United States
Environmental Protection
Agency
Risk Reduction
Engineering Laboratory
Cincinnati, Ohio 45268
Research and Development
EPA/600/S2-89/046 Mar. 1990
&EPA Project Summary
Predicting the Inactivation of
Giardia lamb Ha:
A Mathematical anjj Statistical
Model *^
Robert M. Clark, Dennis A. Black, Shirley H. Pien, and Eleanor J. Read
The 1986 amendments to the Safe
Drinking Water Act (SDWA) require
the U.S. Environmental Protection
Agency (EPA) to promulgate primary
drinking water regulations (a)
specifying criteria under which
filtration would be required, (b)
requiring disinfection as a treatment
technique for all public water
systems, and (c) establishing maxi-
mum contaminant levels (MCLs) or
treatment requirements for control of
Giardia lamblla, viruses, Legionella,
heterotrophic plate count bacteria,
and turbidity. Because the Giardia
lamblla organism Is one of the most
resistant to chlorine disinfection, the
proposed Surface Water Treatment
Rule (SWTR) specifies "Ct" values
(the product of concentration of
disinfectant in mg/L and disinfectant
contact time in minutes) for 99.9%
inactivation of Giardia cysts. Many
factors influence G. lamblla reaction
kinetics Including temperature, pH,
chlorine concentration, and inacti-
vation level. A model is developed to
describe these interactions and to
predict Ct values based on specific
model Inputs. A strategy is proposed
that uses the model to provide
conservative C1 values for regulatory
purposes.
This Project Summary was
developed by EPA's Risk Reduction
Engineering Laboratory, Cincinnati,
OH, to announce key findings of the
research project that Is fully
documented in a separate report of
the same title (see Project Report
ordering information at back).
Introduction
EPA has proposed surface water
treatment technique requirements to fulfill
the SDWA requirements for systems
using surface waters. Additional
regulations specifying disinfection
requirements for systems using ground
water sources will be proposed and
promulgated at a later date.
Under the proposed SWTR, all
community and noncommunity public
water systems would be required to treat
their surface water sources to control G.
lamblia, enteric viruses, and pathogenic
bacteria. The minimum required
treatment for each surface water would
include disinfection. In addition, unless
the source water is well protected and
meets certain water quality criteria (limits
on total or fecal coliforms and turbidity),
required treatment would also include
filtration. The treatment provided, in any
case, would be required to achieve a
99.9% removal and/or inactivation of
Giardia cysts, and at least 99.99%
removal and/or inactivation of enteric
viruses. Unfiltered systems would be
required to demonstrate that disinfection
alone achieve the minimum performance
requirements. Filtered systems that meet
certain turbidity removal and disinfection
performance criteria and that comply with
design and operating criteria specified by
the State would be considered to be in
compliance with these requirements.
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To demonstrate a water system is
achieving a specified percent inactivation,
the system would monitor disinfectant
residual(s), disinfectant contact time(s),
pH, and water temperature, and apply
these data to determine if its "C't" [the
product of disinfectant concentration
(mg/L) and disinfectant contact time
(minutes)] value equaled or exceeded the
C't value specified in EPA's rule or
Guidance Manual. Because the G.
lamblia organism is one of the most
resistant to chlorine disinfection to be
found in water, much interest and effort
has been devoted to determining its C't
values. The C't values necessary to
achieve 99.9% inactivation of Giardia
cysts by various disinfectants and under
various conditions are specified in EPA's
SWTR, and C't values recommended for
filtered systems, depending on the
appropriate level of inactivation, are
specified in the Guidance Manual
associated with the SWTR.
Many factors influence G. lamblia
reaction kinetics. Much effort was made
to develop an adquate model to describe
G. lamblia reactions with free chlorine
and then to estimate the model
parameters. This Project Summary
presents an overview of the model
development and parameter estimation
process resulting from this project.
The Ct Concept
In comparing the biocidal effective-
ness of disinfectants, major con-
siderations are the disinfectant
concentration and time needed to attain
inactivation of a certain proportion of the
population exposed under specified
conditions. The C't concept in current use
is based on the following empirical
equation:
K = C"t (1)
where
K = constant for a specific micro-
organism exposed under
specific conditions
C = disinfectant concentration in
mg/L
t = the contact time required for
a fixed percent inactivation in
minutes
It is based on the van't Hoff equation
used for determining the nature of
chemical reactions in which the value of n
determines the order of the chemical
reaction.
The application of this equation to
disinfection studies requires multiple
experiments where the effectiveness of
several variables, such as pH,
temperature, and the disinfectant
concentration, are examined to determine
how they affect the inactivation of
microbial pathogens. The value of n is a
very important factor in determining the
degree to which data extrapolated from
disinfection experiments is valid.
Destroying pathogens by chlorination
depends on a number of factors,
including water temperature, pH,
disinfectant contact time, degree of
mixing, turbidity, presence of interfering
substances, and concentrations of
chlorine available. The pM, especially,
has a significant effect on inactivation
efficiency because it determines the
species of chlorine found in solution.
The effect of temperature on
disinfection efficiency is also significant.
For example, virus destruction by
chlorine indicates that contact time must
be increased two to three times when the
temperature is lowered 10°C. Disinfection
by chlorination can inactivate Giardia
cysts, but only under the most favorable
conditions. Researchers have concluded
that (1) these cysts are among the most
resistant pathogens known, (2)
disinfection at low temperatures is
especially difficult, and (3) treatment
processes before disinfection are
important.
Studies on the use of in vitro
excystation to determine cyst viability
have shown that greater than 99.8% of
Giardia cysts can be killed by exposure
to 2.5 mg/L of chlorine for 10 min at 15°C
and pH 6, or after 60 min at pH 7 or 8. At
5"C, exposure to 2 mg/L of chlorine for
60 min killed at least 99.8% of all cysts at
pH 6 and 7. The same percentage of
cysts were killed by 8 mg/L at pH 6 and 7
after 10 min as were killed by 8 mg/L at
pH 8 after 30 min. C't values for 99%
inactivation of G. lamblia by free chlorine
at different temperatures and pH values
are shown in Table 1. The higher C't
values indicated inactivation rates
decreased at lower temperatures and at
higher pH values.
Animal Infectivity Studies
Much Giardia inactivation data are
based on excystation techniques
because few Giardia cyst inactivation
data are available based on the use of
animal infectivity as a measure of cyst
viability. Some investigators compared
mouse infectivity and excystation for
determining the viability of G. muris cysts
exposed to chlorine and reported that
both methods gave similar result
recent experiment used Mongc
gerbils to determine the effect
chlorine on G. lamblia cysts. In a s
of experiments, cysts were expose*
various time periods to free chk
concentrations ranging from 0.4 to
mg/L at 0.5, 2.5, and 5.0°C and pH
and 9. Each of five gerbils was fed
104 of the chlorine-exposed cysts
subsequently examined for evident
infection. Since the test animals had
received a dose of 5 x 104 cysts
since infectivity studies \
unchlorinated cysts showed
approximately 5 cysts usually constil
an infective dose, the follov
assumptions were made depending
the infectivity patterns occurring in
animals receiving chlorine exposed c
If all five animals were infected, tt»
was assumed that the C't had prodi
less than 99.99% inactivation; il
animals were infected, the C't
produced greater than 99.J
inactivation. It is impossible to deten
the exact level of inactivation for t
results. If, however, one to four ani
were infected, it was assumed thai
level of viable cysts were five per ar
and that 99.99% of the original
population has been inactivated.
Table 2 summarizes data for
different experimental condit
examined. Column 3 shows the ranj
chlorine concentrations in mg/L to w
cysts were exposed before being f«
the gerbils, and Column 7 shows
number of experiments which yieldet
infected gerbils out of 5. Column 4 si
the mean cyst exposure times
Column 5 contains mean C't values
are the product of the chlo
concentration and cyst exposure time
In addition to the animal infect
several other data sets were consid
as a data base for a log linear mod
Giardia cysts. The studies on w
these data sets were based
characterized (Table 3). The first que
to arise is the statistical compatibilil
the data sets. Because of the size o
data set and the fact that it is base
animal infectivity, set 2 data v
considered in all combinations.
approach used was to construe!
indicator random variable to move
regression intercept or slope
compensate for data set differences.
significance of the indicator ran
variable would support the hypothes
different regression surfaces,
incompatibility of the data sets chc
The indicator random variable
created in such a way as to ah
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Table 1. Ct Values for 99% Inactivation of Giardia lamblia Cysts by Free Chlorine
Range
Disinfectant
Temp Concentration Time Mean
(°C) pH (mg/L) (min) C't C't
5 6 1.0-8.0 6-47 47-84 65
7 2.0-8.0 7-42 56-152 97
8 2.0-8.0 72-164 72-164 110
15 6 2.5-3.0 7 18-21 20
7 2.5-3.0 6-18 18-45 32
8 2.5-3.0 7-21 21-52 37
25 6 1.5 <6 <9 <9
7 1.5 < 7 <10 <10
8 1.5 <8 <12 <12
Table 2. Ct Values for 99.99 % Inactivation Based on Animal Infectivity Data
Range of Range of Mean Cyst Range of
Temp Concentration Exposure Time Range of Mean C t Predicted C t
pH °C (mg/L) (mm) Values from Data Values
6 0.5 0.56-3.93 39-300 113-263 136-192
6 2.5 0.53-3.80 18-222 65-212 107-151
6 5 0.44-3.47 25-287 50-180 93-134
7 0.5 0.51-4.05 75-600 156-306 205-295
7 2.5 0.64-4.23 55-350 124-347 169-235
7 5 0.73-4.08 47-227 144-222 156-211
8 0.5 0.49-3.25 132-593 159-526 294-410
8 2.5 0.50-3.24 54-431 175-371 233-324
8 5 0.48-3.67 95-417 200-386 209-299
Table 3. Characterization of G. lamblia Free Chlorine Inactivation Studies
Used in Predictive Models
Data Cyst
Set Source Viability Assay Comments
1 Symptomatic human Excystation Conventional survival
curves based on
multiple samples. End
point - 0.1%
survival
2 Gerbils, adapted from Gerbil infectivity (1 0 No survival curves.
infected humans animals/sample) Endpoint sought ~
(CDC isolate) 0.01 % survival
No. of
Exp.
4
3
3
2
2
2
1
1
1
Number of
Observations
25
15
26
14
14
15
22
21
15
Symptomatic and
nonsymptomatic
humans
Gerbils adapted from
infected humans
(several isolates
used)
Excystation
Excystation
Conventional survival
curves based on
multiple samples. End
point ~ 0.1%
survival
Conventional survival
curves based on
multiple samples. End
point ~ 0.1%
survival
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differentiate between data set 2 and other
data sets considered and to move the
regression intercept not the slope. The
indicator random variable is defined as
follows:
= 0.12I027C°'19pH!i'54temP
-0.15
(8)
rO data set 2
-I data set 2
(2)
Therefore the model to be used
was defined as follows:
t = RIaCbpHctempd10" (3)
or
logt = logR + alogl + blogC +
c log pH + d log temp + ez (4)
In equations 2 and 3, when z = 0,
equation 2 is defined over data set 2, and
t = RIaCbpHctempd (5)
where
t
C
PH
temp
R,a,b,c,d
time to a given level of
inactivation
ratio of organisms
remaining at time t to
organisms at time
zero
concentration of
chlorine in mg/L
jog of the hydrogen
ion concentration
temperature in
degrees C
Regression constants
When z - 1 equation 3 is defined over
the remaining data and
(R'10«)I«CbpH<:teinpd
(6)
For data sets 1 and 2, the indicator
random variable for the intercept variable
was not significant (p-value = 0.3372). All
other data bases considered had a
significant indicator random variable at
the 0.05 level of significance. A formal
test for differences of intercept and/or
slope between data sets 1 and 2 was
conducted and no difference was
detected. Thus, statistical analysis
supports the use data sets 1 and 2 for
extending the model development and
the parameters in equation 2 were
reestimated using these data.
Model Development
With the use of the indicator random
variable approach parameters for the
predicting equations were reestimated
resulting in the following equation:
t = 0.121-0'27 C-°'81 PH2 M temp °'15 (7)
multiplying equation 7 by C yields
Equation 8 is used to calculate C't values.
Table 4 summarizes the parameter
estimates and diagnostic statistics for the
equation. The fit of the model was good,
with the regression variables explaining
86% of the variation in log (t).
The 95% confidence intervals of the
parameter estimates of equation 8 based
on the Bonferroni method are:
R: (0.0384, 0.4096)
a: (-0.2321, -0.3031)
1+ b: ( 0.0792, 0.2977)
c: (1.9756, 3.1117)
d: (-0.2192, -0.0724)
Regulatory Application
Many of the uncertainties about the
various data sets might be used to
calculate C't values. The random variable
analysis shows the statistical incom-
patibility among most of these data sets.
More work must be done to define the
impact of strain variation and in vivo
verses in vitro techniques on Ct values.
In order to provide conservative esti-
mates for Cl values when using the best
available methodology the authors sug-
gest the approach illustrated in Figure 1.
In Figure 1, the 99% confidence
interval at the 4 log inactivation level is
calculated. First order kinetics are then
assumed so that the inactivation "line"
passes through 1 at C't = 0 and the
upper 99% confidence interval of the C't
value at 4 logs of inactivation. As can be
seen the inactivation line consists of
higher C't values than do all of the mean
predicted C't values (mean) from
equation 17, and most of the data from
data set 1 and most of data set 2 data
points. Conservative C't values for a
specified level of inactivation can be
obtained from the inactivation line
prescribed by the disinfection conditions.
For the example indicated in Figure 1,
the appropriate C't for achieving 99.9%
inactivation would be 105. This approach
(assumption of first order kinetics) also
provides the basis for establishing credits
for sequential disin-fection steps.
Table 5 compares the C't values
calculated, with the use of the modified
approach, to the C't values from the
SWTR.
Summary and Conclusions
Amendments to the SDWA clearly
require that all surface water suppliers in
the United States filter and/or disinfect to
protect the health of their customers. G.
lamblia has been identified as one of the
leading causes of waterborne dise
outbreaks in the United States. G. lam
cysts are also one of the most resis
organisms to disinfection by f
chlorine. EPA's Office of Drinking W
has adopted the Cl concept to quai
the inactivation of G. lamblia cysts
disinfection. If a utility can assure th
large enough C't can be maintaine(
ensure adequate disinfection tr
depending upon site specific factor
may not be required to install filtra1
Similarly, the C't concept can be app
to filtered systems for determir
appropriate levels of protection.
In this paper, an equation has b
developed that can be used to predic
values for the inactivation of G. Ian
by free chlorine based on the interac
of disinfectant concentration, ti
perature, pH, and inactivation level.
parameters for this equation have t
derived from a set of animal infect
data and excystation data. The eque
can be used to predict C't values
achieving 0.5 to 4 logs of inactiva
within temperature ranges of 0.5 to I
chlorine concentration ranges up t
mg/L, and pH levels of 6 to 8. Althc
the equation was not based on pH va
above 8, the model is still considc
applicable to pH levels of 9 for rea;
discussed elsewhere. The equa
shows the effect of disproportioi
increases of C't versus inactivation le>
With the use of 99% confidence inter
at the 4 log inactivation levels and
applying first order kinetics to these
points a conservative regulatory strai
for defining C't at various levelj
inactivation has been proposed.
approach represents an alternative to
regulatory strategy previously proposi
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Table 4. Parameter Estimates for Equation 12
Variable DF
INTERCEP 1
LOGI 1
LOGCHLOR 1
LOGPH 1
LOGTEMP 1
Parameter
Estimate
-0.902
-0.268
-0.812
2.544
-0.146
Standard
Error
0.200
0.014
0.042
0.221
0.028
T for HO:
Parameter = 0
-4.518
-19.420
-19.136
11.535
-5.117
PROB > 1 1 1
0.0001
0.0001
0.0001
0.0001
0.0001
Variance
Inflation
0.000
1.183
1.033
1.032
1.179
1.0000 v
0.0000
O (C-t)-Pred.
• Actual (C-t)
A 99% Conf. Interval
20
40
60
80 100 120
(C
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Robert M. Clark (also the EPA Protect Officer) is with the Risk Reduction
Engineering Laboratory. Cincinnati, OH 45268 (see below); Dennis A.
Black is with the University of Nevada, Las Vegas, NV 89108; and Shirley
H. Pien and Eleanor J. Read are with the Computer Sciences Corp.,
Cincinnati, OH 45268.
The complete report, entitled "Predicting the Inactivation of Giardia lamblia: A
Mathematical and Statistical Model," (Order No. PB 89-233 4721 AS; Cost:
$15.95, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Risk Reduction Engineering Laboratory
U.S. Environmental Protection Agency
Cincinnati, OH 45268
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
U.S. OFFICIAL MAi
Official Business
Penalty for Private Use $300
EPA/600/S2-89/046
000085833 PS
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