Harnessing the theoretical foundations of the exponential and beta-Poisson dose-response models to quantify parameter uncertainty using Markov Chain Monte Carlo

Two risk assessments: Evaluating the use of indicator HF183 Bacteroides versus pathogen measurements for modelling recreational illness risks in an urban watershed

The purpose of this study was to evaluate the performance of HF183 Bacteroides for estimating pathogen exposures during recreational water activities. We compared the use of Bacteroides-based exposure assessment to exposure assessment that relied on pathogen measurements. We considered two types of recreational water sites: those impacted by combined sewer overflows (CSOs) and those not impacted by CSOs. Samples from CSO-impacted and non-CSO-impacted urban creeks were analysed by quantitative polymerase chain reaction (qPCR) for HF183 Bacteroides and eight human gastrointestinal pathogens. Exposure assessment was conducted two ways for each type of site (CSO-impacted vs. non-CSO impacted): 1) by estimating pathogen concentrations from HF183 Bacteroides concentrations using published ratios of HF183 to pathogens in sewage and 2) by estimating pathogen concentrations from qPCR measurements. QMRA (quantitative microbial risk assessment) was then conducted for swimming, wading, and fishing exposures. Overall, mean risk estimates varied from 0.27 to 53 illnesses per 1,000 recreators depending on exposure assessment, site, activity, and norovirus dose-response model. HF183-based exposure assessment identified CSO-impacted sites as higher risk, and the recommended HF183 risk-based threshold of 525 genomic copies per 100 mL was generally protective of public health at the CSO-impacted sites but was not as protective at the non-CSO-impacted sites. In the context of our urban watershed, HF183-based exposure assessment over- and under-estimated risk relative to exposure assessment based on pathogen measurements, and the etiology of predicted pathogen-specific illnesses differed significantly. Across all sites, the HF183 model overestimated risk for norovirus, adenovirus, and Campylobacter jejuni, and it underestimated risk for E. coli and Cryptosporidium. To our knowledge, this study is the first to directly compare health risk estimates using HF183 and empirical pathogen measurements from the same waterways. Our work highlights the importance of site-specific hazard identification and exposure assessment to decide whether HF183 is applicable for monitoring risk.

Occurrence, transmission and risks assessment of pathogens in aquatic environments accessible to humans

Pathogens are ubiquitously detected in various natural and engineered water systems, posing potential threats to public health. However, it remains unclear which human-accessible waters are hotspots for pathogens, how pathogens transmit to these waters, and what level of health risk associated with pathogens in these environments. This review collaboratively focuses and summarizes the contamination levels of pathogens on the 5 water systems accessible to humans (natural water, drinking water, recreational water, wastewater, and reclaimed water). Then, we showcase the pathways, influencing factors and simulation models of pathogens transmission and survival. Further, we compare the health risk levels of various pathogens through Quantitative Microbial Risk Assessment (QMRA), and assess the limitations of water-associated QMRA application. Pathogen levels in wastewater are consistently higher than in other water systems, with no significant variation for Cryptosporidium spp. among five water systems. Hydraulic conditions primarily govern the transmission of pathogens into human-accessible waters, while environmental factors such as temperature impact pathogens survival. The median and mean values of computed public health risk levels posed by pathogens consistently surpass safety thresholds, particularly in the context of recreational waters. Despite the highest pathogens levels found in wastewater, the calculated health risk is significantly lower than in other water systems. Except pathogens concentration, variables like the exposure mode, extent, and frequency are also crucial factors influencing the public health risk in water systems. This review shares valuable insights to the more accurate assessment and comprehensive management of public health risk in human-accessible water environments.

A beta-Poisson model for infectious disease transmission

Outbreaks of emerging and zoonotic infections represent a substantial threat to human health and well-being. These outbreaks tend to be characterised by highly stochastic transmission dynamics with intense variation in transmission potential between cases. The negative binomial distribution is commonly used as a model for transmission in the early stages of an epidemic as it has a natural interpretation as the convolution of a Poisson contact process and a gamma-distributed infectivity. In this study we expand upon the negative binomial model by introducing a beta-Poisson mixture model in which infectious individuals make contacts at the points of a Poisson process and then transmit infection along these contacts with a beta-distributed probability. We show that the negative binomial distribution is a limit case of this model, as is the zero-inflated Poisson distribution obtained by combining a Poisson-distributed contact process with an additional failure probability. We assess the beta-Poisson model's applicability by fitting it to secondary case distributions (the distribution of the number of subsequent cases generated by a single case) estimated from outbreaks covering a range of pathogens and geographical settings. We find that while the beta-Poisson mixture can achieve a closer to fit to data than the negative binomial distribution, it is consistently outperformed by the negative binomial in terms of Akaike Information Criterion, making it a suboptimal choice on parsimonious grounds. The beta-Poisson performs similarly to the negative binomial model in its ability to capture features of the secondary case distribution such as overdispersion, prevalence of superspreaders, and the probability of a case generating zero subsequent cases. Despite this possible shortcoming, the beta-Poisson distribution may still be of interest in the context of intervention modelling since its structure allows for the simulation of measures which change contact structures while leaving individual-level infectivity unchanged, and vice-versa.

An extended colloid filtration theory for modeling Escherichia coli transport in 3-D fracture networks

Microbial transport in fractured carbonate rock using enhanced solutions is a significant and neglected research topic in the literature. We propose an extended colloid filtration theory (CFT) combined with a particle-tracking following streamlines (PTFS) model for the rapid prediction of breakthrough curves (BTCs) and plumes of pathogens in three-dimensional (3-D) discrete fracture networks (DFNs). We adapted CFT in porous media to pathogen transport in fractures containing Terra Rossa (soil) deposits. As an example of the model capability, a simulation was used to predict the 3-D motion field and Escherichia coli count in groundwater originating from the Forcatella managed aquifer recharge (MAR) Facility (Brindisi, Italy) using a DFN composed of 3,900 fractures. In arid regions, MAR facilities are significant for sustaining basic human needs, such as freshwater supply for drinking and crop production. The Markov chain Monte Carlo (MCMC) technique was applied to E. coli counts in the collected water samples to increase data representativeness. The pathogen transport coefficients were further supported by batch filtration tests carried out in the CNR/IRSA Laboratory (Bari, Italy). The mean E. coli attachment rate coefficient of 0.15 × 10-8 m2 d-1 (sticking efficiency = 1.1 × 10-8 m) resulted in a 2.1 log10 removal in 600 m of reclaimed water filtration. The simulation output visualized the E. coli 3-D pathways in groundwater and the positions of contaminated groundwater spring outflows on Forcatella Beach. The simulation results agreed with the mean MCMC output of E. coli concentrations in bathing water under unperturbed geochemical and environmental flow and transport conditions. However, results indicate that concentrations of pathogenic strains, parasites, and enteric viruses may enter the marine environment of MAR sites during flood periods.

Modeling the Risk of HIV Transfusion Transmission

BACKGROUND

Blood donations are routinely screened for HIV to prevent an infectious unit from being released to the blood supply. Despite improvements to blood screening assays, donations from infected donors remain undetectable during the window period (WP), when the virus has not yet replicated above the lower limit of detection (LOD) of a screening assay. To aid in the quantitative risk assessments of WP donations, a dose-response model describing the probability of transfusion-transmission of HIV over a range of viral RNA copies was developed.

METHODS

An exponential model was chosen based on data fit and parsimony. A data set from a HIV challenge study using a nonhuman primate model and another data set from reported human blood transfusions associated with HIV infected donors were separately fit to the model to generate parameter estimates. A Bayesian framework using No-U-Turn Sampling (NUTS) and Monte Carlo simulations was performed to generate posterior distributions quantifying uncertainty in parameter estimation and model predictions.

RESULTS

The parameters of the exponential model for both nonhuman primate and human data were estimated with a mean (95% credible intervals) of 2.70 × 10 -2 (7.74 × 10 -3 , 6.06 × 10 -2 ) and 7.56 × 10 -4 (3.68 × 10 -4 , 1.31 × 10 -3 ), respectively. The predicted ID 50 for the animal and human models was 26 (12, 90) and 918 (529, 1886) RNA copies transfused, respectively.

CONCLUSION

This dose-response model can be used in a quantitative framework to estimate the probability of transfusion-transmission of HIV through WP donations. These models can be especially informative when assessing risk from blood components with low viral load.

Bioaerosols emission characteristics from wastewater treatment aeration tanks and associated health risk exposure assessment during autumn and winter

Aeration tanks from activated sludge wastewater treatment plants (WWTPs) can release a large amount of bioaerosols that can pose health risks. However, risk characterization of bioaerosols emissions form wastewater treatment plants is currently not systematically carried out and still in its infancy. Therefore, this study investigated emission characteristic of two indicator model bioaerosols Staphylococcus aureus and Escherichia coli, emitted from aeration tanks of a municipal WWTP. Monte Carlo simulation was then used to quantitatively assess microbial risk posed by different aeration modes under optimistic and conservative estimates. Further to this, two different exposure scenarios were considered during 3 days sampling campaign in autumn and winter. Results showed that the bioaerosol concentration from microporous aeration tank (20-262 CFU m^-3) was one order of magnitude lower than rotating disc aeration tank. Average aerosolization rate was 7.5 times higher with mechanical aeration mode. Health risks of exposed populations were 0.4 and 9.6 times higher in winter than in autumn for E. coli and S. aureus bioaerosol, respectively. Health risks of staff members were 10 times higher than academic visitors. Interesting results were observed for academic visitors without personal protective equipment (PPE) respectively exposed to S. aureus and E. coli bioaerosol in autumn and winter: while the derived infection risk met the United States Environmental Protection Agency (U.S. EPA) benchmark under optimistic estimation, the disease risk burden was over the World Health Organization (WHO) benchmark under conservative estimation. These revealed that only satisfying one of the two benchmarks didn't mean absolute acceptable health risk. This study could facilitate the development of better understanding of bioaerosol quantitative assessment of risk characterizations and corresponding appropriate risk control strategies for wastewater utilities.

Quantitative Microbial Risk Assessment for Contaminated Private Wells in the Fractured Dolomite Aquifer of Kewaunee County, Wisconsin

BACKGROUND

Private wells are an important source of drinking water in Kewaunee County, Wisconsin. Due to the region's fractured dolomite aquifer, these wells are vulnerable to contamination by human and zoonotic gastrointestinal pathogens originating from land-applied cattle manure and private septic systems.

OBJECTIVE

We determined the magnitude of the health burden associated with contamination of private wells in Kewaunee County by feces-borne gastrointestinal pathogens.

METHODS

This study used data from a year-long countywide pathogen occurrence study as inputs into a quantitative microbial risk assessment (QMRA) to predict the total cases of acute gastrointestinal illness (AGI) caused by private well contamination in the county. Microbial source tracking was used to associate predicted cases of illness with bovine, human, or unknown fecal sources.

RESULTS

Results suggest that private well contamination could be responsible for as many as 301 AGI cases per year in Kewaunee County, and that 230 and 12 cases per year were associated with a bovine and human fecal source, respectively. Furthermore, Cryptosporidium parvum was predicted to cause 190 cases per year, the most out of all 8 pathogens included in the QMRA.

DISCUSSION

This study has important implications for land use and water resource management in Kewaunee County and informs the public health impacts of consuming drinking water produced in other similarly vulnerable hydrogeological settings. https://doi.org/10.1289/EHP7815.

Antimicrobial Resistance Risk Assessment Models and Database System for Animal-Derived Pathogens

(1) Background: The high use of antibiotics has made the issue of antimicrobial resistance (AMR) increasingly serious, which poses a substantial threat to the health of animals and humans. However, there remains a certain gap in the AMR system and risk assessment models between China and the advanced world level. Therefore, this paper aims to provide advanced means for the monitoring of antibiotic use and AMR data, and take piglets as an example to evaluate the risk and highlight the seriousness of AMR in China. (2) Methods: Based on the principal component analysis method, a drug resistance index model of anti-E. coli drugs was established to evaluate the antibiotic risk status in China. Additionally, based on the second-order Monte Carlo methods, a disease risk assessment model for piglets was established to predict the probability of E. coli disease within 30 days of taking florfenicol. Finally, a browser/server architecture-based visualization database system for animal-derived pathogens was developed. (3) Results: The risk of E. coli in the main area was assessed and Hohhot was the highest risk area in China. Compared with the true disease risk probability of 4.1%, the result of the disease risk assessment model is 7.174%, and the absolute error was 3.074%. Conclusions: Taking E. coli as an example, this paper provides an innovative method for rapid and accurate risk assessment of drug resistance. Additionally, the established system and assessment models have potential value for the monitoring and evaluating AMR, highlight the seriousness of antimicrobial resistance, advocate the prudent use of antibiotics, and ensure the safety of animal-derived foods and human health.

Evaluation of the 50% Infectious Dose of Human Norovirus Cin-2 in Gnotobiotic Pigs: A Comparison of Classical and Contemporary Methods for Endpoint Estimation

Human noroviruses (HuNoVs) are the leading causative agents of epidemic and sporadic acute gastroenteritis that affect people of all ages worldwide. However, very few dose–response studies have been carried out to determine the median infectious dose of HuNoVs. In this study, we evaluated the median infectious dose (ID₅₀) and diarrhea dose (DD₅₀) of the GII.4/2003 variant of HuNoV (Cin-2) in the gnotobiotic pig model of HuNoV infection and disease. Using various mathematical approaches (Reed–Muench, Dragstedt–Behrens, Spearman–Karber, logistic regression, and exponential and approximate beta-Poisson dose–response models), we estimated the ID₅₀ and DD₅₀ to be between 2400–3400 RNA copies, and 21,000–38,000 RNA copies, respectively. Contemporary dose–response models offer greater flexibility and accuracy in estimating ID₅₀. In contrast to classical methods of endpoint estimation, dose–response modelling allows seamless analyses of data that may include inconsistent dilution factors between doses or numbers of subjects per dose group, or small numbers of subjects. Although this investigation is consistent with state-of-the-art ID₅₀ determinations and offers an advancement in clinical data analysis, it is important to underscore that such analyses remain confounded by pathogen aggregation. Regardless, challenging virus strain ID₅₀ determination is crucial for identifying the true infectiousness of HuNoVs and for the accurate evaluation of protective efficacies in pre-clinical studies of therapeutics, vaccines and other prophylactics using this reliable animal model.

Application of QMRA to MAR operations for safe agricultural water reuses in coastal areas

A pathogenic Escherichia coli (E.coli) O157:H7 and O26:H11 dose-response model was set up for a quantitative microbial risk assessment (QMRA) of the waterborne diseases associated with managed aquifer recharge (MAR) practices in semiarid regions. The MAR facility at Forcatella (Southern Italy) was selected for the QMRA application. The target counts of pathogens incidentally exposed to hosts by eating contaminated raw crops or while bathing at beaches of the coastal area were determined by applying the Monte Carlo Markov Chain (MCMC) Bayesian method to the water sampling results. The MCMC provided the most probable pathogen count reaching the target and allowed for the minimization of the number of water samplings, and hence, reducing the associated costs. The sampling stations along the coast were positioned based on the results of a groundwater flow and pathogen transport model, which highlighted the preferential flow pathways of the transported E. coli in the fractured coastal aquifer. QMRA indicated tolerable (<10^-6 DALY) health risks for bathing at beaches and irrigation with wastewater, with 0.4 infectious diseases per year (11.4% probability of occurrence) associated with the reuse of reclaimed water via soil irrigation even though exceeding the E. coli regulation limit of 10 CFU/100 mL by five times. The results show negligible health risk and insignificant impacts on the coastal water quality due to pathogenic E. coli in the wastewater used for MAR. However, droughts and reclaimed water quality can be considered the main issues of MAR practices in semiarid regions suggesting additional reclaimed water treatments and further stress-tests via QMRAs by considering more persistent pathogens than E. coli.

Some aspects of deep-bed filtration dynamics in QMRA for drinking water

Unlike most unit processes in drinking water treatment, the performance of deep-bed filtration processes vary systematically on short time-scales; the particle removal capacity changes with time since the previous backwash, even when the influent water quality is stable. For microorganisms, the removal efficiency may vary by orders of magnitude. In this note, the potential impact of such dynamics on microbial risk estimates is studied, using representative experimental filtration data for viruses and bacteria in conjunction with single-hit dose-response models for microbial infection. Assuming that filtration is the only source of variation in pathogen concentrations on the time-scale of a single filter cycle, it is concluded that such variations are unlikely to substantially affect risk estimates, except possibly in an outbreak situation with extremely high pathogen concentrations; it is generally sufficient to know the mean pathogen concentrations. Future studies should include concurrent variation in the performance of other unit processes and raw water pathogen concentrations. Experimental work should focus on capturing the variation in filtration performance in order to correctly estimate mean removal rates.

Recognizing Structural Nonidentifiability: When Experiments Do Not Provide Information About Important Parameters and Misleading Models Can Still Have Great Fit

In the quest to model various phenomena, the foundational importance of parameter identifiability to sound statistical modeling may be less well appreciated than goodness of fit. Identifiability concerns the quality of objective information in data to facilitate estimation of a parameter, while nonidentifiability means there are parameters in a model about which the data provide little or no information. In purely empirical models where parsimonious good fit is the chief concern, nonidentifiability (or parameter redundancy) implies overparameterization of the model. In contrast, nonidentifiability implies underinformativeness of available data in mechanistically derived models where parameters are interpreted as having strong practical meaning. This study explores illustrative examples of structural nonidentifiability and its implications using mechanistically derived models (for repeated presence/absence analyses and dose-response of Escherichia coli O157:H7 and norovirus) drawn from quantitative microbial risk assessment. Following algebraic proof of nonidentifiability in these examples, profile likelihood analysis and Bayesian Markov Chain Monte Carlo with uniform priors are illustrated as tools to help detect model parameters that are not strongly identifiable. It is shown that identifiability should be considered during experimental design and ethics approval to ensure generated data can yield strong objective information about all mechanistic parameters of interest. When Bayesian methods are applied to a nonidentifiable model, the subjective prior effectively fabricates information about any parameters about which the data carry no objective information. Finally, structural nonidentifiability can lead to spurious models that fit data well but can yield severely flawed inferences and predictions when they are interpreted or used inappropriately.

Listeria monocytogenes risk assessment on cold smoked and salt-cured fishery products in Finland - A repeated exposure model

Listeria monocytogenes causes severe consequences especially for persons belonging to risk groups. Finland is among the countries with highest number of listeriosis cases in the European Union. Although most reported cases appear to be sporadic and the maximum bacterial concentration of 100 cfu/g is not usually exceeded at retail, cold smoked and salt-cured fish products have been noted as those products with great risk especially for the elderly. In order to investigate the listeriosis risk more carefully, an exposure assessment was developed, and laboratory results for cold smoked and salt-cured salmon products were exploited. L. monocytogenes exposure was modeled for consumers in two age groups, the elderly population as a risk group and the working-age population as a reference. Incidence was assessed by estimating bacterial growth in the food products at three temperatures. Bayesian estimation of the risk was based on bacterial occurrence and product consumption data and epidemiological population data. The model builds on a two-state Markov chain describing repeated consumption on consecutive days. The cumulative exposure is probabilistically governed by the daily decreasing likelihood of continued consumption and the increasing bacterial concentrations due to growth. The population risk was then predicted with a Poisson distribution accounting for the daily probabilities of purchasing a contaminated product and the cumulative total probability of infection from its use. According to the model presented in this article, elderly Finns are at a greater risk of acquiring listeriosis than healthy adults. The risk for the elderly does not fully diminish even if the products have been stored at the recommended temperature (between 0 and 3 °C). It can be concluded that the stage after retail, i.e. food handling and storage by consumer or professional kitchens, is essential to protection against listeriosis. The estimation model provides means for assessing the joint impacts of these effects.

Confirming the need for virus disinfection in municipal subsurface drinking water supplies

Enteric viruses pose the greatest acute human health risks associated with subsurface drinking water supplies, yet quantitative risk assessment tools have rarely been used to develop health-based targets for virus treatment in drinking water sourced from these supplies. Such efforts have previously been hampered by a lack of consensus concerning a suitable viral reference pathogen and dose-response model as well as difficulties in quantifying pathogenic viruses in water. A reverse quantitative microbial risk assessment (QMRA) framework and quantitative polymerase chain reaction data for norovirus genogroup I in subsurface drinking water supplies were used herein to evaluate treatment needs for such water supplies. Norovirus was not detected in over 90% of samples, which emphasizes the need to consider the spatially and/or temporally intermittent patterns of enteric pathogen contamination in subsurface water supplies. Collectively, this analysis reinforces existing recommendations that a minimum 4-log treatment goal is needed for enteric viruses in groundwater in absence of well-specific monitoring information. This result is sensitive to the virus dose-response model used as there is approximately a 3-log discrepancy among virus dose-response models in the existing literature. This emphasizes the need to address the uncertainties and lack of consensus related to various QMRA modelling approaches and the analytical limitations that preclude more accurate description of virus risks.

Validation of Quantitative Microbial Risk Assessment Using Epidemiological Data from Outbreaks of Waterborne Gastrointestinal Disease

The assumptions underlying quantitative microbial risk assessment (QMRA) are simple and biologically plausible, but QMRA predictions have never been validated for many pathogens. The objective of this study was to validate QMRA predictions against epidemiological measurements from outbreaks of waterborne gastrointestinal disease. I screened 2,000 papers and identified 12 outbreaks with the necessary data: disease rates measured using epidemiological methods and pathogen concentrations measured in the source water. Eight of the 12 outbreaks were caused by Cryptosporidium, three by Giardia, and one by norovirus. Disease rates varied from 5.5 × 10^-6 to 1.1 × 10^-2 cases/person-day, and reported pathogen concentrations varied from 1.2 × 10^-4 to 8.6 × 10² per liter. I used these concentrations with single-hit dose-response models for all three pathogens to conduct QMRA, producing both point and interval predictions of disease rates for each outbreak. Comparison of QMRA predictions to epidemiological measurements showed good agreement; interval predictions contained measured disease rates for 9 of 12 outbreaks, with point predictions off by factors of 1.0-120 (median = 4.8). Furthermore, 11 outbreaks occurred at mean doses of less than 1 pathogen per exposure. Measured disease rates for these outbreaks were clearly consistent with a single-hit model, and not with a "two-hit" threshold model. These results demonstrate the validity of QMRA for predicting disease rates due to Cryptosporidium and Giardia.

Current Stormwater Harvesting Guidelines Are Inadequate for Mitigating Risk from Campylobacter During Nonpotable Reuse Activities

Campylobacter is a pathogen frequently detected in urban stormwater worldwide. It is one of the leading causes of enteric disease in many developed countries and is the leading cause of enteric disease in Australia. Prior to harvesting stormwater, adequate treatment is necessary to mitigate risks derived from such harmful pathogens. The goal of this research was to estimate the health risks associated with the exposure to Campylobacter when harvesting urban stormwater for toilet flushing and irrigation activities, and the role treatment options play in limiting risks. Campylobacter data collected from several urban stormwater systems in Victoria, Australia, were the inputs of a Quantitative Microbial Risk Assessment model. The model included seven treatment scenarios, spanning wetlands, biofilters, and more traditional treatment trains including those recommended by the Australian Guidelines for Water Recycling. According to our modeling and acceptable risk thresholds, only two treatment scenarios could supply water of sufficient quality for toilet flushing and irrigation end-uses: (1) using stormwater biofilters coupled with UV-treatment and (2) a more conventional coagulation, filtration, UV, and chlorination treatment plant. Importantly, our modeling results suggest that current guidelines in place for stormwater reuse are not adequate for protecting against exposure to Campylobacter. However, more research is required to better define whether the Campylobacter detectable in stormwater are pathogenic to humans.

Changing US Population Demographics: What Does This Mean for Listeriosis Incidence and Exposure?

Listeria monocytogenes is an important cause of foodborne illness hospitalization, fetal loss, and death in the United States. Listeriosis incidence rate varies significantly among population subgroups with pregnant women, older persons, and the Hispanic population having increased relative risks compared with the other subpopulations. Using estimated rates of listeriosis per subpopulation based on FoodNet data from 2004 to 2009, we evaluate the expected number of cases and incidence rates of listeriosis in the US population and the pregnant women subpopulation as the demographic composition changes over time with respect to ethnicity, pregnancy status, and age distribution. If the incidence rate per subpopulation is held constant, the overall US population listeriosis incidence rate would increase from 0.25 per 100,000 (95% confidence interval [CI]: 0.19-0.34) in 2010 to 0.28 (95% CI: 0.22-0.38) in 2020 and 0.32 (95% CI: 0.25-0.43) in 2030, because of the changes in the population structure. Similarly, the pregnancy-associated incidence rate is expected to increase from 4.0 per 100,000 pregnant women (95% CI: 2.5-6.5) in 2010 to 4.1 (95% CI: 2.6-6.7) in 2020 and 4.4 (95% CI: 2.7-7.2) in 2030 as the proportion of Hispanic pregnant women increases. We further estimate that a reduction of 12% in the exposure of the US population to L. monocytogenes would be needed to maintain a constant incidence rate from 2010 to 2020 (current trend), assuming infectivity (strain virulence distribution and individual susceptibility) is unchanged. To reduce the overall US population incidence rate by one-third (Healthy People 2020 goal) would require a reduction in exposure (or infectivity) to L. monocytogenes of 48% over the same time period. Reduction/elimination in exposure of pregnant and Hispanic subpopulations alone could not meet this target. This information may be useful in setting public health targets, developing risk management options, and in interpreting trends in the public health burden of foodborne listeriosis in the United States.

Quantitative Microbial Risk Assessment for Spray Irrigation of Dairy Manure Based on an Empirical Fate and Transport Model

BACKGROUND

Spray irrigation for land-applying livestock manure is increasing in the United States as farms become larger and economies of scale make manure irrigation affordable. Human health risks from exposure to zoonotic pathogens aerosolized during manure irrigation are not well understood.

OBJECTIVES

We aimed to a) estimate human health risks due to aerosolized zoonotic pathogens downwind of spray-irrigated dairy manure; and b) determine which factors (e.g., distance, weather conditions) have the greatest influence on risk estimates.

METHODS

We sampled downwind air concentrations of manure-borne fecal indicators and zoonotic pathogens during 21 full-scale dairy manure irrigation events at three farms. We fit these data to hierarchical empirical models and used model outputs in a quantitative microbial risk assessment (QMRA) to estimate risk [probability of acute gastrointestinal illness (AGI)] for individuals exposed to spray-irrigated dairy manure containing Campylobacter jejuni, enterohemorrhagic Escherichia coli (EHEC), or Salmonella spp.

RESULTS

Median risk estimates from Monte Carlo simulations ranged from 10^-5 to 10^-2 and decreased with distance from the source. Risk estimates for Salmonella or EHEC-related AGI were most sensitive to the assumed level of pathogen prevalence in dairy manure, while risk estimates for C. jejuni were not sensitive to any single variable. Airborne microbe concentrations were negatively associated with distance and positively associated with wind speed, both of which were retained in models as a significant predictor more often than relative humidity, solar irradiation, or temperature.

CONCLUSIONS

Our model-based estimates suggest that reducing pathogen prevalence and concentration in source manure would reduce the risk of AGI from exposure to manure irrigation, and that increasing the distance from irrigated manure (i.e., setbacks) and limiting irrigation to times of low wind speed may also reduce risk. https://doi.org/10.1289/EHP283.

Guidelines for Use of the Approximate Beta-Poisson Dose-Response Model

For dose-response analysis in quantitative microbial risk assessment (QMRA), the exact beta-Poisson model is a two-parameter mechanistic dose-response model with parameters α>0 and β>0, which involves the Kummer confluent hypergeometric function. Evaluation of a hypergeometric function is a computational challenge. Denoting PI(d) as the probability of infection at a given mean dose d, the widely used dose-response model PI(d)=1-(1+dβ)-α is an approximate formula for the exact beta-Poisson model. Notwithstanding the required conditions α<<β and β>>1, issues related to the validity and approximation accuracy of this approximate formula have remained largely ignored in practice, partly because these conditions are too general to provide clear guidance. Consequently, this study proposes a probability measure Pr(0 < r < 1 | α̂, β̂) as a validity measure (r is a random variable that follows a gamma distribution; α̂ and β̂ are the maximum likelihood estimates of α and β in the approximate model); and the constraint conditions β̂>(22α̂)0.50 for 0.02<α̂<2 as a rule of thumb to ensure an accurate approximation (e.g., Pr(0 < r < 1 | α̂, β̂) >0.99) . This validity measure and rule of thumb were validated by application to all the completed beta-Poisson models (related to 85 data sets) from the QMRA community portal (QMRA Wiki). The results showed that the higher the probability Pr(0 < r < 1 | α̂, β̂), the better the approximation. The results further showed that, among the total 85 models examined, 68 models were identified as valid approximate model applications, which all had a near perfect match to the corresponding exact beta-Poisson model dose-response curve.

Dose-response relationships for environmentally mediated infectious disease transmission models

Environmentally mediated infectious disease transmission models provide a mechanistic approach to examining environmental interventions for outbreaks, such as water treatment or surface decontamination. The shift from the classical SIR framework to one incorporating the environment requires codifying the relationship between exposure to environmental pathogens and infection, i.e. the dose-response relationship. Much of the work characterizing the functional forms of dose-response relationships has used statistical fit to experimental data. However, there has been little research examining the consequences of the choice of functional form in the context of transmission dynamics. To this end, we identify four properties of dose-response functions that should be considered when selecting a functional form: low-dose linearity, scalability, concavity, and whether it is a single-hit model. We find that i) middle- and high-dose data do not constrain the low-dose response, and different dose-response forms that are equally plausible given the data can lead to significant differences in simulated outbreak dynamics; ii) the choice of how to aggregate continuous exposure into discrete doses can impact the modeled force of infection; iii) low-dose linear, concave functions allow the basic reproduction number to control global dynamics; and iv) identifiability analysis offers a way to manage multiple sources of uncertainty and leverage environmental monitoring to make inference about infectivity. By applying an environmentally mediated infectious disease model to the 1993 Milwaukee Cryptosporidium outbreak, we demonstrate that environmental monitoring allows for inference regarding the infectivity of the pathogen and thus improves our ability to identify outbreak characteristics such as pathogen strain.

Comparison of Risk Predicted by Multiple Norovirus Dose-Response Models and Implications for Quantitative Microbial Risk Assessment

The application of quantitative microbial risk assessments (QMRAs) to understand and mitigate risks associated with norovirus is increasingly common as there is a high frequency of outbreaks worldwide. A key component of QMRA is the dose-response analysis, which is the mathematical characterization of the association between dose and outcome. For Norovirus, multiple dose-response models are available that assume either a disaggregated or an aggregated intake dose. This work reviewed the dose-response models currently used in QMRA, and compared predicted risks from waterborne exposures (recreational and drinking) using all available dose-response models. The results found that the majority of published QMRAs of norovirus use the ₁ F₁ hypergeometric dose-response model with α = 0.04, β = 0.055. This dose-response model predicted relatively high risk estimates compared to other dose-response models for doses in the range of 1-1,000 genomic equivalent copies. The difference in predicted risk among dose-response models was largest for small doses, which has implications for drinking water QMRAs where the concentration of norovirus is low. Based on the review, a set of best practices was proposed to encourage the careful consideration and reporting of important assumptions in the selection and use of dose-response models in QMRA of norovirus. Finally, in the absence of one best norovirus dose-response model, multiple models should be used to provide a range of predicted outcomes for probability of infection.

Risk-based enteric pathogen reduction targets for non-potable and direct potable use of roof runoff, stormwater, and greywater

This paper presents risk-based enteric pathogen log reduction targets for non-potable and potable uses of a variety of alternative source waters (i.e., locally-collected greywater, roof runoff, and stormwater). A probabilistic Quantitative Microbial Risk Assessment (QMRA) was used to derive the pathogen log10 reduction targets (LRTs) that corresponded with an infection risk of either 10-4 per person per year (ppy) or 10-2 ppy. The QMRA accounted for variation in pathogen concentration and sporadic pathogen occurrence (when data were available) in source waters for reference pathogens in the genera Rotavirus, Mastadenovirus(human adenoviruses), Norovirus, Campylobacter, Salmonella, Giardia and Cryptosporidium. Non-potable uses included indoor use (for toilet flushing and clothes washing) with occasional accidental ingestion of treated non-potable water (or cross-connection with potable water), and unrestricted irrigation for outdoor use. Various exposure scenarios captured the uncertainty from key inputs, i.e., the pathogen concentration in source water; the volume of water ingested; and for the indoor use, the frequency of and the fraction of the population exposed to accidental ingestion. Both potable and non-potable uses required pathogen treatment for the selected waters and the LRT was generally greater for potable use than non-potable indoor use and unrestricted irrigation. The difference in treatment requirements among source waters was driven by the microbial quality of the water - both the density and occurrence of reference pathogens. Greywater from collection systems with 1000 people had the highest LRTs; however, those for greywater collected from a smaller population (~ 5 people), which have less frequent pathogen occurrences, were lower. Stormwater had highly variable microbial quality, which resulted in a range of possible treatment requirements. The microbial quality of roof runoff, and thus the resulting LRTs, remains uncertain due to lack of relevant pathogen data.

Managing Microbial Risks from Indirect Wastewater Reuse for Irrigation in Urbanizing Watersheds

Limited supply of clean water in urbanizing watersheds creates challenges for safely sustaining irrigated agriculture and global food security. On-farm interventions, such as riverbank filtration (RBF), are used in developing countries to treat irrigation water from rivers with extensive fecal contamination. Using a Bayesian approach incorporating ethnographic data and pathogen measurements, quantitative microbial risk assessment (QMRA) methods were employed to assess the impact of RBF on consumer health burdens for Giardia, Cryptosporidium, rotavirus, norovirus, and adenovirus infections resulting from indirect wastewater reuse, with lettuce irrigation in Bolivia as a model system. Concentrations of the microbial source tracking markers pepper mild mottle virus and HF183 Bacteroides were respectively 2.9 and 5.5 log10 units lower in RBF-treated water than in the river water. Consumption of lettuce irrigated with river water caused an estimated median health burden that represents 37% of Bolivia's overall diarrheal disease burden, but RBF resulted in an estimated health burden that is only 1.1% of this overall diarrheal disease burden. Variability and uncertainty associated with environmental and cultural factors affecting exposure correlated more with QMRA-predicted health outcomes than factors related to disease vulnerability. Policies governing simple on-farm interventions like RBF can be intermediary solutions for communities in urbanizing watersheds that currently lack wastewater treatment.

QMRA for Drinking Water: 2. The Effect of Pathogen Clustering in Single-Hit Dose-Response Models

Spatial and/or temporal clustering of pathogens will invalidate the commonly used assumption of Poisson-distributed pathogen counts (doses) in quantitative microbial risk assessment. In this work, the theoretically predicted effect of spatial clustering in conventional "single-hit" dose-response models is investigated by employing the stuttering Poisson distribution, a very general family of count distributions that naturally models pathogen clustering and contains the Poisson and negative binomial distributions as special cases. The analysis is facilitated by formulating the dose-response models in terms of probability generating functions. It is shown formally that the theoretical single-hit risk obtained with a stuttering Poisson distribution is lower than that obtained with a Poisson distribution, assuming identical mean doses. A similar result holds for mixed Poisson distributions. Numerical examples indicate that the theoretical single-hit risk is fairly insensitive to moderate clustering, though the effect tends to be more pronounced for low mean doses. Furthermore, using Jensen's inequality, an upper bound on risk is derived that tends to better approximate the exact theoretical single-hit risk for highly overdispersed dose distributions. The bound holds with any dose distribution (characterized by its mean and zero inflation index) and any conditional dose-response model that is concave in the dose variable. Its application is exemplified with published data from Norovirus feeding trials, for which some of the administered doses were prepared from an inoculum of aggregated viruses. The potential implications of clustering for dose-response assessment as well as practical risk characterization are discussed.

QMRA for Drinking Water: 1. Revisiting the Mathematical Structure of Single-Hit Dose-Response Models

Dose-response models are essential to quantitative microbial risk assessment (QMRA), providing a link between levels of human exposure to pathogens and the probability of negative health outcomes. In drinking water studies, the class of semi-mechanistic models known as single-hit models, such as the exponential and the exact beta-Poisson, has seen widespread use. In this work, an attempt is made to carefully develop the general mathematical single-hit framework while explicitly accounting for variation in (1) host susceptibility and (2) pathogen infectivity. This allows a precise interpretation of the so-called single-hit probability and precise identification of a set of statistical independence assumptions that are sufficient to arrive at single-hit models. Further analysis of the model framework is facilitated by formulating the single-hit models compactly using probability generating and moment generating functions. Among the more practically relevant conclusions drawn are: (1) for any dose distribution, variation in host susceptibility always reduces the single-hit risk compared to a constant host susceptibility (assuming equal mean susceptibilities), (2) the model-consistent representation of complete host immunity is formally demonstrated to be a simple scaling of the response, (3) the model-consistent expression for the total risk from repeated exposures deviates (gives lower risk) from the conventional expression used in applications, and (4) a model-consistent expression for the mean per-exposure dose that produces the correct total risk from repeated exposures is developed.

Estimating the burden of acute gastrointestinal illness due to Giardia, Cryptosporidium, Campylobacter, E. coli O157 and norovirus associated with private wells and small water systems in Canada

Waterborne illness related to the consumption of contaminated or inadequately treated water is a global public health concern. Although the magnitude of drinking water-related illnesses in developed countries is lower than that observed in developing regions of the world, drinking water is still responsible for a proportion of all cases of acute gastrointestinal illness (AGI) in Canada. The estimated burden of endemic AGI in Canada is 20·5 million cases annually – this estimate accounts for under-reporting and under-diagnosis. About 4 million of these cases are domestically acquired and foodborne, yet the proportion of waterborne cases is unknown. There is evidence that individuals served by private systems and small community systems may be more at risk of waterborne illness than those served by municipal drinking water systems in Canada. However, little is known regarding the contribution of these systems to the overall drinking water-related AGI burden in Canada. Private water supplies serve an estimated 12% of the Canadian population, or ~4·1 million people. An estimated 1·4 million (4·1%) people in Canada are served by small groundwater (2·6%) and surface water (1·5%) supplies. The objective of this research is to estimate the number of AGI cases attributable to water consumption from these supplies in Canada using a quantitative microbial risk assessment (QMRA) approach. This provides a framework for others to develop burden of waterborne illness estimates for small water supplies. A multi-pathogen QMRA of Giardia, Cryptosporidium, Campylobacter, E. coli O157 and norovirus, chosen as index waterborne pathogens, for various source water and treatment combinations was performed. It is estimated that 103 230 AGI cases per year are due to the presence of these five pathogens in drinking water from private and small community water systems in Canada. In addition to providing a mechanism to assess the potential burden of AGI attributed to small systems and private well water in Canada, this research supports the use of QMRA as an effective source attribution tool when there is a lack of randomized controlled trial data to evaluate the public health risk of an exposure source. QMRA is also a powerful tool for identifying existing knowledge gaps on the national scale to inform future surveillance and research efforts.

Norovirus Dose-Response: Are Currently Available Data Informative Enough to Determine How Susceptible Humans Are to Infection from a Single Virus?

Two forms of single-hit infection dose-response models have previously been developed to assess available data from human feeding trials and estimate the norovirus dose-response relationship. The mechanistic interpretations of these models include strong assumptions that warrant reconsideration: the first study includes an implicit assumption that there is no immunity to Norwalk virus among the specific study population, while the recent second study includes assumptions that such immunity could exist and that the nonimmune have no defensive barriers to prevent infection from exposure to just one virus. Both models addressed unmeasured virus aggregation in administered doses. In this work, the available data are reanalyzed using a generalization of the first model to explore these previous assumptions. It was hypothesized that concurrent estimation of an unmeasured degree of virus aggregation and important dose-response parameters could lead to structural nonidentifiability of the model (i.e., that a diverse range of alternative mechanistic interpretations yield the same optimal fit), and this is demonstrated using the profile likelihood approach and by algebraic proof. It is also demonstrated that omission of an immunity parameter can artificially inflate the estimated degree of aggregation and falsely suggest high susceptibility among the nonimmune. The currently available data support the assumption of immunity within the specific study population, but provide only weak information about the degree of aggregation and susceptibility among the nonimmune. The probability of infection at low and moderate doses may be much lower than previously asserted, but more data from strategically designed dose-response experiments are needed to provide adequate information.

Dose-response algorithms for water-borne Pseudomonas aeruginosa folliculitis

We developed two dose-response algorithms for P. aeruginosa pool folliculitis using bacterial and lesion density estimates, associated with undetectable, significant, and almost certain folliculitis. Literature data were fitted to Furumoto & Mickey's equations, developed for plant epidermis-invading pathogens: N l = A ln(1 + BC) (log-linear model); P inf = 1-e(-r c C) (exponential model), where A and B are 2.51644 × 107 lesions/m2 and 2.28011 × 10-11 c.f.u./ml P. aeruginosa, respectively; C = pathogen density (c.f.u./ml), N l = folliculitis lesions/m2, P inf = probability of infection, and r C = 4·3 × 10-7 c.f.u./ml P. aeruginosa. Outbreak data indicates these algorithms apply to exposure durations of 41 ± 25 min. Typical water quality benchmarks (≈10-2 c.f.u./ml) appear conservative but still useful as the literature indicated repeated detection likely implies unstable control barriers and bacterial bloom potential. In future, culture-based outbreak testing should be supplemented with quantitative polymerase chain reaction and organic carbon assays, and quantification of folliculitis aetiology to better understand P. aeruginosa risks.

Bacterial Cooperation Causes Systematic Errors in Pathogen Risk Assessment due to the Failure of the Independent Action Hypothesis

The Independent Action Hypothesis (IAH) states that pathogenic individuals (cells, spores, virus particles etc.) behave independently of each other, so that each has an independent probability of causing systemic infection or death. The IAH is not just of basic scientific interest; it forms the basis of our current estimates of infectious disease risk in humans. Despite the important role of the IAH in managing disease interventions for food and water-borne pathogens, experimental support for the IAH in bacterial pathogens is indirect at best. Moreover since the IAH was first proposed, cooperative behaviors have been discovered in a wide range of microorganisms, including many pathogens. A fundamental principle of cooperation is that the fitness of individuals is affected by the presence and behaviors of others, which is contrary to the assumption of independent action. In this paper, we test the IAH in Bacillus thuringiensis (B.t), a widely occurring insect pathogen that releases toxins that benefit others in the inoculum, infecting the diamondback moth, Plutella xylostella. By experimentally separating B.t. spores from their toxins, we demonstrate that the IAH fails because there is an interaction between toxin and spore effects on mortality, where the toxin effect is synergistic and cannot be accommodated by independence assumptions. Finally, we show that applying recommended IAH dose-response models to high dose data leads to systematic overestimation of mortality risks at low doses, due to the presence of synergistic pathogen interactions. Our results show that cooperative secretions can easily invalidate the IAH, and that such mechanistic details should be incorporated into pathogen risk analysis.

Listeria monocytogenes dose response revisited--incorporating adjustments for variability in strain virulence and host susceptibility

Evaluations of Listeria monocytogenes dose-response relationships are crucially important for risk assessment and risk management, but are complicated by considerable variability across population subgroups and L. monocytogenes strains. Despite difficulties associated with the collection of adequate data from outbreak investigations or sporadic cases, the limitations of currently available animal models, and the inability to conduct human volunteer studies, some of the available data now allow refinements of the well-established exponential L. monocytogenes dose response to more adequately represent extremely susceptible population subgroups and highly virulent L. monocytogenes strains. Here, a model incorporating adjustments for variability in L. monocytogenes strain virulence and host susceptibility was derived for 11 population subgroups with similar underlying comorbidities using data from multiple sources, including human surveillance and food survey data. In light of the unique inherent properties of L. monocytogenes dose response, a lognormal-Poisson dose-response model was chosen, and proved able to reconcile dose-response relationships developed based on surveillance data with outbreak data. This model was compared to a classical beta-Poisson dose-response model, which was insufficiently flexible for modeling the specific case of L. monocytogenes dose-response relationships, especially in outbreak situations. Overall, the modeling results suggest that most listeriosis cases are linked to the ingestion of food contaminated with medium to high concentrations of L. monocytogenes. While additional data are needed to refine the derived model and to better characterize and quantify the variability in L. monocytogenes strain virulence and individual host susceptibility, the framework derived here represents a promising approach to more adequately characterize the risk of listeriosis in highly susceptible population subgroups.

Fractional poisson--a simple dose-response model for human norovirus

This study utilizes old and new Norovirus (NoV) human challenge data to model the dose-response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta-Poisson dose-response model that includes parameters for virus aggregation and for a beta-distribution that describes variable susceptibility among hosts. The quality of the beta-Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two-parameter beta-distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta-Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The model's deviance is similar to that of the beta-Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta-Poisson model. At low, environmentally relevant exposure levels (<100), estimation error is small for the fractional Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low-dose data would be of great value to further clarify the NoV dose-response relationship and to support improved risk assessment for environmentally relevant exposures.

Bacteria, viruses, and parasites in an intermittent stream protected from and exposed to pasturing cattle: prevalence, densities, and quantitative microbial risk assessment

Over 3500 individual water samples, for 131 sampling times, targeting waterborne pathogens/fecal indicator bacteria were collected during a 7-year period from 4 sites along an intermittent stream running through a small livestock pasture system with and without cattle access-to-stream restriction measures. The study assessed the impact of cattle pasturing/riparian zone protection on: pathogen (bacterial, viral, parasite) occurrence, concentrations of fecal indicators, and quantitative microbial risk assessments (QMRA) of the risk of Cryptosporidium, Giardia and Escherichia coli O157:H7 infection in humans. Methodologies were developed to compute QMRA mean risks on the basis of water samples exhibiting potentially human infectious Cryptosporidium and E. coli based on genotyping Crytosporidium, and E. coli O157:H7 presence/absence information paired with enumerated E. coli. All Giardia spp. were considered infectious. No significant pasturing treatment effects were observed among pathogens, with the exception of Campylobacter spp. and E. coli O157:H7. Campylobacter spp. prevalence significantly decreased downstream through pasture treatments and E. coli O157:H7 was observed in a few instances in the middle of the unrestricted pasture. Densities of total coliform, fecal coliform, and E. coli reduced significantly downstream in the restricted pasture system, but not in the unrestricted system. Seasonal and flow conditions were associated with greater indicator bacteria densities, especially in the summer. Norovirus GII was detected at rates of 7-22% of samples for all monitoring sites, and rotavirus in 0-7% of samples for all monitoring sites; pasture treatment trends were not evident, however. Seasonal and stream flow variables (and their interactions) were relatively more important than pasture treatments for initially stratifying pathogen occurrence and higher fecal indicator bacteria densities. Significant positive associations among fecal indicator bacteria and Campylobacter spp. detection were observed. For QMRA, adjusting for the proportion of Cryptosporidium spp. detected that are infectious for humans reduces downstream risk estimates by roughly one order of magnitude. Using QMRA in this manner provides a more refined estimate of beneficial management practice effects on pathogen exposure risks to humans.

Using Campylobacter spp. and Escherichia coli data and Bayesian microbial risk assessment to examine public health risks in agricultural watersheds under tile drainage management

Human campylobacteriosis is the leading bacterial gastrointestinal illness in Canada; environmental transmission has been implicated in addition to transmission via consumption of contaminated food. Information about Campylobacter spp. occurrence at the watershed scale will enhance our understanding of the associated public health risks and the efficacy of source water protection strategies. The overriding purpose of this study is to provide a quantitative framework to assess and compare the relative public health significance of watershed microbial water quality associated with agricultural BMPs. A microbial monitoring program was expanded from fecal indicator analyses and Campylobacter spp. presence/absence tests to the development of a novel, 11-tube most probable number (MPN) method that targeted Campylobacter jejuni, Campylobacter coli, and Campylobacter lari. These three types of data were used to make inferences about theoretical risks in a watershed in which controlled tile drainage is widely practiced, an adjacent watershed with conventional (uncontrolled) tile drainage, and reference sites elsewhere in the same river basin. E. coli concentrations (MPN and plate count) in the controlled tile drainage watershed were statistically higher (2008-11), relative to the uncontrolled tile drainage watershed, but yearly variation was high as well. Escherichia coli loading for years 2008-11 combined were statistically higher in the controlled watershed, relative to the uncontrolled tile drainage watershed, but Campylobacter spp. loads for 2010-11 were generally higher for the uncontrolled tile drainage watershed (but not statistically significant). Using MPN data and a Bayesian modelling approach, higher mean Campylobacter spp. concentrations were found in the controlled tile drainage watershed relative to the uncontrolled tile drainage watershed (2010, 2011). A second-order quantitative microbial risk assessment (QMRA) was used, in a relative way, to identify differences in mean Campylobacter spp. infection risks among monitoring sites for a hypothetical exposure scenario. Greater relative mean risks were obtained for sites in the controlled tile drainage watershed than in the uncontrolled tile drainage watershed in each year of monitoring with pair-wise posterior probabilities exceeding 0.699, and the lowest relative mean risks were found at a downstream drinking water intake reference site. The second-order modelling approach was used to partition sources of uncertainty, which revealed that an adequate representation of the temporal variation in Campylobacter spp. concentrations for risk assessment was achieved with as few as 10 MPN data per site. This study demonstrates for the first time how QMRA can be implemented to evaluate, in a relative sense, the public health implications of controlled tile drainage on watershed-scale water quality.