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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