Wastewater sampling, SARS-CoV-2 detection, and quantification

Untreated (raw) wastewater samples were collected prospectively from the drainage systems in the Nagpur district of Maharashtra, India, during the second wave of the COVID-19 pandemic from January 31st to July 9th, 2021. Nagpur district is divided into 13 rural talukas and the Nagpur urban region, governed under Nagpur Municipal Corporation (NMC). The Nagpur urban region is further divided into ten municipality zones with each further divided into municipal wards. Individual grab samples were collected from sewers within each urban municipality zone as well as open drains/groundwater sources of rural talukas representing the complete Nagpur district, as illustrated in Fig 1 right panel (urban taluka) and left panel (rural talukas in relation to urban taluka). Each sample (1000 mL) was collected in sterile wide-mouth autoclaved plastic bottles sealed in plastic bags and transported under a cold chain at 4°C within 18–24 hours. All sampling was conducted during the morning hours between 07:30 to midday using appropriate COVID-19 precautions. Samples were transported to Dr B. Lal Institute of Biotechnology, Jaipur, for pre-processing, RNA extraction and SARS-CoV-2 detection by RT-qPCR, as previously described [28]. No specific permits were required for this study for field site access. We have only informed NMC regarding this study. Detailed sample processing methodology is presented in S1 Appendix.

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Fig 1. Map of Nagpur district (study area) showing sampling locations for wastewater study.

Each dot represents a location of wastewater collection in Nagpur urban and rural talukas. The map was created using the ArcGIS 10.4 version from a GIS student. Source of map used “ESRI, Maxar, Earthstar, Geographics and the GIS user Community”.

https://doi.org/10.1371/journal.pone.0303529.g001

Data collection for COVID-19 cases and environmental characteristics

Demographics, and climatic factors including the presence of rainfall, air temperature, and relative humidity, along with GPS coordinates, were also recorded by field workers based at the Central Indian Institute of Medical Sciences (CIIMS) and assisted by the NMC. Daily laboratory-confirmed COVID-19 positive cases and deaths between 1st February and 30th July 2021 within the ten different municipality zones in urban Nagpur were obtained from the health department of the NMC.

Epidemiological modelling and estimation of infected individuals

We based our study of the transmission of SARS-CoV-2 infections on a deterministic ordinary differential equation (ODE) disease model in which the individuals in an entire population can present in five mutually exclusive compartments according to their disease status and other measures. These compartments are susceptible, exposed, infectious, confirmed positive and recovered, abbreviated as the SEIPR model, which is a modification of the SEIR model and that described by Acheampong et al. [20], where additional compartments were given to reflect the Ghanaian environment [20]. We denote the proportion of susceptible individuals by S(t), the proportion of asymptomatic infected individuals by E(t), the proportion of symptomatic infectious individuals by I(t), the proportion of confirmed positive infectious individuals by P(t) and the proportion of recovered individuals by R(t). It must be noted here that individuals in the confirmed-positive class are carriers of the SARS-CoV-2 virus who have had clinical confirmation of this status. However, individuals in an infectious class show clear symptoms and have high infectivity but have not yet been clinically confirmed positive. Notably, as highlighted by Acheampong et al. [20], individuals classified within the infectious class I(t) represent an abstract concept that is often unmeasurable. This underscores the significance of introducing a compartment like the confirmed-positive class P(t), enabling comparison with the actual reported cases within the population. The SEIPR model was applied to study COVID-19 dynamics in ten zones within Nagpur’s urban area. Each zone operates independently. Disease transmission is driven by a force of infection (λ), determined by the effective contact rate per day (β₁) and reductions in transmissibility for exposed (β₂) and confirmed positive (β₃) individuals. Disease-induced deaths are assumed to only occur within the infectious (I) and confirmed positive (P) compartments. The model describes how individuals transition between these compartments based on rates of entry and exit, such as exposure to infection (λ), testing (ω), recovery (ρ), and disease-induced death (d). Recovery of individuals (R) depends on recovery rates from the confirmed positive (P) and symptomatic infectious (I) compartments (ρP(t) and ργP(t), respectively). Additionally, no natural birth and death are considered, and their exclusion may be justified given the assumed short-term focus on COVID-19 dynamics and the neglect of population-level demographic changes, simplifying the model for this specific epidemiological context. These underlying assumptions guide the model’s representation of COVID-19 transmission and progression in the Nagpur urban area. The transmission dynamics of the SARS-CoV-2 infections are described by the five nonlinear systems of ODEs shown in Eq (1): (1) with X₀ = [S₀, E₀, I₀, P₀, R₀]^T is initial number of individuals, t denotes time, X_t = [S, E, I, P, R]^T denotes the number of individuals in these compartments at time t, T denotes matrix transposition, denotes the parameter vector and f(⋅) denotes the nonlinear relationship describing the state variable (see S2 Appendix for detailed mathematical derivation of SEIPR model). The force of infection used in this model is λ = β₁(β₂E(t) + β₃P(t) + I(t)), with β₁ denoting the effective contact rate per day, and β₂ and β₃ respectively accounts for the reduction in disease transmissibility of exposed and confirmed positive individuals. A value of epidemiological importance in infectious disease modelling is the basic reproductive number, which in this study is referred to as the number of secondary SARS-CoV-2 infections generated by a single active SARS-CoV-2 infected individual during the entire infectious period [29]. It is given by the Eq (2): (2) where i_T = δ + γρ + d and p_T = ρ + d. The effective reproductive number (R₀) is made up of contributions from secondary infections from the exposed class generated by asymptomatic individuals (first term), confirmed positive individuals’ class (second term), and the infected (symptomatic) class (third term). S⁰ is the proportion of the population that is initially susceptible. Other parameters in Eq (2) are defined as follows: ϵ denotes the incubation period, σ denotes the progression rate of susceptible individuals to the confirmed positive class via testing per day, δ denotes the progression rate of infectious individuals to the confirmed positive class via testing per day, d denotes the disease-induced death rate per day, ω denotes the fraction of exposed individuals that transient to confirmed positive class, γ denotes the fraction of infectious individual that transient to recovery class and ρ denotes the recovery rate of confirmed positive individuals per day. In this study, the nonlinear least squares scheme is used to estimate the parameters involved in the calculation of R₀. The model fitting was first carried out for each zone to obtain zone-specific parameter estimates and secondly for all zones put together as a single unit. Further details about model derivation and parameter estimation can be found in the Supplementary (see S2 Appendix for a full description of model parameters and variables). For this study, the number of SARS-CoV-2 infected individuals within urban Nagpur was estimated using the modelling approach proposed by McMahon et al. [14], which combines our disease model (SEIPR) to the viral concentration estimations [14]. As already mentioned, there are ten zones within urban Nagpur and each zone is modelled independently. Based on McMahon et al. [14], using our SEIPR disease model, the number of newly detected infections on the jth day is modelled as a Poisson process with rate parameter Nβ₁[β₂E(j) + β₃P(j) + I(j)], which is expressed as Eq (3): (3) where N is the total number of individuals that reside in the zone of the drainage systems. The viral load being introduced into the drainage system at time t is (4) where V_ij(t) is the number of copies of SARS-CoV-2 RNA entering the drainage systems via faeces of the ith individual of out the who became infected on day j is modelled according to the Eq (5) (5) for (infected individuals) and j = 1, 2, …, J (days). In Eq (5), ϑ_ij denotes the log₁₀ g of faeces per ith individual who gets infected on the jth day, modelled as a normal distribution with mean of 2.41 and standard deviation of 0.25 per data from lower-middle-income countries [15], ϕ_ij denotes the log₁₀ maximum RNA copies per g being of faeces shed 5 days after being infected, modelled as a normal distribution with mean of 7.6 and standard deviation of 0.8 [14] and ψ_ij denotes the log₁₀ RNA copies per g being of faeces shed 25 days after being infected, modelled as a normal distribution with mean of 3.5 and standard deviation of 0.4. To correlate the viral load being introduced into the drainage system to that being measured, McMahon et al. [14] proposed the Eq (6) called the downstream RNA copies measured, V(t, τ) to account for the time-dependent degradation in the drainage system, (6) where τ is the time elapsed between waste excretion and arrival at the drainage systems modelled as a uniform distribution from τ = 1h to τ = 1.5h, V₀(t) is the viral load introduced into the drainage system modelled by Eq (4), τ* is the temperature-dependent half-life modelled according to Eq (7) (7) where T is the current temperature of the drainage system, modelled as a uniform distribution from T = 19°C to T = 31°C, is the half-life (h) at an ambient temperature of T₀, modelled as a normal distribution with a means of 3 h and 30 h respectively, with standard deviations of 0.7 and 1.5, Q₀ is the temperature-dependent rate of change, modelled as a normal distribution with a mean of 5.5 and standard deviation of 0.5. The choice of distributions and parameter ranges were informed by previous research as well as actual measurements or observations of SARS-CoV-2 in wastewater to inform their selection of parameter ranges for the Monte Carlo simulation. All the above information was used to simulate the viral load of infected individuals generated by our proposed disease model via 500 Monte Carlo simulations, since beyond this number of Monte-Carlo simulations, the value of the simulated RNA copies does not significantly change. Importantly, the number of Monte Carlo samples depends on various factors including the complexity of the model, which is the case here.

Finally, McMahon et al. [14] proposed a model for estimating the number of infected individuals in each day given the measured RNA copies quantified from samples collected from the drainage systems and is given by the Eq (8) (8) where Q denotes the average flow rate at the drainage system in L per day, V denotes the virus copies per L, A is the rate of faeces production per person in g per day with A = 2 × 128 for developing countries [15], and B denotes the maximum rate at which the virus is shed in RNA copies for g of faeces per day with B = 10^7.6 × 128 [14]. In this study, Q was calculated as a point estimate using the product of the at-home population in the catchment of each zone, and the observed average per capita wastewater rate, which we assumed to be either 120 or 135 L/person/day (based on the Ministry of Housing and Urban affairs suggested benchmark for urban water supply).

Statistical analyses

Due to the lack of COVID-19 incidence data for the rural areas in Nagpur, we explored catchment areas within urban Nagpur by zones to gain insight into the concentration of SARS-CoV-2 viral load in the collected wastewater samples. Based on the model parameter estimates, the distribution of the RNA copies per day existing in the drainage systems by zones was estimated, where we used the 2011 population census data as an estimate for each population zone. Of note, the use of the Monte Carlo simulation approach can help estimate uncertainties and account for variability in the data, which provides some indication of potential uncertainty and variability in prevalence estimates despite the limitations of using this census data, making the margin of error not a major problem. Data on continuous variables are presented as median with interquartile ranges (IQR). Categorical variables are shown as counts and percentages in parentheses. The normality of data was assessed using the Shapiro-Wilk test. Student’s t-test was used for comparing variables which were normally distributed. Mann-Whitney test was used when the normality assumption was violated. The Fisher’s exact test and Proportion tests were applied to compare categorical variables. All p− values and confidence intervals (CIs) are two-sided and a p–value of < 0.05 is considered statistically significant. All modelling studies were performed using MATLAB, 2022^o and Rstudio 2022.07.1+554 software on macOS Monterey Version 12.5.1 MacBook Pro (13-inch, M2, 2022).

Ethical approvals

The study was approved by the Faculty of Medicine and Health Sciences Research Ethics Committee at the University of Nottingham (REC No. 131–1120), and the institutional ethics committees of the Central India Institute of Medical Sciences, Nagpuadjust width. Lal Institute of Biotechnology, Jaipur.

SARS-CoV-2 detection in wastewater samples

A total of 983 wastewater samples were analysed, of which 743 (75.6%) were from the urban and 240 (24.4%) from the rural parts of Nagpur district. Overall, 43.7% (95% confidence interval 40.1, 47.4) of wastewater samples in the urban and 30.4% (95% confidence interval 24.66, 36.66), in rural areas tested positive for SARS-CoV-2 (p < 0.001); RT-PCR results revealed significantly higher SARS-CoV-2 viral copies per L in urban zones (p < 0.001). The median temperature of urban Nagpur was 29.0°C, (IQR: 25.75–31.00) and was significantly lower than that of the rural areas (31°C, (IQR: 29–33); p < 0.001). The median humidity was also significantly higher in urban (38%, IQR: 26–53) vs rural (32%, IQR: 22–50) Nagpur (p < 0.001) at the time of sampling (Table 1).

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Table 1. Summary of climatic characteristics and RT-PCR results of wastewater samples collected within urban and rural Nagpur catchment.

https://doi.org/10.1371/journal.pone.0303529.t001

Of the 10 sampled urban catchment zones, two zones (7 and 9) yielded no SARS-CoV-2 RNA detection but did record the highest humidity levels (Table 2). Only 3 zones experienced rainfall; zones 1 and 8, where rainfall was recorded 1 day prior to sample collection, and zone 7, where sample collection took place during heavy rainfall. It is likely that these rainfall events would also contribute to diluting the sewage prior to sampling. Moreover, rainfall events would also contribute to more rapid and effective flushing out within the sewers. In zone 9, wastewater sampling followed the conclusion of the main COVID-19 infection wave, and therefore, the cases of COVID-19 at the time of sampling were expected to be very low, as illustrated in S1A–S1E Fig (S3 Appendix). The distributions of the continuous data and their normality plots by individual zones are shown in S3A–S3D Fig (S3 Appendix). The respective significance p– values shown on the plots are all less than 0.05, indicating the data is not normally distributed. S1 Table (S3 Appendix) summarises the demographic characteristics of the catchment zones where wastewater samples were collected. The demographic and environmental characteristics by zones are presented in S2 and S3 Tables (S3 Appendix).

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Table 2. SARS-CoV-2 RT-PCR results detected per unit of time and detected viral load results of the wastewater samples with climatic and population census information for each Nagpur catchment zone.

https://doi.org/10.1371/journal.pone.0303529.t002

Estimation of infected individuals

We fitted our proposed SEIPR model to the reported confirmed COVID-19 positive cases and deaths in urban Nagpur via the nonlinear least squares method. Fig 2(a) and 2(b) shows the representative model fit for the SEIPR model to data for all 10 Nagpur catchment zones combined as a single unit for the period of March to July 2021.

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Fig 2. Considering a half-life of 30 h.

Model fit to the proportion of the population. (a) (left) confirmed positive COVID-19 infections and (b) (right) confirmed deaths from COVID-19 infections for all zones as a single unit. (c) SEIPR model (1) prediction for the mass rate of SARS-CoV-2 RNA in wastewater over time via Monte-Carlo simulation represented by black points. (d) Zoomed-in plot of predicted number of active COVID-19 cases versus SARS-CoV-2 RNA mass rate with individual Monte-Carlo simulations represented by grey points, where 75% CI and 95% CI are denoted by the green and red solid lines, respectively. Coloured datapoints denote the measured RNA mass rates and estimated infectious individuals based on Eq (8) as presented in Table 4, respectively for an assumed average per capita wastewater rates of 120 L per person per day (red solid points) and 135 L per person per day (blue solid points) for all zones as a single unit.

https://doi.org/10.1371/journal.pone.0303529.g002

Both plots show an increase in confirmed positive cases and deaths up to the first 50 days and then a decrease over the last 100 days. Thus, the SEIPR model predicts a decrease in the susceptible population as individuals become exposed, infected, confirmed positive, and then either recover or are confirmed dead. The remaining model fittings for the urban zones are presented in S5 Fig (S3 Appendix). The corresponding model parameter estimates for the respective catchment zones and R₀ as calculated using clinical incident data only, are presented in Table 3. Each urban catchment zone exhibited different effective contact rates, β₁, signifying different contact patterns. In addition, the basic reproduction number, R₀ is different for each catchment zone with the highest R₀ observed in zone 9 and lowest in zone 2. All the zones have an R₀ greater than 1 except for zone 2. All the zones, when combined as a single unit, gave an R₀ of 1.11. Linear regression analysis to investigate the variation in R₀ and β₁ between the zones revealed a statistically significant positive correlation between R₀ and population density [R² = 0.40, p–value = 0.05] whilst for effective contact rate (β₁) and R₀, there was a negative correlation with humidity [R² = 0.49, p–value = 0.02]. No significant relationship was seen between temperature and R₀ or β₁ (S8 Fig in (S3 Appendix)).

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Table 3. Model parameter estimates and basic reproduction number (R₀) for each catchment zone of Nagpur district.

https://doi.org/10.1371/journal.pone.0303529.t003

Taking all zones combined, Fig 2(c) depicts the distribution of the RNA copies per day, similar to the dynamics observed by McMahon et al. [14].

There is a positive correlation between the concentration of SARS-CoV-2 RNA in the wastewater and the number of confirmed positive individuals as well as recovering individuals and shedding rates. There was a different association between the measured viral RNA concentration and the confirmed positive cases during the earlier stages (January and February 2021) of the wastewater sampling, with high wastewater viral concentrations but low numbers of confirmed positive individuals. Therefore, zone 1 and zone 2 were not considered for the viral RNA load SEIPR modelling (see S2 Fig in the S3 Appendix). Fig 2(d) depicts a zoomed-in plot of the predicted number of active COVID-19 cases versus SARS-CoV-2 RNA mass rate with individual Monte-Carlo simulations represented by grey points. The measured RNA mass rates and estimated number of infectious individuals based on Eq (8) are denoted by the coloured datapoints and fall within the 95% CI denoted by the red solid lines. In this particular study, the sensitivity of the model regarding the viral half-life at an ambient temperature of the drainage is explored. It is observed that for a viral half-life of 3 h, the association between the mass rate of gene copies detected in wastewater and the confirmed positive cases is affected (see S7A Fig in the S3 Appendix). Data for all other catchment zones are given in the S6-S8 Figs (S3 Appendix)) except for zone 7 and zone 9, where wastewater samples from these zones tested negative (Table 2). Furthermore, all plots depicting the entire Monte-Carlo simulations of the predicted number of active COVID-19 cases versus SARS-CoV-2 RNA mass rate are presented in S9 and S10 Figs (S3 Appendix).

Table 4 presents the SARS-CoV-2 RNA wastewater concentrations in samples taken from all the catchment zones considered as a single unit between 1st March and 27th of May, 2021. Results of the other catchment zones are presented in the Supplementary. Each row corresponds to a specific date on which the wastewater samples were taken. The “RNA (copy per L)” column provides the concentration of SARS-CoV-2 genetic material in wastewater, providing insights into the prevalence of the virus in the population. The following columns, titled “Option 1” and “Option 2”, present two separate scenarios based on different wastewater rates per capita (120 L/person/day for Alternative 1). and 135 L/person/day for ‘Option 2). These scenarios are important for estimating the number of infected individuals using RNA concentrations as an indicator of viral activity. Calculated RNA levels are provided for each scenario, showing the rate of change in viral RNA levels per day. In addition, the “Estimated number of infected individuals” column quantifies the number of potential COVID-19 cases inferred from RNA levels, providing a way to assess community spread of the virus.

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Table 4. SARS-CoV-2 RNA concentrations, estimated RNA rate and number of infected individuals from all the catchment zones as a single unit.

https://doi.org/10.1371/journal.pone.0303529.t004

Direct comparison with clinically observed cases is presented in the column “Clinically observed COVID-19 positive cases”, showing actual confirmed positive cases reported by clinical diagnoses. This actual data is used as a benchmark to evaluate the validity of the estimates obtained through wastewater analysis. Side-by-side estimating infected individuals with observed clinical cases helps assess the reliability of using wastewater RNA concentrations as a predictor to monitor trends in COVID-19. Overall, this table highlights the importance of leveraging wastewater-based epidemiology to better understand viral prevalence. The ratio of unreported to reported cases under options 1 and 2 are respectively computed to be 12.42 (95% CI 9.04, 15.15) and 13.97 (95% CI (10.17, 17.0).