A PHOTO JOURNAL BY JAISSON RESTREPO ABOUT THE BOOK ‘’THE COLOR OF WATER’’ BY JAMES MCBRIDE.
McBride 2013 Water-Research
-
Upload
rodolfograna -
Category
Documents
-
view
12 -
download
0
description
Transcript of McBride 2013 Water-Research
ww.sciencedirect.com
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 7
Available online at w
journal homepage: www.elsevier .com/locate /watres
Discharge-based QMRA for estimation of publichealth risks from exposure to stormwater-borne pathogens in recreational waters inthe United States
Graham B. McBride a,*, Rebecca Stott a, Woutrina Miller b, Dustin Bambic c,1,Stefan Wuertz d,e
aNIWA (National Institute of Water and Atmospheric Research), P.O. Box 11-115, Hamilton 3251, New ZealandbDepartment of Pathology, Microbiology, and Immunology, School of Veterinary Medicine, University of California,
Davis, CA 95616, USAcAMEC Earth & Environmental, Nashville, TN 37211, USAdDepartment of Civil & Environmental Engineering, University of California, Davis, CA 95616, USAeSingapore Centre of Environmental Life Sciences Engineering (SCELSE) and School of Civil and
Environmental Engineering, Nanyang Technological University, 60 Nanyang Drive, Singapore
a r t i c l e i n f o
Article history:
Received 19 December 2012
Received in revised form
24 May 2013
Accepted 2 June 2013
Available online 12 June 2013
Keywords:
QMRA
Pathogens
Stormwater
Norovirus
Rotavirus
Health
* Corresponding author. Tel.: þ64 7 856 1726E-mail address: [email protected]
1 Present address: Tetra Tech, 712 Melrose0043-1354/$ e see front matter ª 2013 Elsevhttp://dx.doi.org/10.1016/j.watres.2013.06.001
a b s t r a c t
This study is the first to report a quantitative microbial risk assessment (QMRA) on path-
ogens detected in stormwater discharges-of-concern, rather than relying on pathogen
measurements in receiving waters. The pathogen concentrations include seven “Reference
Pathogens” identified by the U.S. EPA: Cryptosporidium, Giardia, Salmonella, Norovirus,
Rotavirus, Enterovirus, and Adenovirus. Data were collected from 12 sites representative of
seven discharge types (including residential, commercial/industrial runoff, agricultural
runoff, combined sewer overflows, and forested land), mainly during wet weather condi-
tions during which times human health risks can be substantially elevated. The risks
calculated herein therefore generally apply to short-term conditions (during and just after
rainfall events) and so the results can be used by water managers to potentially inform the
public, even for waters that comply with current criteria (based as they are on a 30-day
mean risk). Using an example waterbody and mixed source, pathogen concentrations
were used in QMRA models to generate risk profiles for primary and secondary water
contact (or inhalation) by adults and children. A number of critical assumptions and
considerations around the QMRA analysis are highlighted, particularly the harmonization
of the pathogen concentrations measured in discharges during this project with those
measured (using different methods) during the published doseeresponse clinical trials.
Norovirus was the most dominant predicted health risk, though further research on its
doseeresponse for illness (cf. infection) is needed. Even if the example mixed-source
concentrations of pathogens had been reduced 30 times (by inactivation and mixing), the
predicted swimming-associated illness rates e largely driven by Norovirus infections e
can still be appreciable. Rotavirus generally induced the second-highest incidence of risk
among the tested pathogens while risks for the other Reference Pathogens (Giardia,
.o.nz (G.B. McBride).Avenue, Nashville, TN 37211, USA.ier Ltd. All rights reserved.
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 7 5283
Cryptosporidium, Adenovirus, Enterovirus and Salmonella) were considerably lower. Sec-
ondary contact or inhalation resulted in considerable reductions in risk compared to pri-
mary contact. Measurements of Norovirus and careful incorporation of its concentrations
into risk models (harmonization) should be a critical consideration for future QMRA efforts.
The discharge-based QMRA approach presented herein is particularly relevant to cases
where pathogens cannot be reliably detected in receiving waters with detection limits
relevant to human health effects.
ª 2013 Elsevier Ltd. All rights reserved.
1. Introduction runoff to receiving rivers/streams and often lower rates of
To date, development of recreational microbiological water
quality criteria has mostly focused on coastal waters (Cabelli
et al., 1982; Cabelli, 1983; Pruss, 1998; Zmirou et al., 2003;
Pond, 2005; Wade et al., 2010; Colford et al., 2012) and lakes
(Dufour, 1984; Wade et al., 2006; Marion et al., 2010), using
epidemiological studies pioneered by Stevenson (1953),
Cabelli (1983) and Dufour (1984). In contrast, very few
studies have included flowing inland waters (Ferley et al.,
1989; Wiedenmann et al., 2006; Kay, 2009). In general all the
aforementioned studies, for either coastal and inland waters,
support the view that risks of mild gastrointestinal (GI) illness
(and sometimes respiratory illness) can be enhanced among
swimmers when the water contains some degree of human
fecal contamination, as presumably indicated by concentra-
tions of fecal indicator bacteria (FIB). In most of these epide-
miological studies the dominant pathogenic material present
has been treated human sewage, often from publicly owned
treatment works (POTWs). Studies by Calderon et al. (1991),
Colford et al. (2007) and Fleisher et al. (2010), along with
some of the beaches included in the studies of Cheung et al.
(1990) and McBride et al. (1998), are notable exceptions in
that the dominant sources of fecal matter were animalsdthe
study of Fleisher et al. (2010) was conducted at a site “without
known sources of sewage”. In these non-sewage studies, evi-
dence for associations between animal-sourced fecal con-
centrations and health risk to recreational users is less clear
cut, with claims in support of a linkage (McBride, 1993) and
others against (Dufour et al., 2012). Nonetheless such doubt
should be treated with some caution, perhaps especially with
regard to livestock (Soller et al., 2010b). For example, there is
evidence in New Zealand that strains of Campylobacter spp.
associated with ovine and bovine animals are commonly
found in recreational waters and are associated with human
health impacts, assessed by Multi-Locus Sequence Typing
(MLST) of human isolates (French et al., 2011; McBride et al.,
2011). Notably, campylobacteriosis is the dominant notifiable
disease reported in that country (www.nzpho.org.nz). Simi-
larly, substantial increases in cryptosporidiosis among rural
dwellers in New Zealand commonly arise during the calving
season (Till and McBride, 2004).
Accordingly, epidemiological data are lacking regarding
the human health impacts of the mixtures of anthroponotic
and zoonotic fecal pathogens expected to be found in flowing
inland waters. Contamination by both can be expected in
many rivers and streams for which recreational water contact
may occur. Furthermore, given the proximity of terrestrial
dilution, one might expect higher levels of zoonotic pathogen
contamination inland than occurs at coastal sites. However,
comprehensive information on the degree of pathogen
contamination in USA inland waters is lackingdespecially as
epidemiological studies seldom include their measurement,
relying instead on fecal indicator bacteria (FIB) as represen-
tative of fecal pollution. Extension of findings from predomi-
nantly coastal waters to flowing inlandwaters could therefore
be viewed with scepticism, especially given the growing body
of evidence suggesting that FIB measured in recreational wa-
ters may be uncoupled from pathogen discharges due to
ubiquity, environmental regrowth/resuscitation, differential
inactivation, and/or persistence in sediments and soils
(Desmarais et al., 2002; Ferguson et al., 2003; Byappanahalli
et al., 2010).
Quantitative microbial risk assessment (QMRA) is a prom-
ising tool for predicting risks associated with water contact
given that it requires specific information on pathogens,
rather than fecal indicator bacteria (Till et al., 2008; Ashbolt
et al., 2010). Examples of that approach have been presented
by Schoen and Ashbolt (2010) who compared health impacts
associated with sewage versus seagull sources, Soller et al.
(2010a) who found that Norovirus tended to dominate the
effective pathogens at recent USA epidemiological study sites,
and Soller et al. (2010b)who usedQMRA to compare impacts of
human versus non-human sources. The latter study inferred
that GI illness risks associatedwith fresh cattle faecesmay not
be substantially different from those associated with human
sources, but that risks associated with fresh gull, chicken, or
pig faeces appear to be substantially lower.
The work reported herein had three objectives: (i) use
QMRA to estimate public health risks associated with storm-
water discharges to recreational waters, (ii) analyze the im-
plications of the findings for QMRA applications, and (iii)
examine the consequences of the selection of appropriate
endpoints for QMRA. In order to meet these objectives, an
extensive microbiological sampling program of runoff/
stormwater sources was conducted throughout the USA,
focusing mostly on wet weather and specific land uses as well
as discharge types (e.g., runoff from catchments categorized
as having land uses that are residential, industrial, agricul-
tural, and so forth). Discharges rather than receiving waters
were sampled because these data should be more applicable
to other watersheds/recreational sites. Data from discharges
were synthesized to represent potential recreational sce-
narios, and only short-term risks are reported, that is,
following discharge events.Wemake generalized calculations
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 75284
of risks associated with exposure directly to the source waters
compared with risks at a recreation site, where the source-
water concentrations have been reduced 30-fold. Actual ex-
posures in a site-specific QMRA would of course be based on
hydrodynamic mixing and inactivation modelsdbeyond the
scope of this paper.
2. Methods
While QMRA requires profiles of pathogen concentrations at
the point of exposure, it can be a more efficient use of re-
sources to characterize pathogen concentrations in the sour-
ces to recreational waters (e.g., runoff from regional
agricultural and residential areas) and to then rely on hydro-
dynamic models to convey the pathogens to the exposure
points. Because many stormwater discharges are intermit-
tent, pathogen concentrations at the point of exposuremay be
below the analytical limits of detection (non-detects) or well
below peak concentrations. Accordingly, the field work for
this study involved sampling of discharges-of-concern that
are not well characterized in the literature, in order to char-
acterize themwith regard to the occurrence and abundance of
high Reference Pathogens and source identifiers. With the
exception of the Southern California sites (see below), moni-
toring was performed during rainfall events.
2.1. Filtration and microbiological methods
At each site 50-L water samples were collected into carboys
and concentrated by ultrafiltration at a location near the
sampling sites. This step concentrated the water sample from
about 50 L to approximately 200mL using a Fresenius filtration
system modified from Hill et al. (2007) and Leskinen and Lim
(2008). Concentrated samples were shipped chilled for over-
night delivery to laboratories at the University of California,
Davis. Field duplicates and field blanks were also collected for
quality assurance and quality control.
Themonitoring toolkit employed a combination of genetic-
, cultivation-, and microscopy-based methodologies for mi-
crobes including Salmonella enterica, Campylobacter jejuni,
Cryptosporidium, Giardia, Adenoviruses, Enteroviruses, Nor-
oviruses and Rotaviruses. Prior to filtration, surrogates were
Table 1 e Methods for detection of pathogenic bacteria, protoz
Microbe type Microbe Molecularapproach
Molec
Pathogenic
Bacteria
Salmonella enterica qPCR Malorny et
Campylobacter jejuni qPCR Nogva et a
Protozoa Cryptosporidium parvum qPCR Fontaine a
Giardia lamblia qPCR Guy et al. (
Virus Adenovirus A, B, C
Adenovirus 40/41
qPCR Leruez-Vill
Rajal et al.
Enterovirus qPCR Fuhrman e
Norovirus (GI and GII) qPCR Wolf et al.
Rotavirus qPCR Gutierrez-A
spiked into environmental samples to estimate the percent
recovery of target organisms and to calculate sample-specific
limits of detection (Rajal et al., 2007a,b). This approach differs
from many others in that filtration recoveries and detection
limits were reported for individual samples, providing
important insights for the interpretation of monitoring re-
sults. Table 1 lists the target organisms and associated
quantification methods.
2.2. Site selection and monitoring
Over the duration of the monitoring period (March-
eSeptember 2011), 25 discharge sites were sampled over a
total of 17 monitoring events, selected to represent different
types of discharges-of concern to recreational waters (Table
2). All but the dry weather urban runoff (URBAN) sites were
sampled for multiple events. The number of sites sampled
during each event was dependent primarily on rain patterns
and where adequate precipitation conditions were present,
noting that the URBAN sites were sampled just once, in dry
weather. The number of monitoring events at the combined
sewer overflow (CSO) site were lower than expected because
of limited access during some storm events. Further infor-
mation on sites, monitoring, land use and soil types is given in
the Supplementary Information (SI). The exact locations of
sites were kept anonymous; instead the site locations are
described as general geographic regions (Mid-Atlantic,
Southeast, or Southern California).
2.2.1. Monitoring conditionsOfficial gages were all located at local major airports in each
zone and were supported by the National Weather Service.
Rain gages supplied 15-min data, helpful in assessing the
weather conditions for monitoring events. Local satellite
radar images were used to track storms and to identify loca-
tions where rain was falling.
2.2.2. Time-of-samplingSamples were collected using large-volume grab sampling
techniques, and the timing of each sampling with respect to
the hydrograph was estimated. Sampling was performed at
peak flow when possible under the assumption that most
fecal material was being transported at this time. However,
oa, and human viruses used in this study.
ular methods Conventionalapproach
Conventional methods
al. (2003) Culture U.S. EPA Method 1682,
Pant and Mittal (2008)
l. (2000) Culture Hijnen et al. (2004),
Wong et al. (2004)
nd Guillot (2003) Microscopy U.S. EPA Method 1623
2004) Microscopy U.S. EPA Method 1623
e et al. (2004),
(2007b)
N/A N/A
t al. (2005) N/A N/A
(2007) N/A N/A
guirre et al. (2008) N/A N/A
Table 2 e Description of discharge types and geographical locations.
Discharge type Acronym No. of sites No. of samples Discharge type characteristics
Residential Stormwater RESID 5 16 Separate municipal stormwater system
draining low-medium density residential
lands: Mid-Atlantic, Southeast, Texas.
Commercial/Light Industrial
Stormwater
COMML 3 13 Separate municipal stormwater system
draining shopping malls, restaurants etc.:
Mid-Atlantic, Southeast.
Agricultural Stormwater AGRIC 2 8 Open channel runoff from an agricultural
area with either row crop agricultural or
livestock grazing: Mid-Atlantic, Southeast.
CSO CSO 1 3 Water collected from within a combined
sewer system prior to discharge: Southeast.
Mixed Use Stormwater MIXED 5 12 Municipal separate stormwater system
draining a variety of land uses (residential,
commercial, agricultural): Texas.
Forested Open Space Stormwater FOREO 1 7 Runoff from a small, forested watershed
with little or no human access (no hiking
trails) and no development. Southeast.
Dry Season Urban Runoff URBAN 8 8 Separate stormwater system draining highly
urbanized residential and commercial areas
(exfiltrating groundwater, irrigation, car
washing, etc.). Samples were collected
during dry weather after several months
without rainfall: Southern California.
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 7 5285
the large geographic sampling regions and variability of
rainfall prevented all samples from being collected during
peak flows. During some rainfall events, certain sites received
relatively high rainfall amounts while others remained dry.
Field staff indicatedwhether the volumetric flow rate from the
discharge was rising, at peak, or falling at the time of sam-
pling. See SI for further information.
2.3. QMRA
The following items are described sequentially below: (1)
identifying pathogens and their sources; (2) transport and fate
to and within waterbodies leading to human exposures to the
pathogens; (3) pathogen infectivity (doseeresponse); (4) char-
acterizing the health risks. In so doing, an attempt is made to
characterize fundamental mathematical parameters along
with their variability (such as duration of swimming) and
associated uncertainty (especially with respect to dos-
eeresponse curves). Most parameters are not fixed but instead
are described by statistical distributions that capture the
range and pattern of variation, allowing the use of algorithms
to quantify the level of risk and its variability. These distri-
butions were sampled randomly many times over to build a
risk profile, typically using the Monte Carlo statistical
modeling method (e.g., Haas et al., 1999), in this case using
@RISK software (Palisade Corporation, 2009).
2.3.1. PathogensSeven “Reference Pathogens” were included in this QMRA
study: Salmonella, Cryptosporidium, Giardia, Enterovirus,
Adenovirus, Norovirus and Rotavirus. (Campylobacter was
initially selected also, but our pathogen survey seldom
detected it.) The characteristics of sites to which QMRA has
been applied dictates which of these pathogens (or others)
should be used. For example, Adenoviruses that cause respi-
ratory illness may need to be included where aerosols may be
inhaled (e.g. by water skiers). Salmonella, Cryptosporidium, and
Giardia are included because they are zoonotic and potentially
waterborne, and it should be noted that the type as well as
loading of zoonotic pathogens can be quite variable depending
on factors such as animal host species, animal age, animal
density, distance from the waterway, land management
practices, and season (Cox et al., 2005; Miller et al., 2007). Also
important can be the presence of “supershedder” individuals
in animal herds (French et al., 2005; Chase-Topping et al.,
2008).
2.3.2. ExposuresBecause we report synthesized QMRA results for illustrative
purposes, simple reduction ratios have been adopted (from
source to exposure point), avoiding the need formore complex
contaminant transport and inactivationmodels that would be
required for site-specific assessments.
Few studies are available on swimmers’ ingestion rates
(Schets et al., 2011). In a pilot study, Dufour et al. (2006), used
chloroisocyanurates tracers and found that the average
amount of water swallowed by children and adults during
swimming was 37 mL and 16 mL per event, respectively,
where each event lasted at least 45 min (This was subse-
quently modified in their full study that reported children and
adult rates of 47 mL and 24 mL per event respectivelydEvans
et al., 2006.). One quarter of the swimmers swallowed 85mL or
more, and some swallowed up to 280 mL. Dorevitch et al.
(2010, 2011) used survey methods and chemical testing to
define three modes of contact: low (rowing, boating, fishing,
wading, non-capsizing kayaking and canoeing); Middle
(canoeing and kayaking with occasional capsizing); high
(swimmers). Average ingestions for these three modes (from
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 75286
Dorevitch et al., 2011) were 3.8, 5.8, 10 and mL per event,
respectively, and the authors suggested taking three times
that as a conservative estimate (an “upper confidence limit”).
The duration of each event was generally less than 1 h and
separate ingestion rates between children and adults were not
identified. Haas et al. (1999) used 50 mL ingestion for swim-
ming. Using the ingestion figures from Dufour et al. (2006),
Evans et al. (2006) and Dorevitch et al. (2010, 2011) as a
guide, we have assumed the minimum, mode and maximum
duration of recreational events by adults as 0.25, 0.5 and 2 h,
respectivelydwith associated volumetric intake rates of 10, 50
and 100 mL. The latter rates were increased by 50% for chil-
dren and reduced by 80% for secondary contact or inhalation
(regardless of age). Ingestion per individual per exposure
event is the simple product of the ingestion rate and exposure
duration.
Given the limited number of samples for the pathogens
selected in this study, identification of their appropriate sta-
tistical distributions is challengingdmany distributions
Table 3 e Doseeresponse relationships used in this study.
Pathogen Representative Parameter val
Single-parameter model
Adenovirus Adenovirus 4 r ¼ 0.4172 (2)
Cryptosporidium C. parvum r ¼ 0.05 (14)
Giardia G. lamblia r ¼ 0.02 (35)
Two-parameter model
Enterovirusd Echovirus 12 a, b ¼ 0.401, 2
Norovirus Norwalk virus a, b ¼ 0.04, 0.0
Rotavirus Rotavirus (CJN strain) a, b ¼ 0.2531,
Salmonella Non-typhi Salmonella a, b ¼ 0.33, 13
a ID50 (for infection) values in this column (in parentheses) refer to aver
integer. For the single-parametermodel, Prinf ¼ 1� e�rd and so ID50¼�[n(½
infection given ingestion or inhalation of a single virion. For the two-param
ID50 z b(21/a � 1), where a and b are shape and scale parameters for r’s
applicable for norovirus in which case the ID50 must be obtained by find
Prinf ¼ 1� 1F1(a, aþ b, �d ) ¼½ (Teunis and Havelaar, 2000), where 1F1 is th
Note too that the Adenovirus doseeresponse is for respiratory effects on
others are all for ingestion leading to gastrointestinal effects.
b Based on the proportions of illness exhibited in the relevant trial, regar
2011).
c Mean value of r for the first two models in Exhibit N.20 in U.S. EPA (2005
C. parvum (Teunis, 2009). Soller et al. (2010a) used r ¼ 0.09 (so ID50 z 8) us
strain), as is appropriate for waters impacted by human sources.
d Haas et al. (1999) present a single-parameter model with k (¼1/r) ¼ 78.3
Akin (1981). Thesewere preliminary data for the full trial of 149 volunteers
doses reported by Akin (and by Schiff et al., 1984b) by a factor of 33, thus
different ID50 values for essentially the same trial.
e This QMRA has accounted for a proportion of the exposed population ex
the required secretor phenotype, Teunis et al., 2008). The trial was for No
f This formulation has ID50 ¼ 1003. Other formulations (which exclud
ID50z 20,000 (Haas et al., 1999). Support for a lower ID50 comes from outbr
2008).
would fail to be rejected in a traditional goodness-of-fit test
because the small sample size confers low statistical power on
these tests (McBride, 2005). Instead we used an empirical
“Hockey-stick” distribution, as described in this paper’s
Appendix A, for reasons explained therein. In particular, the
relatively small number of samples collected for each
discharge type poses difficulties for the selection of an
appropriate right-skewed distribution and also this distribu-
tion is “bounded above”, whereasmost standard right-skewed
distributions are not.
2.3.3. DoseeresponseA number of doseeresponse analyses have been reported,
mostly from clinical trials, and can be appliedwithin QMRA. In
general, the doseeresponse data are used to develop a
mathematical function of the likelihood of infection (and
sometimes illness) for given pathogen doses. In this study the
mathematical forms of the infection doseeresponse functions
have been restricted to only those that can be mathematically
ues (ID50)a Prill
b References/comment
50% Couch et al. (1966a,b, 1969),
interpreted by Haas et al. (1999)
50% U.S. EPA (2005) c
45% Rendtorff (1954), Rendtorff and
Holt (1954), interpreted by
Haas et al. (1999)
27.2 (1052) 50% Teunis et al. (1996)
55 (26) 60%e Teunis et al. (2008), with
zero aggregation parameter
0.4265 (6) 35% Ward et al. (1986), interpreted
by Gerba et al. (1996) and Haas
et al. (1999). Note that only
susceptible adults were
recruited for this trial.
9.9 (1003) 100% Rose and Gerba (1991) f
age doses, as administered in a clinical trial, rounded to the nearest
)/rz 0.693/r, where d denotes average dose and r is the probability of
eter approximate (beta-Poisson) model, Prinf z 1� (1 þ d/b)�a and so
beta distribution. Note that the beta-Poisson approximation is not
ing the value of the average dose d satisfying the exact relationship
e confluent hypergeometric function (Abramowitz and Stegun, 1972).
ly (the Couch et al. trial administered Adenovirus 4 by aerosols); the
dless of dose (following the approach of Soller et al., 2010a; Viau et al.,
), consistent with a meta-analysis of the five available trials that used
ing all six available trials (therefore including the “TU502” C. hominis
(so ID50 z 54), using clinical trial data for 60 volunteers presented by
subsequently presented by Schiff et al. (1984a) who alsomultiplied all
accounting for the emergence in the literature of apparently two very
hibiting complete immunity (29% of the clinical trial’s subjects lacked
rwalk virus (G1), assumed to also apply to other G1 and all G2 strains.
e S. Typhimurium and S. Enteritidis, see Coleman et al., 2004) have
eak data related to consumption of contaminated food (Bollaerts et al.,
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 7 5287
derived from fundamental principles (see Teunis et al., 1995;
Haas et al., 1999; McBride, 2005). Other more empirical ap-
proaches may be less generalizable and may not be satisfac-
tory. The development of these restrictedmathematical forms
assumes the following: (i) the clinical trial contains a number
of groups and only the average dose, d, received by each
member of a given group is known (to measure the concen-
tration in each subsample received by each individual is
impractical) and thus the doses received are generally
assumed to follow a Poisson distribution with knownmean d;
(ii) if, with probability r, only one pathogen survives the body’s
defences and reaches a site of the body where infection could
ensue, that is sufficient for that infection to occur (the “single
hit” hypothesis); and (iii) individuals’ susceptibilities and/or a
pathogen’s infectiousness may vary, in which case the single
parameter r is replaced by the more versatile two-parameter
beta distribution. The resulting mathematical functions are
generally well known: either the single-parameter exponen-
tial function (with parameter r) or the two-parameter “beta-
Poisson” function (with parameters a and b). These relation-
ships are described in Table 3 and are depicted in Fig. 1.
It is important to note that if QMRA calculations “expose”
only one person per exposure occasion, then that person be-
comes a representative of all persons exposed on that occa-
siondan “average person”dand so assumption (i) is necessary.
However, for very infectious pathogens (e.g., Adenovirus 4) the
cumulative frequencies of computed infections then become
extremely and implausibly jagged (McBride, 2005). Smooth cu-
mulative frequencies result only if multiple people are exposed
oneachoccasion (and indoing so theoverall infection riskmean
is preserved. In that case assumption (i) is not required (because
their individual computed doses are known) and this consider-
ably simplifies the derivation of doseeresponse curves. This is
Fig. 1 e Doseeresponse curves for infection for the six
Reference Pathogens, also showing the divergent
Norovirus curves when using average doses (1F1 case) or
individual doses (beta-binomial case).
especially important for Norovirus calculations because the
need to evaluate the troublesome confluent hypergeometric
function (seethefirst footnote toTable3)disappears. Inthatcase
infection probabilities are calculated from the beta-binomial
form Prinf ¼ 1 � B(a, b þ i)/B(a, b) (Haas, 2002; McBride, 2005),
where i is an individual’s dose and B is the standard beta func-
tion (Abramowitz and Stegun, 1972). This function is not avail-
able in Excel but it can be calculated from the logarithm of the
gamma function (which is available): B(alpha, beta) ¼EXP(GAMMALN(alpha)þGAMMALN(beta)�GAMMALN(alphaþbeta)). Both functions are displayed in Fig. 1. For the one-
parameter model, abandoning assumption (i) gives rise to the
simple binomial form: Prinf¼ 1� (1� r)i. These simple-binomial
and beta-binomial forms have been used in this work, using
parameter values given in Table 3. All QMRA scenarios reported
are based on exposing 100 people on 1000 independent
occasions.
Considerable care must be taken when using these func-
tions. In particular: (a) The doseeresponse formulation from
trials is always for infection as the endpoint but not always for
consequential illness, so some translation from predicted
cases of infection to cases of illness may be necessary, given
that illness does not always follow from infection. This is a
critical topic because, in commonwith outbreak data analysis
(e.g., Teunis et al., 2005), the epidemiological studies used to
develop recreational water quality criteriameasure the illness
endpoint (not infection); (b) The form of the “dose” used in a
clinical trial needs to be made consistent with the form used
to describe the dose ingested or inhaled. For example, the
relevant Rotavirus clinical trial (Ward et al., 1986) reported
dose as Focus Forming Units (FFU) and there may be multiple
virus particles for each FFU. This is the “harmonization” issue:
if the laboratory method used for pathogen enumeration in
the appropriate clinical trial differs from that used to assay
source-water pathogens, an investigation must be made to
ensure that the results are harmonized, via an adjustment
factor. The approach taken in this study for the seven path-
ogens is summarized in Table 4; (c) Only a limited number of
species or serovars have been examined in clinical trialsdfor
example, only Type 4 Adenovirus data are available, and this
type gives rise to respiratory and conjunctivitis symptoms
(D’Angelo et al., 1979; Mena and Gerba, 2008), whereas the
more commonly monitored Adenovirus 40/41 complex gives
rise to diarrheal illness via ingestion; (d) Trials are performed
on healthy adult volunteers, whereas children, the elderly and
immune-compromised citizens (who likely have different
doseeresponse effects) may be at elevated risk. Additionally,
there is some evidence that among adult groups there can be
differential immunity status (Lake et al., 2011). For example,
adults with regular exposure (e.g., local surfers) may have
acquired a higher immune status than the general adult
population; (e) Uncertainty in the doseeresponse equation
can be captured during the calculation process, in the form of
credible intervals or alternative parameter sets for the dos-
eeresponse curve’s equation.
2.3.4. Risk characterizationFrom repeated random sampling of exposure and pathogen
concentration distributions we obtained a distribution of
doses. Each dose is used in the doseeresponse curve to
Table 4 e Harmonization rules for pathogen detection methods used in the study and those used in clinical trials.
Pathogen This study’s method Clinical trial method Harmonization rule Rationale/Comment
Salmonella qPCR and cultivation CFU: McCullough and
Eisele (1951a,b,c);
Hornick et al. (1970)
Use cultivation results Harmonious with CFU
Cryptosporidium Microscopy IFA cell counts, qPCR:
Okhuysen et al. (1999,
2002); Chappell et al.
(2006)
Microscopy ¼ IFA Assume detects C. parvum and
C. hominis
Giardia Microscopy Microscopy: Rendtorff
(1954); Rendtorff and
Holt (1954)
Microscopy ¼ IFA
Adenovirus 40/41 qPCR (gc) for Adenovirus
A, B, C and 40/41
TCID50 viral particulates
for Adenovirus 4 inhaled
via aerosols; Couch et al.
(1966a,b, 1969)
1 TCID50 ¼ 700 genomes Genome/PFU z 1000 (raw primary
effluentdHe and Jiang, 2005).
1 TCID50 z 0.7 PFU (Dulbecco,
1988).
Enteroviruses qPCR PFU in cell line (Akin, 1981;
Schiff et al., 1984a)
1 PFU ¼ 773 RNA genomes Average genome/PFU based on
results for raw wastewaters and
artificially spiked surface waters
(Jonsson et al., 2009; Puig et al.,
1994)
Norovirus GII qPCR (for GI and GII). qPCR, Teunis et al. (2008) Divide the clinical trial
data by 18.5
Both use RT PCR but on different
genetic target sequences with
differences in critical threshold
standard curves
Rotavirus qPCR for human
rotaviral strains
Focus Forming Units (FFU),
Ward et al. (1986)
Genome: FFU z 1900 Average genome/PFU ¼ 629
(Jonsson et al., 2009; Puig et al.,
1994; de Roda Husman et al., 2009)
and data from
Payne et al. (2006): 1 PFU z 3 FFU.
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 75288
calculate an infection probability, which is then translated to
probabilities of illness, as explained in Table 3. This infection
probability value can be read either from the curve itself (not
allowing for any uncertainty in that curve) or from estimated
uncertainty intervals around the curves (in which case a
“second-order” Monte Carlo analysis may be required, e.g.,
Wu and Tsang, 2004). While some of the latter approach has
been implemented in this study, herein we focus on the
former approachdwithout loss of generality. Our Monte Carlo
simulations exposed 100 people at a site on each of 1000
separate occasions, resulting in 105 iterations. The resulting
cumulative frequency distribution is summarized via the
IIRdIndividual’s Illness Riskddefined as the total number of
individual illnesses predicted divided by the total number of
potential exposures (105). For this 100 � 1000 strategy the IIR
(as a percentage) is numerically identical to the mean value of
the short-term predicted illness risk.
Table 5 e Median and maximum values for the Hockey-Stick ddischarge types.a
RESID COMML A
Salmonella (culture), MPN per 10 L (5, 500) (5, 100) (50,
Cryptosporidium (IFA), oocysts/10 L (5, 100) (5, 100) (10,
Giardia (IFA), cysts/10 L (20, 500) (2, 10) (10,
Adenovirus 40/41 (qPCR), genomes/mL (10, 1 � 103) (10, 500) (10,
Enterovirus (qPCR), genomes/mL (10, 100) (50, 500) (1, 1
Norovirus GII (qPCR), genomes/mL (10, 1 � 103) (50, 500) (100
Rotavirus (qPCR), genomes/mL (100, 2 � 103) (50, 5 � 103) (500
a All minima were set to zero.
3. Results
3.1. Risk profiles
The pathogen concentrations that formed the basis of the
QMRA calculations herein represent the first comprehensive
data set on the abundance and occurrence of Reference
Pathogens (as defined by the U.S. EPA) in wet-weather dis-
charges to inland waters in the United States. Measured
concentrations were used to guide the choice of appropriate
medians and maxima for the Hockey-stick distributions
(Table 5). “End-of-pipe" (no dilution and direct stormwater
contact) risk profiles, and IIR values for childrens’ recreational
water ingestion were constructed for the seven source types
and for six of the seven Reference Pathogens (Cryptosporidium
oocysts, Enterovirus, Giardia cysts, Norovirus GII, Rotavirus
istribution of pathogens obtained for seven freshwater
GRIC CSO MIXED FOREO URBAN
500) (1, 100) (100, 3 � 103) (5, 50) (1, 3 � 103)
500) (10, 1 � 103) (2, 10) (100, 5 � 103) (2, 10)
100) (50, 1 � 104) (2, 20) (10, 100) (1, 50)
1 � 103) (100, 1 � 104) (10, 500) (10, 1 � 103) (10, 100)
0) (1, 1 � 103) (10, 100) (10, 100) (50, 500)
, 2 � 104) (20, 2 � 103) (1, 100) (5, 500) (10, 100)
, 5 � 104) (10, 100) (20, 2 � 104) (20, 2 � 103) (100, 1 � 103)
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 7 5289
and Salmonella); see Fig. 2 (for the ingestion pathway for chil-
dren) and Fig. 3 (for the inhalation or secondary contact
pathways by either age group after a 30-fold dilution). These
two cases span a wide range of risks. Adenovirus was not
included in Fig. 2 because of the lack of doseeresponse re-
lationships for ingestion. These graphs show the cumulative
number of cases of illness out of the 100 people exposed on
any random occasion over 1000 independent occasions: as
Fig. 2 e Risk profiles for a child’s ingestion exposure at end-of-
cysts (G), Norovirus GII (N), Rotavirus (R) and Salmonella (S) for t
which is considered for inhalation only. Prominent IIR values (%
explained above, that number numerically corresponds to the
probability of illness given random exposure. For example,
consider the predictedNorovirus illness for childrens’ primary
exposure to agricultural (AGRIC) discharges. Then for 50% of
the time (i.e., 500 of the 1000 occasions) there will be no more
than 22 Norovirus illness cases among the 100 people exposed
to this undiluted wet-weather source, and at no time will
there be more than 35 cases.
pipe for Cryptosporidium oocysts (C), Enterovirus (E), Giardia
he seven discharge types: Note the absence of Adenovirus,
) are shown on the profiles.
Fig. 3 e Risk profiles for secondary exposure (children) and inhalation (any age) after a 30-fold dilution for Cryptosporidium
oocysts (C), Enterovirus (E), Giardia cysts (G), Norovirus GII (N), Rotavirus (R) and Salmonella (S) for the seven discharge types:
Note the inclusion of Adenovirus (for inhalation only). Prominent IIR values (%) are shown on the profiles.
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 75290
Fig. 4 presents an example (synthesized) application of
QMRA for evenly-composited mixtures of pathogens found in
this study for four stormwater sources (excluding the dry-
weather urban runoff [URBAN] discharges): residential
(RESID), commercial (COMML), agricultural (AGRIC), and
forested open space (FOREO). These calculations move away
from “end-of-pipe” scenarios, which are likely to be highly
conservative, and instead synthesize a scenario for exposure
to a hypothetical receiving water by allowing a 30:1 dilution of
the source waters, representing the fact that some dilution
and inactivation of pathogens typically occurs between the
source waters and the exposure site. Three groups of swim-
mers were considered (primary contact by adults, primary
contact by children, secondary contact) for ingestion of any or
Fig. 4 e Hypothetical example of recreational risks at a site
impacted by discharge-of-concern, with four types of
stormwater discharges diluted 30:1.
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 7 5291
all of the six Reference Pathogens presented in Fig. 2. Fig. 5
shows the same type of analysis, but with Norovirus
excluded (by setting its concentration to zero).
3.2. Sources of risk
Figs. 2e5 show that Norovirus is the most dominant predicted
health risk. Even after source concentrations have been
Fig. 5 e Hypothetical example of recreational risks at a site
impacted by discharge-of-concern, with four types of
stormwater discharges diluted 30:1, with Norovirus
excluded.
reduced 30 times, the predicted short-term Norovirus illness
rates still exceed the current (recently-revised) U.S. EPA
criteria numerical limit for “NGI” (gastrointestinal illness not
necessarily accompanied by fever, mean risk ¼ 3.6%, U.S. EPA
2012)dresults not shown. However that limit refers to a 30-
day mean risk and it is possible that water receiving these
discharges could comply with that mean risk, yet, on occa-
sion, exhibit rather higher short-term risks.
Rotavirus generally induced the second-highest incidence
of risk among the tested pathogens. Risks for the other four
other Reference Pathogens (Giardia, Cryptosporidium, Entero-
virus and Salmonella) are considerably lower. Risks for sec-
ondary contact/inhalation are considerably lower than for
primary contact.
Reduction in pathogen concentrations via mixing and
inactivation does not necessarily cause a significant risk
reduction, particularly with respect to Norovirus for some
source types. This occurswhen concentrations are sufficiently
high such that their reduction does not shift the dos-
eeresponse function response down appreciably (i.e., the
doseeresponse curve is “flat” at higher concentrations, in
which case a moderate decrease in ingested Norovirus con-
centration does not significantly reduce the risk, see Fig. 1).
Appreciable risks are also associated with Adenovirus for
inhalation or secondary exposures, although this result must
be considered to be precautionary because an inhalation
exposure pathway has been assumed for Adenovirus 40/41
(which cause gastrointestinal illness not respiratory illness).
Accounting for uncertainty in doseeresponse (results not
shown here) generally causes a decrease in predicted risks
(although not so in the case of Adenovirus). As such, ac-
counting for uncertainty can lead to a less conservative
(lower) estimate of risks.
4. Discussion
This study is the first worldwide to perform QMRA using
pathogens detected in discharges into flowing inland waters
(termed “discharge-based QMRA”) rather than relying on
measurements in receiving waters themselves. Hence path-
ogens were present at higher concentrations, increasing the
likelihood of their detection compared to the much more
dilute concentrations expected in receiving waters. With the
exception of URBAN sites, data were collected (i) from typical
discharge waters and (ii) during wet weather conditions.
Therefore, the QMRA risks derived here apply to short-term
conditions and not necessarily to longer periodsda full risk
assessment should arguably consider both short-term risks
(e.g., a day after significant rainfall) and long-term risks (over a
month or a whole bathing season). U.S. federal criteria typi-
cally apply over a month (U.S. EPA, 2012) and in New Zealand
over a whole bathing season (MfE/MoH, 2003). Accordingly, if
pathogens are transported to rural receiving waters during
rainfall events, then risks posed to swimmers in those waters
during dry-weather periods should generally be lower than
presented here. However, conditions in highly urbanized
catchments (our URBAN sites) may also exhibit elevated risk
in dry conditions.
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 75292
Our results serve to indicate the relative importance of the
Reference Pathogens, and also to illuminate the risks that can
apply during or shortly after rainfall events. Wet weather
sources are typically not well-represented by epidemiological
studies, and pose a significant challenge for public agencies
with requirements to abate stormwater discharges and
comply with recreational water quality criteria. Therefore, in
this regard, QMRA may have an important role in criteria
implementation.
4.1. QMRA procedures
Some caveats must be made concerning QMRA procedures.
First, Adenovirus doseeresponse is for respiratory effects (via
inhalation of aerosols containing Adenovirus 4), so should not
be strictly applied to all adenoviruses. Second, careful
consideration is needed about the appropriate form of the
doseeresponse function. In this work we have paid particular
attention to the appropriate form of the single-parameter and
two-parameter cases. For the two-parameter case (e.g., for
Norovirus or Rotavirus) if we expose multiple individuals on
each exposure occasion, and if we calculate the dose received
by each individual, then the resulting functional form is exact
(the approximate beta-Poisson equation is not required) and is
much simpler to evaluate. Third, results show that children
may deserve special attention in QMRA analyses, even from
the point of view that their water ingestion or inhalation rates
may be higher than is the case for adults (Schets et al., 2011).
For some pathogens at least, children may also be more sus-
ceptible. For example, in a study of children’s consumption of
contaminated milk during farm visits, Teunis et al. (2005) re-
ported stronger responses to Campylobacter comparedwith the
standard infection doseeresponse function derived by
Medema et al. (1996) from clinical trials on healthy adults
(Black et al., 1988). Fourth, when presenting QMRA for use in
assessing human health impacts it will often be advisable to
consider how the uncertainty in doseeresponse curves can be
incorporated into the assessment (results not shown here).
Fifth, although this was a large study, the number of pathogen
concentration data for each discharge type is still rather small
and some of these data contained censored results (less than a
varying detection limit). In the face of that, a precautionary
approach has been taken when assigning the median values
of the pathogen distributions. In particular that resulted in a
higher assigned median rotavirus concentration for the
URBAN category than for a number of other discharge types,
and that has driven a substantial part of rotavirus illness risk
(halving the rotavirus median from 100 to 50 genomes per mL
caused the IIR shown on Fig. 2 to drop from 14.5% to about 9%).
Finally, translating the probability of infection into a proba-
bility of illness needs careful examination, particularly for
Norovirus, as discussed below.
4.2. Norovirus doseeresponse
Based on our QMRA analyses, Norovirus dominated risk pro-
files, driving a large proportion of the risk to recreational
users. Careful attention was given to the incorporation of the
Norovirus doseeresponse curve into our analyses, taking ac-
count of any new information (e.g., Seitz et al., 2011). However,
specific issues arise concerning Norovirus QMRA: aggregation,
illness response, genotype, and analytical method.
(i) Concerning aggregation, the first set of challenges used in
the clinical trial were prepared from a stock suspension in
which the virus particles were highly aggregated, but
administered in relatively low doses (Teunis et al., 2008).
A later part of the trial used an inoculum obtained from a
stool sample from a subject infected in the first part of the
trial. This inoculum was disaggregated but was adminis-
tered only at high doses. Accordingly, there is consider-
able uncertainty in the doseeresponse curve at low doses.
Furthermore the formulae presented by Teunis et al.
(2008) for the aggregation case (in terms of the Gauss
hypergeometric function, 2F1) indicate an ID50 value (for
infection) about two orders-of-magnitude higher than for
the non-aggregation case. Accordingly, Norovirus infec-
tion may be seriously over-estimated were there to be
significant aggregation in these source waters or during
downstream transport. In this study we have followed
others’ practice of ignoring aggregation (Soller et al.,
2010a; Schoen and Ashbolt, 2010; Viau et al., 2011).
(ii) Teunis et al. (2008) report a function for the probability of
illness, given that infection has occurred, predicting
remarkably low values of illness unless dose is very high
(that probability is given by 1 � (1 þ hd )�r, where, for the
non-aggregated case, h¼ 2.55 � 10�3 and r ¼ 0.086). At the
infection ID50 ¼ 26 virions (Table 3) this predicts the
probability of illness to be z0.006. In other words “the
interesting consequence is that low dose exposure may
cause infections with few symptomatic cases, whereas
high doses cause clusters of symptomatic cases” (pers.
comm., Dr P. Teunis, RIVM, The Netherlands). However in
this study we have followed the practice of other authors
(e.g., Schoen and Ashbolt, 2010) and used much higher
values of illness probabilitiesdderived from the trial data
but regardless of dose. Our finding that Norovirus is the
most dominant predicted health risk (as has also been
reported by Sinclair et al., 2009; Soller et al., 2010a) would
be diminished were we to have adopted the Teunis
formulation of the probability of illness.
(iii) TheNorovirus trial was for theNorwalk strain, which falls
into genogroup I. Genogroup II strains also can cause
illness via exposure to contaminated water (Matthews
et al., 2012), so QMRA is forced to consider all strains in
these genogroups to be similarly infectious.
(iv) Several analytical methods have been published for
Norovirus (Kageyama et al., 2003; Wolf et al., 2007, 2010;
Hewitt et al., 2011). For this study, Norovirus concentra-
tions were measured using an assay based on methods
published byWolf et al. (2007). Formost Norovirus assays,
including ours, validation tests have been limited to a
small set of known samples. Although Norovirus (G1 and
G2) is normally assumed to be specific to human fecal
sources, our study detected these viruses in forested open
space with no known human sources. A subset of positive
samples in this study have been sequenced and all were
confirmed to contain Norovirus geneticmaterial. As such,
additional work to validate the performance of Norovirus
assays in environmental waters is warranted.
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 7 5293
4.3. Pathogen fate and transport
The synthesized QMRA results herein applied a single dilu-
tion/attenuation factor (30:1) to all pathogens. In practice,
different discharge types will be subject to varying down-
stream transport (e.g., some discharges are near the exposure
site while others are far away) and pathogens will each have
different characteristics for environmental decay/persistence.
In turn, to address these site-specific issues during discharge-
based QMRA, risk assessors will need to (i) consider applying
fate and transport models to account for spatial- and time-
dependent variables and parameters and (ii) carefully apply
available data regarding the decay and persistence ofmodeled
pathogens.
4.4. Using source identifiers for QMRA
While analytical methods are becoming more readily avail-
able and less expensive, monitoring a suite of pathogens re-
quires significant resources. Quantitative data regarding the
relative importance of animal versus human sources could be
a surrogate for pathogen data. Recent research shows that
contemporary assays of Bacteroidales can quantify the rela-
tive contributions of those sources (Wang et al., 2010). Work is
underway to relate Bacteroidales concentrations to pathogens
in discharges to assess their reliability in predicting human
pathogens in discharges and supporting QMRA efforts.
5. Conclusions
The approach developed here provides a method to estimate
public health risks emanating from recreational exposure at
sites downstream of multiple discharges. Discharge-based
QMRA is particularly valuable where: (i) receiving water
measurements are limited or unavailable and (ii) when path-
ogen concentrations are often ‘non-detect’ with limits of
detection that are higher than values relevant to public health.
We provide the basic tool set to implement site-specific
QMRA, but site-specific analyses regarding the fate and
transport of pathogens-of-concern will be needed. Conclu-
sions include the following:
� This study provides strong evidence that the emerging
QMRA discipline sheds light on the potential for human
health effects caused by combinations of pathogens from
human and animal sources, particularly during and shortly
after rainfall events.
� Under the assumptions made, the findings confirm that
Norovirus infection (and possibly illness) can be the pre-
dominant risk from exposure. However additional research
is needed regarding the illness response of this Norovirus
(cf. its infection response).
� Care needs to be exercised to ensure that laboratory
methods for dose measurements are harmonized between
(i) the method used in the clinical trial that led to the
development of the doseeresponse curve and (ii) the mod-
ern methods used to assay pathogens in discharges or
receiving waters.
Acknowledgments
Funding for this project was provided by grant PATH2R08 from
Water Environment Research Foundation under the Water-
borne Pathogens and Human Health Research Program. We
also thank all of the organizations and individuals that have
come forward to give their time and effort toward this project
as a way to improve the state of the science in water quality,
fecal pathogen pollution, and risk assessment issues. In
particular, the WERF Pathogen and Human Health Project
Subcommittee, Rhonda Kranz, the U.S. Environmental Pro-
tection Agency, Desmond Till, Christobel Ferguson and J.
Soller provided guidance to this project. Harris County Flood
Control District provided valuable resources enabling the
project team to include an additional geographic region. C.
Owen from AMEC provided critical support with sample
collection and data analysis efforts. Sample collection in
Texas was performed by staff at PBS&J, an Atkins company. D.
Wang, A. Adell, A. Schriewer, N. Chouicha, A. Melli, A. Kundu
and J. Buchino are gratefully acknowledged for their help in
data collection and analysis.
Appendix A. The Hockey-stick distribution
The statistical distributions of pathogen concentrations in
environmental waters and sources can be expected to be
strongly right-skewed. However, because the sample size
(number of data) for any discharge type is small (at most 16, in
the RESID category, see Table 2), choosing the underlying
distribution is problematicaldtraditional “goodness-of-fit”
tests have difficulty in rejecting any right-skewed skewed
distribution (lognormal, gamma, extreme-value,.). That is
because these tests have low statistical power for small
sample sizes. Recognizing this, an alternative approach has
been taken in this study: the empirical “Hockey-stick” distri-
bution (McBride, 2005).
The essential idea is to use two triangular distributions,
each abutting a right-angled trapezium, given estimates of the
minimum,median andmaximumof the resulting distribution
(i.e., the percentile values X0, X50 and X100), as depicted by the
solid line in Fig. A1. The left triangle’s abscissa extends from
the minimum to the median, and so in that range the density
is a linear function of the percentile value. But it would be folly
to use a single triangular distribution for the right tail: it would
not allow for the right skewness evident in many microbio-
logical datasets (and the median would only be preserved if
the maximum and the minimum were equidistant from the
median). A simple solution is to join the median and
maximum by a “Hockey-stick”dthe line BCD in Fig. A1dto
impart some right-skew (and allowing for themaximumbeing
further away from the median). To determine the required XP
percentile (corresponding to the unknown point C on that
Figure), one further piece of information is needed: the
percentile (P), with an as-yet-unknown value XP, at which the
trapezium and the triangle on its right are joined. That is the
position of the Hockey-stick’s heel on the X-axis, where the
shaft turns into the blade. For example, we could specify that
the heel start at the 95%ile.
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 75294
To completely specify the distribution, the values of the
probability density ordinates h1 and h2 and the abscissa
percentile XP (see Fig. A1) must be derived, given that X0, X50
and X100 and P will have been stated. These quantities can be
derived from the constraint that the total area under the dis-
tribution should be unity. The algebra includes solving a
resulting quadratic, in the following sequence
h1 ¼ 1X50 � X0
XP ¼ 12
"X50 þ X100 þ 1
h1
þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðX100 � X50Þ2 þ 1
h21
þ X50ð2� 8qÞ þ X100ð2� 8sÞh1
s #
h2 ¼ 2qX100 � XP
where q ¼ 1 � p and s ¼ p � ½ (with p ¼ P/100, as defined in
Fig. A1). [Note that the h2 equation inMcBride (2005) has an X50
on the denominator, but that should be XP.] The values of X0,
X50, XP, X100, h1 and h2 define the Hockey-stick distribution
from which random samples may be drawn. Linear interpo-
lation between the distribution’s breakpoints is used. Note
that unlike many other pathogen concentration distributions
used in QMRA, the Hockey-stick has an upper bound, obtained
via expert judgment. This can be seen as advantage given that
high proportions of risk can be generated from statistical
sampling of the distribution’s tail.
Fig. A1 e The Hockey-stick empirical distribution.
Appendix B. Supplementary data
Supplementary data related to this article can be found at
http://dx.doi.org/10.1016/j.watres.2013.06.001.
r e f e r e n c e s
Abramowitz, M., Stegun, I., 1972. Handbook of MathematicalFunctions. Dover, New York.
Akin, E.W., 1981. A review of infective dose data and other entericmicroorganisms in human subjects. In: Presented at the U.S.EPA Symposium on Microbial Health Considerations of SoilDisposal of Domestic Wastewaters, Norman, OK.
Ashbolt, N.J., Schoen, M.E., Soller, J.A., Roser, D.J., 2010. Predictingpathogen risks to aid beach management: the real value ofquantitative microbial risk assessment (QMRA). WaterResearch 44 (16), 4692e4703.
Black, R.E., Levine, M.M., Clements, M.L., Hughes, T.P., Blaser, M.J.,1988. Experimental Campylobacter jejuni infection in humans.Journal of Infectious Diseases 157 (3), 472e479.
Bollaerts, K., Aerts, M., Faes, C., Grijspeerdt, K., Dewulf, J.,Mintiens, K., 2008. Human salmonellosis: estimation of dose-illness from outbreak data. Risk Analysis 28 (2), 427e440.
Byappanahalli, M.N., Whitman, R.L., Shively, D.A., Nevers, M.B.,2010. Linking nonculturable (qPCR) and culturable enterococcidensities with hydrometerological conditions. Science of theTotal Environment 408, 3096e3101.
Cabelli, V.J., 1983. Health Effects Criteria for Marine RecreationalWaters. Technical Report. EPA 600/1-80-031. U.S.Environmental Protection Agency, Health Effects ResearchLaboratory, Research Triangle Park, NC.
Cabelli, V.J., Dufour, A.P., McCabe, L.J., Levin, M.A., 1982.Swimming-associated gastroenteritis and water quality.American Journal of Epidemiology 115 (4), 606e616.
Calderon, R.L., Mood, E.W., Dufour, A.P., 1991. Health effects ofswimmers and nonpoint sources of contaminated water.International Journal of Environmental Health Research 1,21e31.
Chappell, C.L., Okhuysen, P., Langer-Curry, R., Widmer, G.,Akiyoshi, D., Tanriverdi, S., Tzipori, S., 2006. Cryptosporidiumhominis: experimental challenge of healthy adults. AmericanJournal of Tropical Medicine and Hygiene 75 (5), 851e857.
Chase-Topping, M., Gally, D., Low, C., Matthews, L.,Woolhouse, M., 2008. Super-shedding and the link betweenhuman infection and livestock carriage of Escherichia coli O157.Nature ReviewsjMicrobiology 6, 904e912.
Cheung, W., Chang, K., Hung, R., Kleevens, J., 1990. Health effectsof beach water pollution in Hong Kong. Epidemiology andInfection 105 (1), 139e162.
Coleman, M.E., Marks, H.M., Golden, N.J., Latimer, H.K., 2004.Discerning strain effects in microbial doseeresponse data.Journal of Toxicology and Environmental Health 67, 667e685.
Colford Jr., J.M., Wade, T.J., Schiff, K.C., Wright, C.C., Griffith, J.F.,Sandhu, S.K., Burns, S., Sobsey, M., Lovelace, G.,Weisberg, S.B., 2007. Water quality indicators and the risk ofillness at beaches with nonpoint sources of fecalcontamination. Epidemiology 18 (1), 27e35.
Colford Jr., J.M., Schiff, K.C., Griffith, J.F., Yau, V., Arnold, B.F.,Wright, C.C., Gruber, J.S., Wade, T.J., Burns, S., Hayes, J.,McGee, C., Gold, M., Cao, Y., Noble, R.T., Haugland, R.,Weisberg, S.B., 2012. Using rapid indicators for Enterococcus toassess the risk of illness after exposure to urban runoffcontaminated marine water. Water Research 46 (7),2176e2186.
Couch, R.B., Cate, T., Douglas Jr., R.G., Gerone, P.J., Knight, V.,1966a. Effect of route of inoculation on experimentalrespiratory viral disease in volunteers and evidence forairborne transmission. Bacteriological Review 30 (3), 517e531.
Couch, R.B., Cate, T., Fleet, W.F., Gerone, P.J., Knight, V., 1966b.Aerosol-induced adenoviral illness resembling the naturallyoccurring illness in military recruits. American Review ofRespiratory Diseases 93 (4), 529e535.
Couch, R.B., Knight, V., Douglas Jr., R.G., Black, S.H., Hamory, B.H.,1969. The minimal infectious dose of Adenovirus Type 4, thecase for natural transmission by viral aerosol. Transactions ofthe American Clinical and Climatological Association 80,205e211.
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 7 5295
Cox, P., Griffith, M., Angles, M., Deere, D., Ferguson, C., 2005.Concentrations of pathogens and in animal feces in theSydney watershed. Applied and Environmental Microbiology71 (10), 5929e5934.
de Roda Husman, A.M., Lodder, I.W.J., Rutjes, S.A., Schijven, I.F.J.,Teunis, P.F.M., 2009. Long-term inactivation study of threeenteroviruses in artificial surface and groundwaters, usingPCR and cell culture. Applied and Environmental Microbiology75 (4), 1050e1057.
Desmarais, T.R., Solo-Gabrielle, H.M., Palmer, C.J., 2002. Influenceof soil on fecal indicator organisms in a tidally influencedsubtropical environment. Applied and EnvironmentalMicrobiology 68, 1165e1172.
D’Angelo, L.J., Hierholzer, J.C., Keenlyside, R.A., Anderson, L.J.,Martone, W.J., 1979. Pharyngoconjunctival fever caused byAdenovirus Type 4: report of a swimming pool-relatedoutbreak with recovery of virus from pool water. Journal ofInfectious Diseases 140 (1), 42e47.
Dorevitch, S., Li, A., Liu, L., Scheff, P.A., 2010. Measuring WaterIngestion Among Water Recreators. Draft Report Version 1.2.Project PATH5R09. WERF, Alexandruia, VA.
Dorevitch, S., Panthi, S., Huang, Y., Li, H., Michalek, A.M.,Pratap, P., Wroblewski, M., Liu, L., Scheff, P.A., Li, A., 2011.Water ingestion during water recreation. Water Research 45(5), 2020e2028.
Dufour, A.P., 1984. EPA Health Effects Criteria for FreshRecreational Waters. United States Environmental ProtectionAgency, Toxicology and Microbiology Division, Cincinnati, OH.EPA-600/1-84-004.
Dufour, A.P., Evans, O., Behymer, T.D., Cantu, R., 2006. Wateringestion during swimming activities in a pool: a pilot study.Journal of Water Health 4 (4), 425e430.
Dufour, A.P., Wade, T., Kay, D., 2012. A review ofepidemiological studies on swimmer health effectsassociated with potential exposure to zoonotic pathogensin bathing beach water (Chapter 11). In: Bartram, J.,Bos, R., Dufour, A. (Eds.), Animal Waste, WaterQuality, Human Health. World Health Organization/International Water Association Publishers, Geneva/London.
Dulbecco, R., 1988. The nature of viruses (Chapter 44), pp. 1e26.In: Dulbecco, R., Ginsberg, H.S. (Eds.), Virology. J.B. LippincottCompany, Philadelphia, USA, p. 400.
Evans, O.M., Wymer, L.J., Behymer, T.D., Dufour, A.P., 2006. Anobservational study determination of the volume of wateringested during recreational swimming activities. In: NationalBeaches Conference, Niagara Falls, NY.
Ferguson, C., de Roda Husman, A.M., Altavilla, N., Deere, D., 2003.Fate and transport of surface water pathogens in watersheds.Critical Reviews in Environmental Science and Technology 33,299e361.
Ferley, J.P., Zmirou, D., Balducci, F., Baleux, B., Fera, P.,Larbaigt, G., Jacq, E., Moissonnier, B., Blineau, A., Boudot, J.,1989. Epidemiological significance of microbiological pollutioncriteria for river recreational waters. International Journal ofEpidemiology 18 (1), 198e205.
Fleisher, J.M., Fleming, L.E., Solo-Gabriele, H.M., Kish, J.K.,Sinigalliano, C.D., Plano, L., Elmir, S.M., Wang, J.D.,Withum, K., Shibata, T., Gidley, M.L., Abdelzaher, A., He, G.,Ortega, C., Zhu, X., Wright, M., Hollenbeck, J., Backer, L.C.,2010. The BEACHES study: health effects and exposures fromnon-point source microbial contaminants in subtropicalrecreational marine waters. International Journal ofEpidemiology 39 (5), 1291e1298.
Fontaine, M., Guillot, E., 2003. An immunomagnetic separation-real-time PCR method for quantification of Cryptosporidiumparvum in water samples. Journal of Microbiological Methods54, 29e36.
French, N., Barrigas, M., Brown, N., Ribiero, P., Williams, N.,Leatherbarrow, H., Birtles, R., Bolton, E., Fearnhead, P., Fox, A.,2005. Spatial epidemiology and natural population structure ofCampylobacter jejuni colonizing a farmland ecosystem.Environmental Microbiology 7, 1116e1126.
French, N.P., Marshall, J., Mohan, V., 2011. Campylobacter in Foodand the Environment: New and Emerging Data on Typing ofCampylobacter Strains in Animals, Environmental Matrices andHumans. Final report 07-10436. Molecular Epidemiology andPublic Health Laboratory, Massey University, PalmerstonNorth, New Zealand. Prepared for the New Zealand FoodSafety Authority and Ministry for the Environment. http://www.foodsafety.govt.nz/elibrary/industry/examining-link-with-public-health/new-and-emerging-data-on-typing-of-campylobacter.pdf.
Fuhrman, J.A., Liang, X., Noble, R.T., 2005. Rapid detection ofenteroviruses in small volumes of natural waters by real-timequantitative reverse transcriptase PCR. Applied andEnvironmental Microbiology 71 (8), 4523e4530.
Gerba, C.P., Rose, J.B., Haas, C.N., Crabtree, K.D., 1996. Waterbornerotavirus: a risk assessment. Water Research 30 (12),2929e2940.
Gutierrez-Aguirre, I., Steyer, A., Boben, J., Gruden, K., Poljsak-prijatelj, M., Ravnikar, M., 2008. Sensitive detection of multipleRotavirus genotypes with a single reverse transcription real-time quantitative PCR assay. Journal of Clinical Microbiology46 (8), 2547e2554.
Guy, R.A., Xiao, C., Horgen, P.A., 2004. Real-time PCR assay fordetection and genotype differentiation of Giardia lamblia instool specimens. Journal of Clinical Microbiology 42 (7),3317e3320.
Haas, C.N., 2002. Conditional doseeresponse relationships formicroorganisms: development and application. Risk Analysis22 (3), 455e463.
Haas, C.N., Rose, J.B., Gerba, C.P., 1999. Quantitative MicrobialRisk Assessment. Wiley, NY.
He, J.-W., Jiang, S., 2005. Quantification of enterococci and humanAdenoviruses in environmental samples by real-time PCR.Applied and Environmental Microbiology 71 (5), 2250e2255.
Hewitt, J., Leonard, M., Greening, G.E., Lewis, G.D., 2011. Influenceof wastewater treatment process and the population size onhuman virus profiles in wastewater. Water Research 45 (18),6267e6276.
Hijnen, W.A.M., Schijven, J.F., Bonne, P., Visser, A., Medema, G.J.,2004. Elimination of viruses, bacteria and protozoan oocystsby slow sand filtration. Water Science and Technology 50 (1),147e154.
Hill, V.R., Kahler, A.M., Jothikumar, N., Johnson, T.B., Hah, D.,Cromeans, T.L., 2007. Multistate evaluation of anultrafiltration-based procedure for simultaneous recovery ofenteric microbes in 100-litre tap water samples. Applied andEnvironmental Microbiology 73 (13), 4218e4225.
Hornick, R.B., Greisman, S.E., Woodward, T.E., DuPount, H.L.,Dawkins, A.T., Snyder, M.J., 1970. Typhoid fever: pathogenesisand immunological control. New England Journal of Medicine283 (13), 686e691.
Jonsson, N., Gullberg, M., Lindberg, A.M., 2009. Real-timepolymerase chain reaction as a rapid and efficient alternativeto estimation of Picornavirus titers by tissue culture infectiousdose 50% or plaque forming units. Microbiology andImmunology 53, 149e154.
Kageyama, T., Kojima, S., Shinohara, M., Uchida, K., Fukushi, S.,Hoshino, F.B., Takeda, N., Katayama, K., 2003. Broadly reactiveand highly sensitive assay for Norwalk-like viruses based onreal-time quantitative reverse transcription-PCR. Journal ofClinical Microbiology 41 (4), 1548e1557.
Kay, D., 2009. EPIBATHE Accessible Report. Project 022618, EUFramework 6. University of Wales. http://intranet.iges.aber.ac.
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 75296
uk/files/DRAFT%20Accessible%20report%20Epibathe%2012_05_09.pdf.
Lake, R., Horn, B., Ball, A., 2011. Campylobacter in Food and theEnvironment: Examining the Link with Public Health. Pathwayattribution. Client Report FW10007. A Report for the NewZealand Food Safety Authority and Ministry for theEnvironment. ESR: Christchurch Science Centre. http://www.foodsafety.govt.nz/elibrary/industry/examining-link-with-public-health/campylobacter-in-food-and-the-environment-pathway-attribution.pdf.
Leruez-Ville, M., Minard, V., Lacaille, F., Buzyn, A., Abachin, E.,Blanche, S., Freymuth, F., Rouzioux, C., 2004. Real-time bloodplasma polymerase chain reaction for management ofdisseminated Adenovirus infection. Clinical InfectiousDiseases 38, 45e52.
Leskinen, S.D., Lim, D.V., 2008. Rapid ultrafiltration concentrationand biosensor detection of Enterococci from large volumes ofFlorida recreational water. Applied and EnvironmentalMicrobiology 74 (15), 4792e4798.
Malorny, B., Hoorfar, J., Hugas, M., Heuvelink, A., Fach, P.,Ellerbroek, L., Bunge, C., Dorn, C., Helmuth, R., 2003. Inter-laboratory diagnostic accuracy of a Salmonella specific PCR-based method. International Journal of Food Microbiology 89,241e249.
Marion, J.W., Lee, J., Lemeshow, S., Buckley, T.J., 2010. Associationof gastrointestinal illness and recreational water exposure atan inland U.S. beach. Water Research 44 (16), 4796e4804.
Matthews, J.E., Dickey, B.W., Miller, R.D., Felzer, J.R., Dawson, B.P.,Lee, A.S., Rocks, J.J., Kiel, J., Montes, J.S., Moe, C.L.,Eisenberg, J.N.S., Leon, J.S., 2012. The epidemiology ofpublished Norovirus outbreaks: a review of risk factorsassociated with attack rate and genogroup. Epidemiology andInfection 140 (7), 1161e1172.
McBride, G.B., 1993. Discussion of “Health effects of swimmersand nonpoint sources of contaminated water”, by Calderonet al. International Journal of Environmental Health Research3, 115e116.
McBride, G.B., 2005. Using Statistical Methods for Water QualityManagement: Issues, Problems and Solutions. John Wiley &Sons, New York.
McBride, G.B., Salmond, C.E., Bandaranayake, D.R., Turner, S.J.,Lewis, G.D., Till, D.G., 1998. Health effects of marine bathing inNew Zealand. International Journal of Environmental HealthResearch 8 (3), 173e189.
McBride, G., Ball, A., French, N., Harper, S., Lake, R., Elliott, S.,Marshall, J., van der Logt, P., 2011. Campylobacter in Food andthe Environment: Examining the Link with Public Health.NIWA/ESR/Massey University. Report to the New ZealandMinistry of Agriculture and Forestry and the Ministry for theEnvironment. http://www.foodsafety.govt.nz/elibrary/industry/examining-link-with-public-health/campylobacter-in-food-and-the-environment.pdf.
McCullough, N.B., Eisele, C.W., 1951a. Experimental humansalmonellosis. I. Pathogenicity of strains of Salmonellameleagridis and Salmonella anatum obtained from spray-driedwhole egg. Journal of Infectious Diseases 88, 278e289.
McCullough, N.B., Eisele, C.W., 1951b. Experimental humansalmonellosis. III. Pathogenicity of strains of SalmonellaNewport, Salmonella Derby and Salmonella Bareilly obtainedfrom spray-dried whole egg. Journal of Infectious Diseases 89,209e213.
McCullough, N.B., Eisele, C.W., 1951c. Experimental humansalmonellosis. IV. Pathogenicity of strains of Salmonellapullorum obtained from spray-dried whole egg. Journal ofInfectious Diseases 89, 259e266.
Medema, G.J., Teunis, P.F.M., Havelaar, A.H., Haas, C.N., 1996.Assessment of dose response relationship of Campylobacterjejuni. International Journal of Food Microbiology 30, 101e111.
Mena, K.D., Gerba, C.P., 2008. Waterborne adenovirus. Reviews inEnvironmental Contamination and Toxicology 198, 133e167.
MfE/MoH, 2003. Microbiological Water Quality Guidelines forMarine and Freshwater Recreational Areas. Ministry for theEnvironment and Ministry of Health, Wellington, NewZealand. http://www.mfe.govt.nz/publications/water/microbiological-quality-jun03/.
Miller, W.A., Lewis, D.J., Lennox, M., Pereira, M.D.G.C., Tate, K.W.,Conrad, P.A., Atwill, E.R., 2007. Climate and on-farm riskfactors associated with Giardia duodenalis cysts in storm runofffrom California coastal dairies. Applied and EnvironmentalMicrobiology 73, 6972e6979.
Nogva, H.K., Bergh, A., Holck, A., Rudi, K., 2000. Application of the5’-nuclease PCR assay in evaluation and development ofmethods for quantitative detection of Campylobacter jejuni.Applied and Environmental Microbiology 66 (9), 4029e4036.
Okhuysen, P.C., Chappell, C.L., Crabb, J.H., Sterling, C.R.,DuPont, H.L., 1999. Virulence of three distinct Cryptosporidiumparvum isolates for healthy adults. Journal of InfectiousDiseases 180 (4), 1275e1281.
Okhuysen, P.C., Rich, S.M., Chappell, C.L., Grimes, K.A.,Widmer, G., Feng, X., Tzipori, S., 2002. Infectivity of aCryptosporidium parvum isolate of cervine origin for healthyadults and Interferon-g knockout mice. Journal of InfectiousDiseases 185, 1320e1325.
Palisade Corporation, 2009. @RISK. Advanced Risk Analysis forSpreadsheets, V.5.5.0. Newfield, New York.
Pant, A., Mittal, A.K., 2008. New protocol for the enumeration ofSalmonella and Shigella from wastewater. Journal ofEnvironmental Engineering 134 (3), 222e226.
Payne, A.F., Binduga-Gajewska, I., Kauffman, E.B., Kramer, L.D.,2006. Quantitation of flaviviruses by fluorescent focus assay.Journal of Virology Methods 134, 183e189.
Pond, K., 2005. Water Recreation and Disease Report: Plausibilityof Associated Infections: Acute Effects, Sequelae andMortality. World Health Organization, Geneva, Switzerland.
Puig, M., Jofre, J., Lucena, F., Allard, A., Wadell, G., Girones, R.,1994. Detection of adenoviruses and enteroviruses in pollutedwaters by nested PCR amplification. Applied andEnvironmental Microbiology 60, 2963e2970.
Pruss, A., 1998. A review of epidemiological studies fromexposure to recreational water. International Journal ofEpidemiology 27, 1e9.
Rajal, V.B., McSwain, B.S., Thompson, D.E., Leutenegger, C.M.,Kildare, B.J., Wuertz, S., 2007a. Validation of hollow fiberultrafiltration and real-time PCR using bacteriophage PP7 assurrogate for the quantification of viruses from watersamples. Water Research 41, 1411e1422.
Rajal, V.B., McSwain, B.S., Thompson, D.E., Leutenegger, C.M.,Wuertz, S., 2007b. Molecular quantitative analysis of humanviruses in California stormwater. Water Research 41,4287e4298.
Rendtorff, R.C., 1954. The experimental transmission of humanintestinal protozoan parasites. II. Giardia lamblia cysts given incapsules. American Journal of Hygiene 59, 209e220.
Rendtorff, R.C., Holt, C.J., 1954. The experimental transmission ofhuman intestinal protozoan parasites. IV. Attempts totransmit Entamoeba coli and Giardia lamblia by water. AmericanJournal of Hygiene 60, 327e338.
Rose, J.B., Gerba, C.P., 1991. Use of risk assessment fordevelopment of microbial standards. Water Science andTechnology 24 (2), 29e34.
Schets, F.M., Schijven, J.F., de Roda Husman, A.M., 2011. Exposureassessment for swimmers in bathing waters and swimmingpools. Water Research 45 (7), 2392e2400.
Schiff, G.M., Stefanovic, G.M., Young, E.C., Sander, D.S.,Pennekamp, J.K., Ward, R.L., 1984a. Studies of Echovirus-12 involunteers: determination of minimal infectious dose and the
wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 5 2 8 2e5 2 9 7 5297
effect of previous infection on infectious dose. Journal ofInfectious Diseases 150 (6), 858e866.
Schiff, G.M., Stefanovic, G., Young, B., Pennekamp, J.K.,1984b. Minimum human infective dose of enteric virus(Echovirus 12) in drinking water. Monographs in Virology15, 222e228.
Schoen, M.E., Ashbolt, N.J., 2010. Assessing pathogen risk toswimmers at non-sewage impacted recreational beaches.Environmental Science and Technology 44 (7), 2286e2291.
Seitz, S.R., Leon, J.S., Schwab, K.J., Lyon, G.M., Dowd, M.,McDaniels, M., Abdulhafid, G., Fernandez, M.L.,Lindesmith, L.C., Baric, R.S., Moe, C.L., 2011. Norovirusinfectivity in humans and persistence in water. Applied andEnvironmental Microbiology 77 (19), 6881e6888.
Sinclair, R.G., Jones, E.L., Gerba, C.P., 2009. Viruses in recreationalwater-borne disease outbreaks: a review. Journal of AppliedMicrobiology 107 (6), 1769e1780.
Soller, J.A., Bartrand, T., Ashbolt, N.J., Ravenscroft, J., Wade, T.J.,2010a. Estimating the primary etiologic agents in recreationalfreshwaters impacted by human sources of fecalcontamination. Water Research 44 (16), 4736e4747.
Soller, J.A., Schoen, M.E., Bartrand, T., Ravenscroft, J.E.,Ashbolt, N.J., 2010b. Estimated human health risks fromexposure to recreational waters impacted by human and non-human sources of fecal contamination. Water Research 44(16), 4674e4691.
Stevenson, A.H., 1953. Studies of bathing water quality andhealth. American Journal of Public Health 43, 529e538.
Teunis, P.F.M., 2009. Uncertainty in dose response from theperspective of microbial risk (Chapter 6). In: Cooke, R.M. (Ed.),Uncertainty Modeling in Dose Response. Wiley, Hoboken, NJ.
Teunis, P.F.M., Havelaar, A., 2000. The beta-Poisson model is not asingle hit model. Risk Analysis 20 (4), 513e520.
Teunis, P.F.M., Havelaar, A.H., Medema, G.H., 1995. A LiteratureSurvey on the Assessment of Microbiological Risk for DrinkingWater. Report no. 734301006. RIVM, Bilthoven, TheNetherlands.
Teunis, P.F.M., Moe, C.L., Liu, P., Miller, S.E., Lindesmith, L.,Baric, R.S., Le Pendu, J., Calderon, R., 2008. Norwalk virus: howinfectious is it? Journal of Medical Virology 80, 1468e1476.
Teunis, P.F.M., van den Brandhof, W., Nauta, M., Wagenaar, J., vanden Kerkhof, H., Van Pelt, W., 2005. A reconsideration of theCampylobacter doseeresponse relation. Epidemiology andInfection 133, 583e592.
Teunis, P.F.M., van der Heijden, O.G., van der Giessen, J.W.B.,Havelaar, A.H., 1996. The DoseeResponse Relation in HumanVolunteers for Gastrointestinal Pathogens. RIVM Report No.284 550 002, Antonie van Leeuwenhoeklaan 9, PO Box 1, NL-3720 BA Bilthoven, The Netherlands.
Till, D., McBride, G., Ball, A., Taylor, K., Pyle, E., 2008. Large-scalefreshwater microbiological study: rationale, results and risks.Journal of Water Health 6, 443e460.
Till, D., McBride, G.B., 2004. Potential public health risk ofCampylobacter and other zoonotic waterborne infections inNew Zealand (Chapter 12). In: Cotruvo, J.A., Dufour, A.,Rees, G., Bartram, J., Carr, R., Cliver, D.O., Craun, G.F., Fayer, R.,Gannon, V.P.J. (Eds.), Waterborne Zoonoses: Identification,Causes and Control. World Health Organization (WHO). IWAPublishing, London, UK.
U.S. EPA, 2005. Appendices to the Economic Analysis for the FinalLong Term 2 Enhanced Surface Water Treatment Rule, vol. II.(HeU) Office of Water (4606-M). EPA 815-R-06-001.
U.S. EPA, 2012. Recreational Water Quality Criteria. Office ofWater, 820-F-12-058.
Viau, E.J., Lee, D., Boehm, A.B., 2011. Swimmer risk ofgastrointestinal illness from exposure to tropical coastalwaters impacted by terrestrial dry-weather runoff.Environmental Science and Technology. http://dx.doi.org/10.1021/es200984b.
Wade, T.J., Calderon, R.L., Sams, E., Beach, M., Brenner, K.P.,Willliams, A.H., Dufour, A.P., 2006. Rapidly measuredindicators of recreational water quality are predictive ofswimming associated gastrointestinal illness. EnvironmentalHealth Perspectives 114, 24e28.
Wade, T.J., Sams, E., Brenner, K.P., Haugland, R., Chern, E.,Beach, M., Wymer, L., Rankin, C.C., Love, D., Li, Q., Noble, R.,Dufour, A.P., 2010. Rapidly measured indicators of recreationalwater quality and swimming-associated illness at marinebeaches: a prospective cohort study. Environmental Health 9(66), 14.
Wang, D., Silkie, S.S., Nelson, K.L., Wuertz, S., 2010. Estimatingtrue human and animal host source contribution inquantitative microbial source tracking using the Monte Carlomethod. Water Research 44 (16), 4760e4775.
Ward, R.L., Bernstein, D.L., Young, C.E., Sherwood, J.R.,Knowlton, D.R., Schiff, G.M., 1986. Human Rotavirus studies involunteers: determination of infectious dose and serologicalresponse to infection. Journal of Infectious Diseases 154 (5),871e880.
Wiedenmann, A., Kruger, P., Dietz, K., Lopez-Pila, J.M.,Szewzyk, R., Botzenhart, K., 2006. A randomized controlledtrial assessing infectious disease risks from bathing in freshrecreational waters in relation to the concentration ofEscherichia coli, intestinal enterococci, Clostridium perfringens,and somatic coliphages. Environmental Health Perspectives114 (2), 228e236.
Wolf, S., Williamson, W.M., Hewitt, J., Rivera-Aban, M., Lin, S.,Ball, A., Scholes, P., Greening, G.E., 2007. Sensitive multiplexreal-time reverse transcription PCR assay for the detection ofhuman and animal Noroviruses in clinical and environmentalsamples. Applied and Environmental Microbiology 73 (17),5464e5470.
Wolf, S., Hewitt, J., Greening, G.E., 2010. Viral multiplexquantitative PCR assays for tracking sources of fecalcontamination. Applied and Environmental Microbiology 76(5), 1388e1394.
Wong, T., Whyte, R., Cornelius, A., Hudson, J., 2004. Enumerationof Campylobacter and Salmonella on chicken packs. British FoodJournal 106, 642e650.
Wu, F.-C., Tsang, Y.-P., 2004. Second-order Monte Carlouncertainty/variability analysis using correlated modelparameters: application to salmonid embryo survival riskassessment. Ecological Modeling 177, 393e414.
Zmirou, D., Pena, L., Ledrans, M., Letertre, A., 2003. Risksassociated with the microbiological quality of bodies of freshand marine water used for recreational purposes: summaryestimates based on published epidemiological studies.Archives of Environmental Health 58 (11), 703e711.