 sampling noise, it is challenging to distinguish such potential instances (i.e., a true signal) based 196 on the wastewater data alone. Thus, here we used the infection prevalence estimates, which 197 had accounted for the main underlying transmission factors, to construct the expected SARS-198 CoV-2 viral load for comparison. Specifically, we first computed the daily infection prevalence 199 using the weekly estimates with a spline smoothing function, and then used those as inputs in 200 Eq. 1 to compute the expected daily SARS-CoV-2 viral load (median and 90% confidence 201 intervals [CI]). Given the large variance in both the infection prevalence estimates and SARS-202 CoV-2 viral load data, we deemed a wastewater measurement higher than expected, if it was 203 higher than the 95th percentile (i.e., the upper bound of the 90% CI) of the expected SARS-CoV-204 2 viral load. 205 206 To examine the timing with higher-than-expected SARS-CoV-2 viral load, we grouped the 207 identified anomaly dates into 10-day bins based on calendar time, i.e., the 1st (early), 2nd (mid), 208 and last (late) 10 days of each month; for example, January 1 of 2021, January 5 of 2022, and 209 January 10 of 2023 would all be grouped as “early-January”. This allows recurrent and/or 210 seasonal events to be grouped in the same or nearby bins. To test whether the identified 211 anomalies occurred at random (e.g., due to noise in the data), we further performed a 212 bootstrap test with 5000 random samples. For each bootstrapping set, we randomly sampled 213 nanomaly (i.e., the number of identified anomalies) dates from the wastewater measurements (N 214 = 3794), and then grouped the dates into the same 10-day bins as done for the identified 215 anomalies. We then pooled the 5000 sets together to construct the distribution of each timing. 216 For example, for early-January (the first 10-day calendar bin), with n1, n2, …, and n5000 of the 217 dates falling in that bin for the 5000 sets, the likelihood of having k (k= 0, …, nanomaly, i.e., from 218 none to all) anomalies during early-January would be: 219 𝑃(𝑥 = 𝑘) = ,-./01 34 ,!56 7.3,8 !90 :''' /33!;17<<=,8 ;7.<>0; :''' ; 220 and the likelihood of having k or more anomalies during early-January would be: 221 𝑃(𝑥 ≥ 𝑘) = ,-./01 34 ,!?6 7.3,8 !90 :''' /33!;17<<=,8 ;7.<>0; :''' . 222 223 Sensitivity Analyses 224 In a first sensitivity analysis, we only included SARS-CoV-2 viral load measured by RT-qPCR (i.e., 225 August 31, 2020– April 11, 2023), to examine if the viral shedding rate estimates were affected 226 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 7 by converting RT-dPCR measurements to RT-qPCR equivalents due to changes in testing assays. 227 In a second sensitivity analysis, we included all SARS-CoV-2 viral load measurements but used 228 the sewershed-specific conversion ratios instead of the citywide conversion ratio for all 229 sewersheds. 230 231

232 General trends in measured wastewater SARS-CoV-2 viral load and estimated infection 233 prevalence. 234 During the 3-year study period (August 31, 2020 – August 29, 2023), trends in wastewater 235 SARS-CoV-2 viral load were generally consistent with the trends in estimated infection 236 prevalence (Fig 1). Across the 14 NYC sewersheds (Fig 1A), wastewater SARS-CoV-2 viral load 237 tended to rise and fall around the same time (Fig 1B-D and Figs S1-3), indicating epidemic 238 waves were highly synchronized across the city. However, the magnitudes of wastewater SARS-239 CoV-2 viral load and infection prevalence estimates both varied substantially over time and 240 across sewersheds and may not scale consistently. For example, even though certain 241 sewersheds tended to detect higher SARS-CoV-2 viral loads than others, the rankings changed 242 across different waves (see Fig S1-3, ranked by average viral load). Similar spatial heterogeneity 243 was apparent in the estimated infection prevalence and the discrepancies between wastewater 244 SARS-CoV-2 viral load and estimated infection prevalence appeared larger during the 2nd wave 245 (Fig S1). Such spatial heterogeneity is not unexpected, since several factors such as RNA 246 degradation16 and dilution,16 and the contribution of infected animals17 could all vary by 247 sewershed, and ultimately affect wastewater measurements. In addition, uncertainty in the 248 infection prevalence estimate could also vary by sewershed (e.g., larger uncertainty for those 249 with smaller population size; see, e.g., the wider uncertainty bounds for Oakwood Beach 250 sewershed in Fig S1). 251 252 Estimated fecal viral shedding patterns. 253 Using the wastewater SARS-CoV-2 viral load data and infection prevalence estimates (i.e., 254 source of fecal viral shedding), we examined fecal viral shedding patterns over the entire study 255 period or stratified by variant/time-period, separately. The estimates are generally consistent 256 (Table 1). Among the 15 combinations of fecal viral shedding time-differences and durations 257 tested, the main model (including all waves) identified concurrent infection prevalence 258 estimates (i.e., no time-difference between becoming infectious via respiratory shedding and 259 fecal shedding) and SARS-CoV-2 viral load aggregated over 3 wastewater samples (2 during the 260 same week and 1 in the beginning of the following week, i.e., a 8- to 9- day-time-interval) as the 261 best setting (highest adjusted R-squared; Fig 2A). Using a 4-5-day-lead and aggregation over 4 262 wastewater samples (i.e., one sample 4-5 days before, two during, and one 1-2 days after the 263 infection prevalence estimate) led to the second-best model fit (Fig 2A, 2nd dark bar), and was 264 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 8 the best setting for the Delta wave and weeks after the BA.1 wave in the stratified analysis 265 (Table 1). Model fit degraded quickly with changing time-differences (both leads and lags), 266 when only 2 (roughly a 1-week duration) or 3 (roughly a 1.5-week duration) wastewater 267 samples were included. 268 269 Estimated fecal viral shedding rate was highest for infections during the 2nd wave (mostly due 270 to the ancestral and Iota variants), at 1.44 (95% CI: 1.35 – 1.53) billion RNA copies by RT-qPCR in 271 wastewater per day per infectious person [or 24 (95% CI: 22.49 - 25.51) billion RNA copies per 272 RT-dPCR conversion; see Methods]. The estimated rate decreased by ~20% during the 273 subsequent Delta wave and by 50-60% during the Omicron period (Table 1). Importantly, we 274 note the lower estimates for Delta and Omicron may in part reflect reduced shedding among 275 vaccinees and recoverees, in addition to variant-specific variations. 276 277 Timings with higher-than-expected transmission 278 The infection prevalence estimates have accounted for the general transmission factors (here, 279 population-level mobility, vaccinations, variant-specific properties, and seasonal risk of 280 infection; see Methods), but may have not fully accounted for activities such as increased 281 gatherings during certain time-periods that might increase transmission. In contrast, 282 wastewater SARS-CoV-2 viral load is a composite measure of all transmission events. Thus, 283 comparison of these two quantities could support identification of such events. Following a 284 procedure designed per this mechanism (see Methods), we identified 198 occasions where 285 wastewater SARS-CoV-2 viral loads exceeded the expected levels in any of the 14 sewersheds 286 (see Fig 3A for identified anomalies for Newtown Creek, the sewershed with the largest service 287 population). These anomalies disproportionally occurred during late January, late April - early 288 May, early August, and mid-November to late-December (Fig 3B), with frequencies exceeding 289 the expectation assuming random occurrence. Among the 5000 bootstrapping sets, none had 290 as many or more anomalies as observed in early August or late November (P = 0) and less than 291 5% had as many or more anomalies as observed in late January, late April, early May, late 292 November, and late December (P < 0.05 for all these calendar bins; Table S2). 293 294 Sensitivity analyses 295

from the two sensitivity analyses are consistent with the main analysis. In the 1st 296 sensitivity analysis (i.e., using SARS-CoV-2 viral load measured by RT-qPCR alone, for a shorter 297 study period from 8/31/20 to 4/11/23), similar fecal viral shedding rates were estimated (Table 298 S3). The 2nd sensitivity analysis (using sewershed-specific conversion ratios to convert the RT-299 dPCR measurements after 4/11/23, same study period as the main analysis) estimated the 300 same fecal viral shedding rates as the main analysis, and identified three additional anomalies 301 (i.e., 1 in late-January, 1 in mid-August, and 1 in early-July). 302 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 9 303

304 Wastewater surveillance can be a valuable tool for monitoring SARS-CoV-2 circulation in the 305 population. To further develop understanding of wastewater surveillance data, we have 306 combined independent model-inference estimates of infection prevalence to characterize fecal 307 viral shedding patterns for multiple major SARS-CoV-2 variants. Using NYC as an example, we 308 have also demonstrated that these data and estimates can support the identification of time 309 periods with potentially intensified transmission. 310 311 Importantly, here we examined how wastewater SARS-CoV-2 viral shedding is related to 312 estimated infection prevalence, rather than health outcomes as in previous studies. This choice 313 could lead to certain apparent differences but has several advantages. First, previous studies 314 have reported detection of SARS-CoV-2 in wastewater (e.g., an increase in viral load, or the 315 presence of a new variant) several days ahead of the detection of cases, hospitalizations, or 316 deaths, due to the delay in health outcomes.18-20 Here, infection prevalence is a proxy of 317 respiratory tract shedding, which could precede fecal viral shedding. Indeed, we found 318 wastewater SARS-CoV-2 viral loads measured round 1.5 week of the infection prevalence 319 estimate afforded the best model fit (Table 1). This finding suggests that fecal viral shedding 320 likely starts around the same time an individual becomes infectious and lasts slightly longer 321 than the shedding from respiratory tract. Consistent with our finding, studies have shown that 322 fecal SARS-CoV-2 RNA was detectable in patients within the first week of COVID-19 diagnosis 323 and could last longer than respiratory shedding.16,21 324 325 Second, case-, hospitalization-, or death-to-wastewater-viral-load ratio could decrease with 326 increased vaccinations/reinfections and circulation of milder variants (e.g., Omicron) due to 327 reduced severity or testing, and such reductions have been reported.19,22 In contrast, as our 328 estimates included all infections regardless of severity or testing, the infection-to-wastewater-329 viral-load ratio (roughly, the inverse of estimated per-infection fecal viral shedding rate; Table 330 1) is relatively stable during each variant wave. For example, the wave-stratified analysis 331 estimated similar fecal viral shedding rates for the BA.1 wave and weeks after BA.1 (Table 1). 332 Importantly, using the infection prevalence estimates, we are able to quantify the fecal viral 333 shedding rate for each major SARS-CoV-2 variant/time-period (Table 1). These estimates can be 334 used to account for changes in underlying infection rate during this study period (e.g. 335 converting wastewater SARS-CoV-2 viral loads to infection prevalence per Table 1) and help 336 examine changes in COVID-19 severity (e.g., changes in hospitalization rate and infection-337 fatality risk). Such wastewater-viral-load and infection-based estimates may be more accurate 338 than case-based measures, which are subject to test-seeking biases. 339 340 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 10 Third, previous studies have measured viral loads in clinical samples from the respiratory tract. 341 Based on the reported cycle threshold (CT) values, the respiratory tract viral load was higher in 342 Delta and Omicron infections than the ancestral variant,23-28 consistent with the higher 343 infectiousness of these variants of concern. In contrast, fecal viral shedding is not a main mode 344 of transmission,29,30 and here using variant circulation time-period as a proxy, we estimate that 345 the fecal viral shedding rate was the highest for the ancestral/Iota variants, followed by Delta 346 (~20% lower), and then Omicron (~50-60% lower; Table 1). Early studies of ancestral SARS-CoV-347 2 infections found that patients with diarrhea shed more viruses than patients without diarrhea 348 (see, e.g., a review in ref. 16), suggesting fecal viral shedding may be associated with diarrhea. In 349 addition, studies found that vaccinations reduced the number of diarrhea episodes,31 and that 350 rates of diarrhea were highest among patients infected with the ancestral SARS-CoV-2, followed 351 by patients infected with Delta and then Omicron.32,33 Our estimates are consistent with the 352 fecal viral shedding studies,16,31-33 and support a difference in viral load between SARS-CoV-2 353 fecal shedding and respiratory tract shedding, in addition to the timing difference noted above. 354 355 In addition to characterizing SARS-CoV-2 fecal viral shedding pattern, we are also able to 356 identify certain time-periods with intensified transmission. In NYC, analysis based on calendar 357 timing showed likely intensified transmission during late-November through December (Fig 3B). 358 Increased transmission also occurred during early August and late January. It is possible that 359 other factors such as travel, holidays, or specific COVID-19 sub-variants could help explain these 360 periods of intensified transmission, but further investigation is needed to determine their 361 impact. 362 363 Lastly, we note several limitations. First, given the biweekly sampling dates for wastewater and 364 weekly estimates for infection prevalence, we were unable to test finer time-differences and 365 durations when examining SARS-CoV-2 fecal shedding pattern. Second, the estimates here were 366 based on population data and thus represent an average of all individuals undergoing different 367 disease stages in the population. As such, the estimated fecal shedding duration may be shorter 368 than that reported in studies based on individual patient data (e.g., days or weeks after 369 respiratory tract samples became negative16). Third, our infection prevalence estimates have 370 accounted for the main transmission factors, through the information encapsulated in the 371 COVID-19 case, ED visit, and mortality data used for model estimation. Thus, the expected 372 SARS-CoV-2 viral load constructed using these estimates and in turn the identified anomalies 373 are both conservative estimates and may have missed additional anomalies. In addition, 374 wastewater collected from sewersheds may represent individuals who are residents of NYC as 375 well as outside NYC, while infection prevalence estimates are based on NYC residents only. 376 377 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 11 In summary, we have characterized the fecal viral shedding pattern of SARS-CoV-2 in 378 wastewater in New York City from 2020-2023. These estimates can be used to account for 379 changes in underlying infection rate and help more accurately quantify changes in COVID-19 380 transmission and severity over time. We have also demonstrated that wastewater surveillance 381 data combined with model-inference estimates can support the identification of time-periods 382 that potentially intensify transmission. Additional studies are needed to better understand 383 these periods and the potential to mitigate SARS-Cov-2 transmission. 384 385

386 This study was supported by the National Institute of Allergy and Infectious Diseases (AI175747) 387 and Centers for Disease Control and Prevention (CDC) and the Council of State and Territorial 388 Epidemiologists (CSTE; contract no.: NU38OT00297). The authors thank Lauren Firestein for 389 overseeing the data use agreement and facilitating data sharing for this project; Ramona Lall for 390 providing syndromic surveillance emergency department data; Wenhui Li for providing COVID-391 19-associated mortality data; Iris Cheng for providing immunization data; Jubayer Ahmed, 392 Nelson De La Cruz, and Brandon Nguyen for managing and providing wastewater data; the NYC 393 DOHMH Respiratory Pathogens data team for overarching data management and provision of 394 data for this project; and Shama Ahuja, Sharon Greene, Scott Harper, Elizabeth Luoma, Ulrike 395 Siemetzki-Kapoor, Celia Quinn, and Faten Taki for their input on this manuscript. 396 397 Author contributions: WY designed the study, performed the analysis, and wrote the first draft; 398 EO, AO, and EAW oversaw provision of the SARS-CoV-2 wastewater surveillance data; HP and EL 399 oversaw provision of the COVID-19 case and emergency department visit data. All authors 400 contributed to the final draft. 401 402 Conflict of interest: 403 The authors declare that they have no conflict of interest. 404 405

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(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 14 Table 1. Estimated patterns of SARS-CoV-2 fecal viral shedding in wastewater. Note in this study, SARS-CoV-2 RNA concentration was measured using quantitative reverse transcription polymerase chain reaction (RT-qPCR) assays during August 31, 2020, through April 11, 2023, and reverse transcription digital PCR (RT-dPCR) assays from November 1, 2022, through August 29, 2023. Based on samples tested using both assays, the RT-qPCR and RT-dPCR measures differed by a factor of 16.7. We used this conversion factor to convert measures from the two

and provide estimates for RT-qPCR and RT-dPCR assays, separately. model wave shedding rate (billion copies per day per infectious person, mean and 95% Confidence interval) lag (days) number of samples adjusted R2 Include all variant waves 2nd wave (08/31/20- 06/26/21) 1.44 (1.35, 1.53) per qPCR; 24.0 (22.49, 25.51) per dPCRa 0 3 0.84 Delta wave (06/27/21- 12/04/21) 1.13 (0.86, 1.4) per qPCR; 18.9 (14.45, 23.35) per dPCRa 0 3 0.84 Omicron period (12/05/21-08/29/23) 0.6 (0.59, 0.61) per qPCR; 9.96 (9.76, 10.16) per dPCRb 0 3 0.84 Stratified by wave/ period 2nd wave (08/31/20- 06/26/21) 1.44 (1.37, 1.52) per qPCR; 24.07 (22.85, 25.28) per dPCRa 0 4 0.74 Delta wave (06/27/21- 12/04/21) 1.09 (0.91, 1.27) per qPCR; 18.14 (15.21, 21.08) per dPCRa -5 4 0.37 Omicron period (12/05/21-08/29/23) 0.6 (0.59, 0.61) per qPCR; 9.98 (9.76, 10.2) per dPCRb 0 3 0.86 Omicron BA.1 (12/05/21-03/05/22) 0.59 (0.56, 0.61) per qPCR 9.78 (9.32, 10.23) per dPCRa 0 3 0.91 After BA.1 (03/06/22- 08/29/23) 0.72 (0.7, 0.75) per qPCR; 12.11 (11.72, 12.5) per dPCRb -5 4 0.78 aRT-qPCR assays were used to measure SARS-CoV-2 RNA concentration during this period; the dPCR estimates were made by conversion (see Methods); bRT-qPCR assays were used to measure SARS-CoV-2 RNA concentration through April 11, 2023 and RT-dPCR assays were used afterwards; conversion was used to obtain estimates for the entire period (see Methods). All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 15 Figures Fig 1. Trends in wastewater SARS-CoV-2 viral load in the 14 sewersheds in NYC. The map in (A) shows 14 sewersheds (delineated by color) and 42 United Hospital Fund neighborhoods (delineated by lines). Dots show the per-capita SARS-CoV-2 viral load in each of the 14 sewersheds (right y-axis, in million copies per day per population by RT-qPCR; color coded per the legend) during the 2nd wave (B), Delta wave (C), and Omicron period (D). For comparison, we overlay the citywide estimates of infection prevalence (left y-axis; blue line = median; darker blue area = 50% CI and lighter blue area = 95% CI). All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 16 Fig 2. Model fit. (A) shows model performance based on the adjusted R-squared (higher number represents better performance) for different settings of time from becoming infectious to fecal viral shedding and time window of the wastewater samples are aggregated. The asterisk indicates the setting with the highest adjusted R-squared (i.e., best-fit model). (B) shows the model fit compared to the data. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 17 Fig 3. Identified time-periods with intensified transmission in any of 14 NYC sewersheds. (A) shows an example of the measured (dots) and expected wastewater SARS-CoV-2 viral load (blue line = median; darker blue area = 50% CI and lighter blue area = 95% CI), and identified anomalies with SARS-CoV-2 viral load exceeding the expected (red labels). (B) shows the distribution of all identified anomalies. Asterisks indicate time-periods that exceeded the expected wastewater SARS-CoV-2 viral load with a frequency higher than chance assuming random occurrence per a bootstrapping test (* for P < 0.1 and ** for P < 0.05). Spatial distribution of the anomalies is shown in Fig S4. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 18 Supplement Tables and Figures Table S1. Summary statistics for the wastewater samples statistics value n percentage Total No. of samples - 3794 100% Day of sampling Sunday 1834 48.3% Day of sampling Tuesday 1736 45.8% Day of sampling Wednesday 126 3.3% Day of sampling Monday 98 2.6% Sampling frequency 2 per week 1610 73.7% Sampling frequency 1 per week 574 26.3% Calendar time late-Aug 168 4.4% Calendar time early-Aug 140 3.7% Calendar time late-Jan 140 3.7% Calendar time mid-Jul 140 3.7% Calendar time mid-Sep 140 3.7% Calendar time late-May 126 3.3% Calendar time mid-Dec 126 3.3% Calendar time mid-Oct 126 3.3% Calendar time early-Jan 112 3% Calendar time early-May 112 3% Calendar time early-Nov 112 3% Calendar time late-Jul 112 3% Calendar time late-Jun 112 3% Calendar time late-Mar 112 3% Calendar time late-Nov 112 3% Calendar time late-Sep 112 3% Calendar time mid-Apr 112 3% Calendar time mid-Jun 112 3% Calendar time early-Apr 98 2.6% Calendar time early-Dec 98 2.6% Calendar time early-Jun 98 2.6% Calendar time late-Feb 98 2.6% Calendar time late-Oct 98 2.6% Calendar time mid-Aug 98 2.6% Calendar time mid-Jan 98 2.6% Calendar time mid-Mar 98 2.6% Calendar time mid-May 98 2.6% Calendar time early-Feb 84 2.2% Calendar time early-Mar 84 2.2% Calendar time late-Apr 84 2.2% Calendar time mid-Nov 84 2.2% Calendar time early-Jul 70 1.8% Calendar time early-Oct 70 1.8% All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 19 Calendar time early-Sep 70 1.8% Calendar time late-Dec 70 1.8% Calendar time mid-Feb 70 1.8% All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 20 Table S2. Likelihood of having the same or higher frequency of anomalies during each calendar time as the observed, based on bootstrapping. timing number anomalies during this time total number of anomalies observed frequency P-value: probability based on bootstrapping early-Aug 24 198 0.1212 0.0000 late-Jan 19 198 0.0960 0.0002 late-Dec 11 198 0.0556 0.0008 late-Nov 12 198 0.0606 0.0124 early-May 12 198 0.0606 0.0138 late-Apr 9 198 0.0455 0.0286 mid-Nov 8 198 0.0404 0.0680 late-Jun 9 198 0.0455 0.1292 late-Aug 9 198 0.0455 0.5122 mid-Jun 6 198 0.0303 0.5364 late-Mar 6 198 0.0303 0.5380 late-Feb 5 198 0.0253 0.5850 early-Apr 5 198 0.0253 0.5860 mid-Jul 7 198 0.0354 0.6134 mid-Dec 6 198 0.0303 0.6546 late-Jul 5 198 0.0253 0.7060 mid-Feb 3 198 0.0152 0.7068 early-Oct 3 198 0.0152 0.7148 early-Dec 4 198 0.0202 0.7582 early-Jan 4 198 0.0202 0.8450 mid-Apr 4 198 0.0202 0.8490 early-Jun 3 198 0.0152 0.8900 early-Nov 3 198 0.0152 0.9384 early-Mar 2 198 0.0101 0.9386 late-May 3 198 0.0152 0.9634 mid-Oct 3 198 0.0152 0.9634 mid-Jan 2 198 0.0101 0.9686 mid-Aug 2 198 0.0101 0.9720 early-Jul 1 198 0.0051 0.9772 mid-Sep 3 198 0.0152 0.9788 late-Sep 2 198 0.0101 0.9830 early-Feb 1 198 0.0051 0.9888 late-Oct 1 198 0.0051 0.9924 mid-Mar 1 198 0.0051 0.9956 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 21 Table S3. Estimated patterns of SARS-CoV-2 fecal viral shedding in wastewater, using RT-qPCR data alone through April 11, 2023. All estimates here are based on RT-qPCR measures. model wave shedding rate (billion copies per day per infectious person, mean and 95% confidence interval) lag (days) number of samples adjusted R2 Include all variant waves 2nd wave (08/31/20- 06/26/21) 1.45 (1.36, 1.54) 0 3 0.84 Delta wave (06/27/21- 12/04/21) 1.16 (0.88, 1.44) 0 3 0.84 Omicron period (12/05/21-04/11/23) 0.59 (0.58, 0.6) 0 3 0.84 Stratified by wave/ period 2nd wave (08/31/20- 06/26/21) 1.44 (1.37, 1.52) 0 4 0.74 Delta wave (06/27/21- 12/04/21) 1.09 (0.91, 1.27) -5 4 0.37 Omicron period (12/05/21-04/11/23) 0.59 (0.58, 0.61) 0 3 0.86 Omicron BA.1 (12/05/21-03/05/22) 0.59 (0.56, 0.61) 0 3 0.91 After BA.1 (03/06/22- 04/11/23) 0.72 (0.69, 0.75) -5 4 0.76 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 22 Fig S1. Per-capita wastewater SARS-CoV-2 viral load in each of the 14 NYC sewersheds during the 2nd wave. Dots showed aggregated wastewater SARS-CoV-2 viral load for each week. For comparison, we overlay the corresponding estimates of infection prevalence (blue line = median; darker blue area = 50% CI and lighter blue area = 95% CI). The sewersheds are ordered by the mean viral load during this time period (from the highest to the lowest). All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 23 Fig S2. Per-capita wastewater SARS-CoV-2 viral load in each of the 14 NYC sewersheds during the Delta wave. Dots showed aggregated wastewater SARS-CoV-2 viral load for each week. For comparison, we overlay the corresponding estimates of infection prevalence (blue line = median; darker blue area = 50% CI and lighter blue area = 95% CI). The sewersheds are ordered by the mean viral load during this time period (from the highest to the lowest). All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 24 Fig S3. Per-capita wastewater SARS-CoV-2 viral load in each of the 14 NYC sewersheds during the Omicron period. Dots showed aggregated wastewater SARS-CoV-2 viral load for each week. For comparison, we overlay the corresponding estimates of infection prevalence (blue line = median; darker blue area = 50% CI and lighter blue area = 95% CI). The sewersheds are ordered by the mean viral load during this time period (from the highest to the lowest). All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint 25 Fig S4. The total number of anomalies identified for each sewershed during the study period (n; see numbers in the map; darker colors indicate larger numbers). All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprintthis version posted August 3, 2024. ; https://doi.org/10.1101/2024.08.02.24311410doi: medRxiv preprint