The value of environmental surveillance for pandemic response

Abstract

Environmental sampling surveillance (ESS) technologies, such as wastewater genomic surveillance and air sensors, have been increasingly adopted during the COVID-19 pandemic to provide valuable information for public health response. However, ESS coverage is not universal, and public health decision-makers need support to choose whether and how to expand and sustain ESS efforts. This paper introduces a model and approach to quantify the value of ESS systems that provide leading epidemiological indicators for pandemic response. Using the COVID-19 pandemic as a base-case scenario, we quantify the value of ESS systems in the first year of a new pandemic and demonstrate how the value of ESS systems depends on biological and societal parameters. Under baseline assumptions, an ESS system that provides a 5-day early warning relative to syndromic surveillance could reduce deaths from 149 (95% prediction interval: 136–169) to 134 (124–144) per 100,000 population during the first year of a new COVID-19-like pandemic, resulting in a net monetary benefit of $1,450 ($609-$2,740) per person. The system’s value is higher for more transmissible and deadly pathogens but hinges on the effectiveness of public health interventions. Our findings also suggest that ESS systems would provide net-positive benefits even if they were permanently maintained and pathogens like SARS-Cov-2 emerged once every century or less frequently. Our results can be used to prioritize pathogens for ESS, decide whether and how to expand systems to currently uncovered populations, and determine how to scale surveillance systems’ coverage over time.

Introduction

Novel environmental sampling surveillance (ESS) technologies (e.g., wastewater genomic surveillance and air sensors) were increasingly adopted in the US and globally during the COVID-19 pandemic¹. For example, wastewater-based surveillance (WBS) systems were used to provide an early warning system for pandemic response², examine trends in disease prevalence and project future hospitalizations³, and detect new SARS-CoV-2 variants⁴, and this information was used to estimate the latent number of infections in COVID-19 transmission models⁵. However, ESS capabilities are nascent, and the coverage of wastewater surveillance is uneven worldwide⁶.

ESS may strengthen pandemic response in several ways. The first benefit is that ESS systems do not require testing of symptomatic individuals, reducing the lag from disease transmission to detection of pathogens that are shed by humans into the environment. WBS data provide a 4- to 10-day earlier warning of the start of COVID-19 waves than case data⁷ and predict hospitalizations before case data⁸. This is a crucial aspect of ESS technologies, as they do not depend on access to healthcare, care-seeking, clinical decision-making, or testing availability. Secondly, ESS systems can monitor many communities simultaneously without requiring additional outreach or resources.

Although ESS systems may help improve pandemic response, and qualitative frameworks to guide the adoption of ESS systems exist^9,10, their net benefits to society have yet to be quantified. Quantifying the value of ESS systems in monetary terms can be helpful for several reasons: (i) it helps policymakers justify the decision to maintain those systems; (ii) it may help policymakers choose when to expand sampling, where to sample, and which pathogens require sampling, (iii) it requires one to explicitly articulate how the system will be used for decision-making, and iv) it also offers a clear decision rule to determine when ESS should trigger public health action: decision-makers should only act on early warning if the value of ESS information is positive – that is, using the system to make a decision produces more societal benefits than costs.

This paper introduces a parsimonious simulation model and approach to quantify the value that ESS systems produce through better-targeted nonpharmaceutical interventions (NPIs). Our model depicts a network of jurisdictions, each making sequential decisions to introduce or remove public health interventions using the information provided by their surveillance systems. In this paper, ESS systems are assumed to improve only two parameters relative to syndromic surveillance systems alone: (i) they reduce the lag with each public health decision makers observe disease incidence, and (ii) they reduce the case ascertainment bias inherent to the surveillance system. Hence, they change the information available for decision-making but do not reduce uncertainty about disease parameters. In our framework, “value” is defined as the net monetary benefit (NMB) of the system – i.e., the benefits afforded by the system (value of lives saved and disease averted with better-targeted interventions) minus the costs of operating the system and of public health interventions triggered by the ESS. We parameterize our model with disease characteristics and economic parameters reflecting the first year of the COVID-19 pandemic and explore scenarios to clarify the conditions under which ESS systems provide the most or the least NMB.

Results

Value of ESS under baseline assumptions

Assuming no NPIs are implemented (“No NPIs” scenario), a new COVID-19-like pandemic would cause substantial harm, causing 550 (525–574) deaths per 100,000 people [mean (95% prediction interval)] over a one-year timeframe (Table 1). In the absence of any behavioral change, the unmitigated pandemic would infect 92.6 (90.7–94.3) percent of the population, costing 4,760 (4,660-4,840) dollars per person due to illness, and 62,700 (59,800 − 65,400) dollars due to deaths. The total health cost would be projected at 67,400 (64,500 − 70,300) dollars per person.

If policymakers followed our base-case NPI policy, the death toll of the pandemic would be reduced from 550 (525–574) to 149 (136–169) deaths per 100,000 population if a baseline syndromic surveillance system is used to trigger NPIs (NPIs w/o ESS scenario). Such an achievement would involve a substantial public health effort. Under baseline assumptions, this effort would require 327 (323–330) days of public health interventions, of which 121 (86.3–153) days are spent under the most restrictive policy intervention level. We project this effort to cost on the order of 13,500 (12,700 − 14,200) dollars per person. Based on those assumptions, the total cost of the pandemic would be reduced from 67,400 (64,500 − 70,300) to 32,000 (29,600 − 35,100) dollars per person.

Table 1 Base-case results.

Under baseline assumptions, ESS systems provide net-positive value to society because they enhance the effectiveness of NPIs (i.e., preventing illness and death) more than they increase the costs of additional interventions introduced due to the early warning (Fig. 1). Even an early warning system that provides only a 2-day early warning relative to a conventional pandemic response system (NPI + 2-day ESS scenario) is projected to reduce the pandemic death toll from 149 (136–169) to 141 (129–159) deaths per 100,000 population. Health benefits increase if the system can provide earlier warning, but we observe a saturation effect beyond 5 days of early warning. A system that provides a 5-day early warning (NPIs + 5-day ESS scenario) would be projected to result in 134 (124–144) deaths per 100,000 population, and a 10-day early warning would result in 133 (123–145) deaths per 100,000 people.

Fig. 1

Health costs, economic costs, and net benefit of alternative surveillance systems. Notes: Dots indicate posterior mean estimates and lines cover 95% of the posterior predictive distribution. Purple scenarios are the ones in which the ESS is used, whereas the blue scenario represents a case with conventional (i.e., syndromic) surveillance. This plot shows that better surveillance improves health outcomes reducing health costs, but also increases NPI costs per person. On balance, total costs (Health + NPI cost) are reduced with improved surveillance, resulting in a positive net-monetary benefit under baseline assumptions - even for a system that only provides a 2-day earlier warning.

Early warning would result in earlier public health intervention, increasing the number of days under NPIs from 327 (323–330) to 331 (330–336) days for a system providing a 5-day early warning signal. That said, the number of days at the maximum intervention level (i.e., a “lockdown”) was projected to decrease with the early warning system in our base-case scenario, as earlier action prevented surges from reaching alarming levels that prompted blunt interventions. For example, a system that provided a 5-day early warning reduced the number of days under the maximum intervention level from 121 (86.3–153) to 89 (49–135) days. Still, the net effect of the ESS was to marginally increase NPI intervention costs, from 13,500 (12,700 − 14,200) to 13,800 (13,100 − 14,700) dollars per person, assuming a 5-day early warning system. Hence, the early warning system reduced the total pandemic costs from 32,000 (29,600 − 35,100) to 30,500 (28,600 − 32,500) dollars per person. The difference between the two costs is the net monetary benefit of the system, which is estimated at 1,450 (609-2,740) dollars per person in the first year of the pandemic.

Sensitivity analyses

Epidemiological parameters

A pathogen that is 50% more transmissible than wild-type SARS-Cov-2 would pose a greater challenge for pandemic response, causing 335 (293–390) deaths per 100,000 people even if mitigated with the same NPI policy considered in our base-case scenario (Supplementary Table S1, Supplementary Figure S1). Such a pandemic would cause a substantial societal cost of 55,200 (50,500 − 60,900) dollars per person. In those conditions, the ESS would be particularly valuable, reducing the pandemic’s death toll to 293 (240–347) per 100,000 people and would provide an NMB of 3,850 (2,250-5,620) dollars per person. Conversely, a pathogen that is 50% less transmissible than SARS-Cov-2 would result in a lower death toll of 46.9 (36.8–58.8) without the ESS system, reducing the net monetary benefit of the system to 73.1 (-379-512) dollars per person. The value of the ESS system also depends on the infection fatality rate of the pathogen, but the net benefit of the ESS would be positive even for a pathogen that is half as deadly as SARS-Cov-2. All else being equal, the ESS would still yield an NMB of 599 (107-1,250) dollars per person in a pandemic caused by a pathogen that is 50% less deadly than SARS-Cov-2 and would yield 2,310 (1,120-4,240) dollars per person in responding to a pathogen that is 50% more deadly than COVID-19.

NPI costs

NPI costs had a moderate effect on the value of surveillance systems. If NPI costs were 50% higher than assumed in our base-case scenario (i.e., if achieving the same NPI effectiveness were to cost 50% more than assumed under our base-case scenario), then the total cost of the pandemic would increase from 32,000 (29,600 − 35,100) to 38,700 (36,000–42,100) dollars per person with the conventional surveillance system. (Supplementary Figure S1, Supplementary Table S1). Despite that increase, the NMB of the system would only be reduced from 1,450 (609-2,740) to 1,260 (441-2,470) dollars per person because the ESS system only marginally increased the duration of interventions.

Policy lags and stringency

Although longer NPI decision and implementation lags have an overall negative effect on the total costs of the pandemic, longer decision lags would increase the net benefit of ESS systems for pandemic response because they would “buy time” for decision-makers to react. Our base-case scenario assumes that decision-makers take one week to decide and implement NPIs. If policymakers took two weeks to implement interventions, the total pandemic cost would increase from 32,000 (29,600 − 35,100) to 34,100 (31,000–37,900) dollars per person, assuming conventional surveillance. The early warning system effectively helps to compensate decision lags, reducing total costs to 31,600 (29,500 − 33,900) dollars per person, yielding an NMB of 2,440 (1,270-4,220) relative to conventional surveillance. Conversely, in contexts where NPI implementation is swift (i.e., decisions are made within 3 days), the NMB of ESS would be lower but still positive at 925 (249-1,750) dollars per person.

Policy stringency (i.e., how stringent the case thresholds are used to introduce or remove interventions) has a similar effect on the value of ESS relative to decision lags - the ESS provides the most value under the least desirable conditions for disease prevention. In a context where decision-makers are 50% more stringent than in our base-case assumptions (i.e., their case thresholds are half of its base-case), society can avert a substantial number of deaths, reducing mortality from 149 (136–169) to 84.6 (76.1–96.9) deaths per 100,000 population without the ESS. In that scenario, the ESS yields 1,010 (460-1,720) dollars per person of net benefit since more deaths would already be prevented through more stringent NPIs. Conversely, if policymakers were more lenient, policy choices would change the system’s overall outcomes and result in a higher value of the enhanced surveillance system.

NPI effectiveness

NPI effectiveness (i.e., the % reduction in infectious contacts induced by NPIs) had a non-linear and non-monotonic effect on the value of surveillance systems to pandemic response (Fig. 2). If NPI effectiveness is 0%, an improved surveillance system has no value, as expected. The value of the enhanced surveillance system increases slowly with NPI effectiveness for maximum NPI effectiveness below around 50% and peaks when the maximum NPI effectiveness reaches 60%, enough to reduce the baseline R0 of 2.5 below 1 at the pandemic onset. The value of the ESS appeared to peak at a maximum NPI effectiveness value of around 1 − 1/R0 across the scenarios we investigated. Beyond that point, increases in NPI effectiveness resulted in lower total pandemic costs, but the value of the surveillance system started to decrease.

Minimum pandemic frequency for net-positive benefit

Under base-case assumptions, an ESS system that costs 10 dollars per person per year would provide net-positive benefits even if a SARS-Cov-2-like pandemic only occurred every 145 (61–274) years. Even a pandemic caused by a pathogen 50% less deadly than SARS-Cov-2 would only need to happen every 60 (11–130) years to justify the permanent operation of an ESS system with the characteristics assumed in this study. We also explored the minimum pandemic frequency for net-positive benefit considering ESS systems that cost in the range of $5 to $100 per person per year across all scenarios (Supplementary Figure S2).

Fig. 2

ESS net monetary benefit as a function of R0 and NPI effectiveness. Notes: Dots indicate posterior mean estimates and lines cover 95% of the posterior predictive distribution. ESS net monetary benefit is a non-monotonic function of R0 (represented in different colors) and the maximum NPI effectiveness (i.e., the fraction of infectious contacts reduced by the maximum intervention level). The vertical dashed line represents the NPI effectiveness in our base-case scenario (see Supplementary Methods). Lines represent the average net monetary benefit of a 5-day early warning system, and shaded areas represent 95% prediction intervals computed over 1,000 stochastic replications.

Discussion

ESS systems could yield thousands of dollars of value per person in a new pandemic

Lipsitch et al.¹¹ identify a set of pandemic response decisions for which surveillance data is required, outlining the link between surveillance needs and decision-making. However, there is a lack of research that quantifies the societal benefit of improvements in surveillance in monetary terms. This paper helps to close this gap by quantifying the net-benefits of ESS adoption via better, more timely non-pharmaceutical interventions (decisions 2, 3 and 7 in Lipsitch et al.¹¹). Our simulation results demonstrate that ESS systems that provide early warning could provide benefits valued at low to mid-thousand dollars per person by helping prevent deaths and illness in a new pandemic (see Supplementary Table S1). Baseline results estimate these benefits to be $1,450 per person. The system’s value results from earlier and improved alignment of interventions with the timing of epidemic progression. Benefits could be as high as $3,850 per person for more transmissible pathogens and are greater when diseases are more severe, interventions are less costly, and decision lags are longer. The relationships between the benefits of ESS and these parameters provide additional insights for taking advantage of ESS. These results corroborate the proposition that better surveillance can meaningfully improve decision-making during an ongoing pandemic.

ESS helps to mitigate worst-case pandemic scenarios

The worse the pandemic, the more value early warning systems have. Hence, more transmissible and deadly pathogens should be prioritized for ESS. This is an intuitive yet important finding. The value of ESS increases linearly with mortality but non-linearly with transmissibility.

ESS helps mitigate the effects of poor adherence to NPIs and decision lags

Implementing earlier and more targeted interventions can provide policymakers with flexibility. Public health outcomes are better when interventions are implemented decisively, stringent, and adhered to by the public. Our results demonstrate that decision-making supported by ESS reduces the costs that accrue when adherence to NPIs drops or decision-making must be slower or favors less stringent interventions. As a result, ESS may afford policymakers options to better manage the net costs of a pandemic when managing uncertainty and competing demands of a pandemic.

The benefits of ESS may outweigh their costs even if a pathogen as severe and transmissible as SARS-CoV-2 were to emerge only once a century (or even less frequently)

Our results describe benefits from ESS that are only realized when a pandemic occurs, but severe pandemics for which these benefits materialize may occur infrequently. Although the magnitude of benefits presented in these results vary, the net benefits of a permanent ESS system that costs 10 dollars per person may be justified even if a SARS-Cov-2-like pandemic were to occur as infrequently as once every 150 years. Experiences with ESS during the COVID-19 pandemic (i.e., wastewater surveillance) suggest that the implementation costs of the system could be under 5 dollars per person. Hence, this research suggests public health decision-makers have a rationale to install and maintain ESS systems even if a SARS-Cov-2 pandemic were not to happen in the next several decades.

The value of ESS must be evaluated in the context of the costs and benefits of the interventions it triggers

This analysis demonstrates that the value of an ESS is influenced by the characteristics of the disease event, the costs and effectiveness of response options, and how decisions are made to implement interventions. The primary benefit of the ESS is the reduction in deaths caused by a pandemic. The realization of reduced deaths is associated with higher economic costs of interventions. However, ESS can potentially reduce the duration of the most stringent interventions and costs associated with those severe measures that are not captured well in economic terms.

ESS effectiveness is influenced by nucleic acid testing implementation decisions

Our analysis modeled the benefits ESS benefits based on the number of days of early warning provided compared to clinical surveillance signals. In practice, ESS can incorporate a variety of nucleic acid testing approaches, including pathogen-specific tests, pathogen-agnostic tests, and metagenomic analysis using Next Generation Sequencing. These choices affect the ESS system’s performance in multiple ways. Different approaches vary in terms of operational costs and the time required to obtain results. Selection among nucleic acid testing approaches also determines whether the system is limited to known agents, can support monitoring of mutations, or can identify unexpected or novel agents¹². Although we did not model these factors explicitly, our model and framework could be extended to reflect the performance of specific types of testing approaches against different types of pathogens with pandemic potential.

The net monetary benefit of ESS operationalizes existing guidance for adopting and using ESS systems

Qualitative frameworks to guide the adoption of ESS systems (primarily, wastewater-based surveillance) have been put forth by several entities^9,10, and national and international surveillance networks have been set up to organize and sustain ESS activities^13,14. For instance, the National Academy of Sciences published a report containing a framework with criteria for adopting wastewater-based surveillance. The criteria are (i) the public health significance of the threat, (ii) analytical feasibility for wastewater surveillance (i.e., the pathogen is shed by humans and can be detected in the environment), and (iii) the usefulness of community-level wastewater surveillance data to inform public action⁹. Similarly, WHO’s existing guidance also qualitatively articulates the sources of value of ESS systems and the rationale for their implementation¹⁰. The model and framework we propose complement and operationalize those guidance documents by quantifying the societal value of ESS systems.

Recent H5N1 policy responses demonstrate the need for increased ESS capabilities

Recently, highly pathogenic pandemic influenza A (H5N1) has been detected in dairy cows in Texas and infected a worker¹⁵, and was also detectable in wastewater in 19 cities in Texas¹⁶. So far, H5N1 risk is considered “low” for the general public per the CDC, but high levels of H5N1 were found in unpasteurized milk¹⁷. In response, CDC introduced recommendations to reduce exposure to Novel Influenza A viruses¹⁸. Although H5N1 transmission is not human-to-human (so far), the detection in wastewater, clinical detection of one case, and subsequent policy recommendations to suppress transmission to humans¹⁹, demonstrate the full cycle from detection to response we simulate in this study, and show that ESS systems can support policy responses.

Ultimately, the value of early warning hinges on the effectiveness of the public health interventions it informs

Low effectiveness and adherence to NPIs reduce the potential value of the ESS systems. As presented in Fig. 2, the benefits of an ESS increase as NPI effectiveness increases until NPIs can contain the spread of a pandemic. However, the benefits of ESS are non-monotonic with NPI effectiveness. Once NPIs are effective enough to contain a disease outbreak, public health outcomes are improved, but the value of the ESS decreases. This threshold increases as disease transmissibility increases. As a result, the benefits of ESS to policymakers will be greatest for more severe diseases for which NPIs are justified. The benefit of ESS will be lower if the policymakers are not willing to introduce NPI interventions or the public is not willing to comply with them.

Limitations

Future research can address the following limitations of our analysis. First, this paper only simulated the first year of a COVID-19-like pandemic, against which the population has no immunity. Although our approach can be expanded to other pathogens that are detectable in the environment, our results cannot be generalized to any arbitrary pathogen without further tailoring our model to a specific pathogen and population. ESS systems will only be valuable in public health responses against pathogens that are shed in detectable quantities in the environment. We only simulate the benefit of the system before vaccines are expected to be available. We also do not simulate the introduction of new SARS-Cov-2 variant strains or other pathogens with different progression timeframes and different viral shedding dynamics (see Parkins et al.²⁰ Fig. 5B). We also did not assess the system’s value during the endemic phase in this study. However, this model and approach can be extended for those conditions.

We also assumed that ESS systems provide a leading, unbiased, absolute disease incidence estimate, which can be used to trigger public health action as disease incidence surpasses pre-defined thresholds. Implementing such a system might require a substantial effort since the data reported by wastewater surveillance efforts provide RNA concentration estimates, which cannot be easily translated to an absolute disease incidence estimate without further inference. That said, wastewater data is being used by the CDC to forecast hospitalizations³ and has been used by multiple groups to estimate or “nowcast” COVID-19 prevalence^21,22,23,24, demonstrating that ESS systems can provide absolute disease estimates if coupled with proper inference approaches.

Moreover, this paper evaluated the value of ESS by comparing a group of jurisdictions where no jurisdiction has access to ESS versus a group of jurisdictions where all have access to the same ESS and use the system consistently over one year. However, jurisdictions have heterogeneous surveillance systems and may not use them throughout the year. Future work might explore the marginal value of additional surveillance, both in space (i.e., optimizing which jurisdictions and settings should be covered by the system) and in time (i.e., optimizing when to scale up the system). Future work might explore how to tailor and “right-size” surveillance systems for maximum net societal benefit. Finally, this study focused on the benefits of biosurveillance for a new pandemic. If intentionally implemented and flexible, ESS also provides benefits for managing endemic diseases. Future work could explore how options that provide these benefits could be integrated into pandemic ESS.

Conclusion

Environmental sampling surveillance systems could provide substantial public health value in mitigating the impacts of future pandemics. Our results demonstrate that ESS could yield net benefits valued at thousands of dollars per person by enabling timely and better-targeted public health interventions. We also demonstrate that ESS systems can provide net-positive benefits even if a pandemic on the same scale as COVID-19 occurred only once per century or less frequently. However, benefits hinge on the effectiveness of and adherence to non-pharmaceutical interventions. In summary, this analysis suggests that maintaining ESS capabilities is a good investment for pandemic preparedness and offers a framework for evaluating ESS system design and implementation decisions.

Methods

Model

We developed a stochastic metapopulation model that simulates the dynamics of a new pandemic over a set of $\:n\:$jurisdictions (Supplementary Methods). In this paper, jurisdictions are parameterized to have the average population size of a US county (approximately 100,000 individuals), but the approach generalizes to other jurisdiction sizes. The model describes the dynamics of a new pandemic, assumes no pre-existing immunity to the new pathogen, and individuals are assumed to acquire sterilizing immunity after infection that endures the timeframe of the simulation (one year). We parametrize the model to represent the COVID-19 pandemic as a base case (Supplementary Table S2).

Nonpharmaceutical intervention policy

In our framework, the value of better surveillance accrues due to more timely and better-targeted public health non-pharmaceutical interventions (NPIs). Hence, first, we specify an NPI policy (i.e., a method for introducing public health interventions) that reacts to data produced by the surveillance system; then, we specify how better surveillance improves the performance of the NPI policy. Following the structure of tiered COVID-19 public health response plans such as California’s Blueprint for a Safer Economy²⁵, each jurisdiction $\:i\in\:\{1,\dots\:,n\}$ in our model introduces and removes nonpharmaceutical interventions (NPIs) based on estimated disease incidence $\:{\widehat{C}}_{i,t}$ following a pre-specified policy. $\:{x}_{t,i}$ represents an NPI portfolio (i.e., a set of interventions such as mandating mask wearing, restricting in-person gatherings, etc.) in place in jurisdiction $\:i$, where $\:{x}_{t}=0$ implies no intervention, and $\:{x}_{t}={x}_{max}\:$is the highest intervention level. Intermediate levels of intervention are denoted by $\:{x}_{t}\in\:\left\{1,\dots\:,5\right\}$ and represent other policy portfolios with increasing effectiveness and costs. The jurisdiction-level target NPI $\:{x}_{i,t}^{*}$ is calculated as

$$\:\begin{array}{c}{x}_{i,t}^{\text{*}}=\text{min}\left(\frac{{10}^{5}{\:\widehat{C}}_{i,t}}{{N}_{i}{p}_{i}{d}_{i}},\:{x}_{max}\right)\:\:\end{array}$$

(1)

where $\:{N}_{i}$ is the population size in jurisdiction $\:i$, $\:{x}_{max}$ is the maximum intervention level, set to 5 in this analysis, $\:{p}_{i}$ is a case ascertainment bias (i.e., proportion of cases that are identified by surveillance) and $\:{d}_{i}$ is a disease incidence threshold used to increase interventions by one level. Equation 1 results in policy such that the target jurisdiction-level NPI level increases proportionally to disease incidence until it reaches a maximum intervention level $\:{x}_{max}$. Public health decisions take time to be made, interventions take time to be implemented, and policymakers do not update policies instantaneously; hence $\:{x}_{i,t}^{\text{*}}$ is only a target intervention level. We model this process accounting for those decision and implementation lags. In the model, the actual intervention level taking place $\:{\mathbf{L}}_{t,i}\in\:\{\text{0,1},\dots\:,\:{x}_{max}\}\:$ evolves discretely and depends on an exponentially weighted moving average of past surveillance data (Supplementary Methods). In this paper, NPIs’ sole effect is to suppress disease transmission. Further, NPIs are assumed to have a linear effect on reducing infectious contacts, hence the $\:n\:\times\:\:n$ time-varying contact matrix $\:{\varvec{\upbeta\:}}_{t}$ becomes $\:{\varvec{\upbeta\:}}_{t}=\left(1-{{\uptau\:}\mathbf{L}}_{t,i}\right){\varvec{\upbeta\:}}_{b}$, where $\:{\varvec{\upbeta\:}}_{b}$ is the baseline contact matrix in the absence of interventions and $\:{\uptau\:}\in\:(\text{0,1}/{x}_{max})$ is the marginal NPI effectiveness to reduce transmission, and $\:\tau\:{x}_{max}$ is the maximum NPI effectiveness to reduce transmission (i.e., the fraction of infectious contacts reduced when society makes its highest effort to reduce transmission.

This model is purposefully parsimonious, and there are a few advantages to this formulation: (i) Eq. 1 has the same structure of real-world policies adopted during the COVID-19 pandemic, such as the California Blueprint for a Safer Economy²⁵, (ii) Eq. 1 can be a function of any absolute disease incidence measure; hence the public health policy directly becomes itself a function of the surveillance system that produces the disease surveillance signal$\:{\:\widehat{C}}_{i,t}$, (iii) the effectiveness of NPIs to reduce transmission $\:{\uptau\:}$ is a single parameter, which can be traced to the existing literature on NPIs, and (iv) more generally, $\:{x}_{i,t}^{\text{*}}$ can represent any policy that endogenously reacts to the surveillance system in jurisdiction (or sub-population) i. For instance, $\:{x}_{i,t}^{\text{*}}=1$ could include testing of asymptomatic individuals in jurisdiction $\:i$ which in turn reduces their transmissibility.

Surveillance

The estimated disease incidence $\:{\:\widehat{C}}_{i,t}\:$is a stochastic, lagged estimate of the true disease incidence and is affected by the surveillance system in place in each jurisdiction. In this analysis, $\:{\:\widehat{C}}_{i,t}$ evolves daily as a binomial draw:

$$\:\begin{array}{c}{\:\widehat{C}}_{i,t}\:\sim\:B\left(-{\Delta\:}{S}_{i,t-{l}_{i}}\:,\:{p}_{i}\right)\:\end{array}$$

(2)

where $\:-{\Delta\:}S$ is the unobserved daily rate of new infections. A surveillance system’s performance may be parsimoniously represented by two variables: a case ascertainment rate parameter $\:{p}_{i}\in\:\left(\text{0,1}\right)$ and a surveillance lag $\:{l}_{i}$, expressed as the number of days from infection to detection (i.e., the time it takes for an unobserved exposure event that leads to an infection to be reflected in the epidemiological time-series tracked by public health officials). While surveillance systems that rely on clinical testing have lower, and potentially time-varying $\:{p}_{i}$, environmental sampling systems have higher $\:{p}_{i}$ because they detect a disease signal from all the population within the catchment area where the system operates. Hence, our framework estimates the indirect effect that reducing the surveillance lag $\:{l}_{i}$ and increasing the case ascertainment rate $\:{p}_{i}$ has through NPIs. Naturally, Eq. (2) can only appropriately represent environmental surveillance of pathogens that are shed in the environment by humans and that have a peak shedding rate in the acute phase of infection. While both conditions hold for SARs-Cov-2, this is not true for all pathogens.

Population

The model simulates disease spreading through six US interconnected jurisdictions that independently make nonpharmaceutical decisions. Individuals can travel and work across jurisdiction lines, and the six jurisdictions each have a population of 100,000 individuals. Travel rates and inter-jurisdiction mixing rates were set to reflect the level of travel and mixing observed in the US Northeast metropolitan areas (Supplementary Methods). Mortality parameters were chosen to reflect mortality rates observed in the United States during the first year of the COVID-19 pandemic.

Base case scenario

We parameterize our model to represent the COVID-19 pandemic during its first year. Supplementary Table S2 contains parameter values and supporting references. The baseline scenario with conventional surveillance assumes a syndromic surveillance system based upon confirmed case counts. The syndromic surveillance system entails a thirteen-day time span from exposure to the pathogen to case detection by the public health authority. This thirteen-day lag covers the disease incubation phase (6.6 days)²⁶ and testing and reporting delays (6 days)²⁷.

The conventional surveillance system is assumed to have a constant 30% case ascertainment rate in our baseline scenario, which is within the range of case ascertainment rates estimated during the COVID-19 pandemic in the US²⁸. In reality, case ascertainment rates from syndromic surveillance are not constant because they depend on the patients’ choice to get tested. Public health officials countered those biases by attempting to adjust case rates for the test positivity in their decisions²⁵. We do not model those time-varying testing self-selection processes in this paper; hence our assumption that case ascertainment rates are constant favors syndromic surveillance systems and serves as a boundary condition for the purposes of this analysis.

SARS-Cov-2 concentration with wastewater has been shown to lead new COVID-19 cases by 4–10 days²⁹, which is consistent with a 3.5 day incubation period estimate²⁶. Hence, in our base-case scenario, we assume the environmental sampling system can provide absolute, unbiased disease incidence estimates that lead the case counts by 5 days. We explore longer and shorter lead times, from 2 to 10 days in sensitivity analyses. Moreover, this analysis assumed that all the populations within the jurisdictions are covered by the ESS system (or equivalently, that the sampled population is a representative sample of all the population within the jurisdiction). The Supplemental Materials also include detailed information about other model inputs, including the health costs of infection and economic costs of interventions.

Outcomes

The primary health outcome of this study is the average mortality per 100,000 population caused by the infectious pathogen. We also compute the cost of illness due to disease, using COVID-19 parameters as the base-case scenario. We also account for economic costs caused by the nonpharmaceutical interventions introduced (discussed in the Supplementary Methods). All outcomes are computed over one year from the pandemic onset and are averages computed across the jurisdictions in our model. Since the model is stochastic and there is uncertainty in calibrated parameters, we present 95% prediction intervals (calculated with the 2.5% and the 97.5% percentiles) for each outcome and scenario, across 1,000 stochastic replications, each simulated over 1,000 parameter sets obtained via Bayesian calibration (Supplementary Methods). Since we calibrate the model via an approximate Bayesian computation approach³⁰, this interval approximates encompasses 95% of the posterior predictive distribution of model outcomes.

Net monetary benefit

Although ESS systems can improve health outcomes by allowing a swift response to the outbreak, the use of NPIs also carries significant costs, which need to be accounted for in the analysis since a more responsive surveillance system may result in earlier and longer intervention periods and higher intervention costs. As noted above, for this analysis, we use a net monetary benefit measure of value and, therefore, measure the value of ESS systems by computing the health costs of the outbreak $\:{Y}_{h}$, which include the cost of death and illness per person caused by the disease, and the costs of NPIs per person $\:{Y}_{npi}$, which are a function of model parameters $\:\theta\:$, and the surveillance system used in the outbreak (Supplementary Methods). The overall cost of the outbreak per person is the sum of the two costs $\:Y=\:{Y}_{h}+\:{Y}_{npi}$. Let $\:\:\varvec{s}\varvec{{\prime\:}}=({p}_{i},{s}_{i})$ represent the surveillance system configuration of a single jurisdiction and $\:\varvec{s}$ the baseline surveillance system configuration for all jurisdictions. We compute the NMB of ESS systems as

$$NM{B_{s'}}|\theta = E[Y|\theta ,s'] - E[Y|\theta ,s] - Y_s$$

(4)

where $\:{Y}_{s}\:$is the marginal cost of the improved surveillance system $\:{\varvec{s}}^{\varvec{{\prime\:}}}$, and the expectation is taken across stochastic model replications. Also, ESS systems are not assumed to resolve any uncertainty around exogenous parameters in $\:\theta\:$. If that were the case, it would be possible to estimate the value of information (VOI) provided by wastewater surveillance systems using an expected value of partial perfect information method³¹. Nevertheless, if $\:{Y}_{s}$ set to zero, Eq. 4 yields the maximum (per person) dollar value policymakers should be willing to invest in installing and maintaining the surveillance system for a specific outbreak.

Sensitivity analyses

We investigate the sensitivity of the net monetary benefit estimates by varying model parameters one at a time. This exercise aims to assess the robustness of the net monetary benefit of ESS systems to our base-case assumptions. Our sensitivity analysis explored key epidemiological parameters (R0 and the infection fatality rate), economic inputs (NPI costs), the effectiveness of NPI interventions (presented as the percent reduction in infectious contacts induced by the highest intervention level, or $\:\tau\:{x}_{max}$), and the stringency of interventions (parameter $\:{d}_{i}$ in Eq. 1). We also performed a separate sensitivity analysis with a finer-grained experimental design combining three levels of R0 (1.25, 2.5 and 3.75) and twenty evenly spaced NPI effectiveness values exploring the full range of $\:\tau\:{x}_{max}\in\:\left(\text{0,1}\right)$ to shed light on the non-linear relationship between NPI effectiveness and NMB (Fig. 2).

Minimum pandemic frequency for net-positive benefit

Equation 4 computes the NMB of the system conditioning on the occurrence of a pandemic. That is, if a pandemic with characteristics $\:\theta\:$ were to happen, Eq. 4 yields the NMB of the system if it is used with policy parameters also encoded in $\:\theta\:$. It is likely impossible and misleading to assign a defensible joint probability distribution of $\:\theta\:$ for all possible pandemics; hence it is also unfeasible to provide a meaningful expected net monetary benefit estimate that accounts for the likelihood of all such pandemics. Hence, the decision to permanently maintain ESS systems must be made under deep uncertainty³². Still, to provide a straightforward approximation of the likelihood needed of a pandemic such that an ESS system provides net-positive benefit, we simply find $\:{p}_{\theta\:}-\:$the annual probability of $\:\theta\:$ that would render the ESS’ net monetary benefits equal to a set net cost of ESS per person. $\:\frac{1}{{p}_{\theta\:}}\:$is the “frequency” of the pandemic that would make the net benefits of the ESS system equal to the net costs of the ESS system if the system was designed for a single pathogen. The minimum pandemic frequency for a positive expected net benefit $\:1/{p}_{\theta\:}$ can be obtained by dividing the system’s benefits by its annual costs. We present the minimum pandemic frequency for positive net benefit for an ESS system that costs from 5 dollars to 100 US dollars per year per person.