escherichia coli o157:h7 ( eco157 ) usually causes uncomplicated diarrhoea , 
 but occasionally , it is responsible for causing severe forms of illness including 
 haemorrhagic colitis , and potentially lethal haemolytic uraemic syndrome ( hus ) in humans 
 [ 1 , 2 ] . 

humans can become exposed to eco157 through direct 
 contact with an infected animal or a contaminated farm environment .
the most common mode of human exposure is through the consumption of 
 contaminated foods including meat , milk , raw vegetables and fruits .
the majority of outbreaks or illnesses with eco157 in humans , either 
 foodborne or otherwise can be traced back to cattle [ 1 , 7 , 8 ] .
a large body of information on the epidemiology of eco157 in cattle has accumulated as 
 awareness of human illness due to this pathogen has increased .
studies on 
 the presence of eco157 in cattle and their environments have revealed a seasonal pattern 
 with increased prevalence of eco157 faecal shedding during summer and early autumn [ 1012 ] . 

experimental inoculation studies have identified the sites of localization of the bacterium 
 in the gastrointestinal tract of cattle , including the jejunum , ileum , caecum , colon and 
 recto - anal junction .
the magnitude and duration 
 of shedding and the associated risk factors have been studied under both experimental [ 13 , 14 ] and 
 observational [ 15 , 16 ] settings .
a few studies have quantified eco157 transmission in 
 cattle using mathematical modelling [ 12 , 17 , 18 ] . while 
 these studies have been useful in describing eco157 transmission dynamics and identified 
 potential control strategies , the transmission rate [ often partitioned into the direct and 
 indirect ( environmental ) rate ] used in those models and the contribution of the direct and 
 environmental transmission routes to the overall infection spread , were largely assumed .
the 
 transmission rate ,  , is defined as the product of contact rate ( number of 
 contacts per unit time ) and the probability of transmission given the contact .
this is a very important quantity in modelling of 
 infectious diseases because it determines the dynamics of the infection spread predicted by 
 the model .
environment settings 
 that can be impacted by host population density and age - related susceptibility , pathogen 
 strain colonization ability and environmental factors affecting any of these 
 characteristics
. therefore , in mathematical modelling studies it is important yet 
 challenging to choose a value that closely represents the true rate of transmission . in 2004 ,
laegreid & keen estimated the transmission of eco157 in beef calves using 
 seroconversion data .
more recently , another 
 group used experimental transmission data to quantify eco157 transmission in dairy calves 
 . however , there are two major problems with 
 the transmission rates reported in these two studies : ( i ) they did not consider how the 
 level of environmental contamination with the bacterium may influence transmission , which is 
 important given that eco157 is spread by the faecal  oral route and ( ii ) they did not 
 consider the possibility of a difference in transmission among strains of eco157 .
a recent , 
 experimental inoculation study has highlighted the strain - specific differences in the 
 probability of colonization post - inoculation and in the faecal shedding pattern of colonized 
 cattle . given that different strains of eco157 
 have different host colonization abilities and shedding patterns in cattle , it is likely 
 that transmission dynamics and the transmission rate will also vary between strains of 
 eco157 .
transmission experiments under controlled settings provide a valuable means to study 
 the effect of a few selected factors ( e.g. strain type ) in which the confounding variation 
 due to other factors is minimized . the objective of this study was to estimate and compare the transmission rates for three 
 different strains of eco157 in steers under controlled experimental conditions that involved 
 joining susceptible ( non - inoculated ) steers and steers inoculated with a three - strain 
 mixture of eco157 .
the hypotheses to be tested were : ( i ) that different strains of eco157 
 have different rates of transmission from infectious to susceptible animals , and ( ii ) that 
 the rate of transmission in cattle is affected by the level of eco157 environmental 
 contamination . in an effort to explain the mechanism by which environmental contamination 
 influences eco157 transmission in animals , an in vitro experiment was 
 conducted to test survival of the three eco157 strains in bovine faeces .
all procedures were approved by the university of wisconsin  madison school of veterinary 
 medicine institutional animal care and use committee ( protocol no .
twenty - two holstein steers , aged 67 months , were selected for the transmission 
 experiment .
these steers had been used previously in a separate study involving single 
 strain challenge experiments with one of three strains of eco157 ( but no infection 
 transmission among animals )   and they were 
 reused in the current experiment for ethical reasons ( to minimize the number of animals to 
 be sacrificed ) . moreover , the experimental design partially controlled for the confounding 
 effect of host factors which might have been introduced by enrolment of different animals . 
 following the termination of the single strain challenge experiments on 23 july 2010 , the 
 steers were cleared of residual infection with eco157 by orally dosing them with 6  g neomycin ( neomycin oral solution 200  mg / ml ; agrilabs , usa ) , once daily for 5 days . 
 after completing the course of the antibiotic treatment , the steers
were confirmed to be 
 clear of eco157 by testing negative by culture and polymerase chain reaction ( pcr ) for at 
 least three consecutive recto - anal mucosal swabs ( rams ) taken on alternate days .
rams were 
 obtained by inserting sterile cotton - tipped applicators 12 inches into the rectum and 
 rubbing 34 times along the mucosal surface . 
 out of the 22 steers , 12 were randomly selected and separated for inoculation as the 
 infectious group and housed in two separate pens ( six steers each ) in one room . pens 
 within a room were separated by a corridor to prevent contact of animals between groups . 

the remaining 10 steers were housed in a separate room to serve as the susceptible 
 contacts in two replicates of the transmission experiment .
pen environment was made free 
 of eco157 by disinfection and eco157-free status was confirmed by taking environmental 
 samples before housing the steers .
the two replicates of the transmission experiment were 
 conducted to capture possible variations between experiments , so that a reliable estimate 
 of transmission could be measured .
more than two replicates for the experiment were not 
 feasible due to financial and ethical constraints . on day 0 , the 12 steers in the 
 infectious group were inoculated orally with a cocktail of three eco157 strains , each at a 
 dose of 10 colony - forming units ( c.f.u . ) .
the simultaneous inoculation of three strains was chosen in order to control 
 for the confounding effect of host factors and under the assumption that the strains do 
 not have any effect ( synergistic or antagonistic ) on each other .
each of the 12 steers was 
 inoculated by mixing 1  ml inoculum with ~10  ml clean tap water in a drinking cup .
a 
 procedure described previously   was followed 
 to ensure the inoculum was consumed .
the infection status of the inoculated steers was 
 determined 1 day post - inoculation ( p.i . ) by bacteriological culture of rams : the steers 
 were considered infectious if they were shedding at least one of the three inoculated 
 strains .
the three inoculated strains were frik47 , frik1641 and frik2533 , which have been 
 described in previous studies [ 22 , 24 ] .
briefly , the three strains have different 
 genotypes   ( e.g. frik1641 and frik2533 lacked 
 stx1 and hly933 , respectively ) and ecological 
 histories ( frik47 was involved in a ground beef - associated human outbreak , frik1641 was recovered from a raccoon and was 
 selected as a representative of non - bovine adapted strains , and frik2533 was obtained from water on a cattle farm ) . for 
 brevity , from here
onwards we will refer to frik47 , frik1641 and frik2533 strains as 
 st1 , st2 and st3 , respectively .
one day after 
 confirmation of the infectious status ( i.e. day 2 p.i . ) , five randomly selected animals 
 each from the susceptible contact group were joined with five randomly selected infectious 
 animals and each newly formed group of 10 animals was housed in one of the two separate 
 rooms .
the two groups of steers , each with five infectious and five susceptible steers , 
 established the two replicates of the experiment . for brevity
both groups were followed for 30 days to monitor eco157 colonization 
 status and environmental contamination over time by testing rams and environmental 
 samples , respectively .
the length of 30 days was chosen based on the expectation that the 
 duration of eco157 infection will not exceed 30 days .
shedding of eco157 in cattle is intermittent in nature , and so we adopted a frequency of sampling every other day , which 
 was considered frequent enough to capture the intermittent shedding behaviour and was 
 logistically feasible .
the protocol for collection of rams and environmental samples is described in kulow 
 et al . .
the rams from 
 each individual steer and samples from selected environmental locations were collected the 
 day after mixing ( i.e. day 3 p.i . ) and on alternate days thereafter for the follow - up 
 period , for a total of 15 sampling occasions . sampled environmental locations
included : 
 animal hides , feed troughs , drinking water , water - cup run - offs and pen floors .
the details 
 of the performed eco157 isolation and enumeration and pcr confirmation were as described 
 previously .
briefly , rams were placed into a 
 sterile tube containing 5  ml modified e. coli broth ( mec ; remel , usa ) and 
 novobiocin ( 002  mg / ml , mecnov ; remel ) . drinking water ( 10  ml ) was sampled directly from 
 water cups . to collect samples of hides and feed troughs ,
we used sterile cellulose 
 sponges ( 2    35    1 inch ) moistened with mecnov broth ; after sampling , a sponge was 
 placed in a sterile whirl - pak ( nasco , usa ) containing 10  ml mecnov broth .
samples from 
 water - cup run - offs and pen floor were collected using sterile nylon ropes about 3-feet 
 long and 8-mm thick ( ~52  g ; koch industries , usa ) .
colonies suspected to be eco157 were 
 presumptively identified using the rim e. coli o157:h7 latex test 
 ( remel ) . for each sample containing colonies that were positive by the latex agglutination 
 test , up to 10 randomly selected colonies were taken for strain differentiation ( i.e. to 
 identify st1 , st2 and st3 ) using pcr .
the minimum 
 detection limit was ~2 c.f.u./ml , i.e. 10 c.f.u./rams and 10 c.f.u./environmental 
 sample .
bovine faeces collected from a local farm was processed as described previously   and the water content of the faeces was reduced 
 to a final aw between 087 and 090 by heating small aliquots 
 ( ~2030  g wet feces ) in a glass dish until an aw of 087089 
 was achieved .
the 
 aw was determined using an aqualab model 4te aw 
 meter ( decagon devices , usa ) according to the manufacturer 's instructions .
the faeces were 
 then sterilized at 121c , 15 psi , for 15  min , which did not significantly change the 
 aw .
the three bacterial strains ( st1 , st2 , 
 st3 ) were grown from a single colony in 5  ml luria bertani ( lb ) broth at 37c for 
 2224  h and diluted 1:10 in 1    pbs to a concentration of ~10 c.f.u./ml .
the 
 diluted culture ( 650  l ) was mixed with 65  g dried faeces in sterile 
 dishes and incubated at 30c for 28 days .
samples were taken on days 0 , 1 , and 3 during 
 the first week and twice a week thereafter .
samples ( 05  g faeces ) were serially diluted 
 in pbs and plated in duplicate on lb agar plates , incubated at 37c for 2224  h , and the 
 number of c.f.u . enumerated .
three independent 
 experiments were performed . to facilitate proper analysis of the data , the infectious status of the individual 
 animals at each sampling day was determined and categorized into one of the three groups : 
 susceptible ( s ) , infectious ( i ) or latent 
 ( l ) . in this study , infectious ( i ) is used to indicate 
 the shedding state of an animal that is capable of infecting ( colonizing ) susceptible 
 animals .
the latent ( l ) class is used to indicate an infected ( colonized ) 
 animal during its transient non - shedding periods , when the animal is considered to be 
 non - infectious .
thus , an infected animal is intermittently in either i or 
 l class and a non - infected animal is in s class .
the infection status for each steer on each of the 15 sampling days was determined under 
 the following assumptions that reflected the intermittent shedding pattern of eco157 by 
 the infected animals as reported in gautam et al . :
( i ) an animal testing positive was considered infectious 
 ( i ) , ( ii ) an animal testing negative could be classified either as 
 latent ( l ) or susceptible ( s ) depending on the timing 
 and the number of consecutive samples that were test - negative .
if an animal was negative 
 on 4 consecutive samplings ( i.e. 8 days ) following a positive sample , it was classified 
 as latent ( l ) , otherwise susceptible ( s ) .
a steer that 
 was introduced into the experiment as a susceptible animal was considered susceptible 
 until it tested positive for the first time .
similarly , an animal that was found negative 
 on more than four consecutive sampling days ( i.e. > 8 days ) after the last positive 
 test was considered recovered from colonization , and thus susceptible again .
if an animal 
 tested negative towards the end of the study and it was not possible to apply the 
 criterion mentioned above to classify the animal into one of the two possible non - shedding 
 classes ( l or s ) because of too few negative samples , 
 then that particular sampling observation on the individual animal was censored . using the 
 above information and considering that incidents of new infections ( cases ) at consecutive 
 samplings are governed by a stochastic process
, the transmission of strain - specific eco157 
 can be described by a modified  susceptible - infectious - susceptible ( sisl ) 
 mathematical model where the infectious state branches into a latent state ( fig .
although there were three strains in the 
 transmission experiment , st3 was only detected a few times in only one 
 inoculated steer and was not detected in any of the other inoculated and susceptible 
 steers in the two groups . since no new cases of cattle colonized with st3 
 were observed the transmission rate for this strain was considered zero ( the statistical 
 estimation of the transmission rate was not possible because no new case was observed ) . 

schematic representation of the sisl transmission model of eco157 in 
 cattle . in a closed population of size
n  =  s+i+l  =  10 , the 
 number of susceptible individuals that may become infectious per time interval , 
 t , depends only on the transmission rate  ( the rate at 
 which a randomly chosen susceptible animal had successful infectious contacts in the time 
 interval t ) , the number of susceptible ( s ) animals , the 
 number of infectious ( i ) animals and the total population size 
 n. if the number of new cases c at the end of each time 
 interval ( t ) is considered a stochastic process based on a binomial 
 distribution with s possible outcomes , then the transmission rate 
  can be estimated using a function of i , s , c , n and 
 t   and can be represented 
 for our sisl system as follows:(1)where s is the number of susceptible 
 s(t ) individuals at the start of the interval , 
 i is the average number of infectious 
 i(t ) individuals during the interval , n 
 is the population size ( here n  =  10 ) and t is the 
 sampling interval . taking log on both sides , equation ( 1 ) can be expressed as:(2)here and onwards , log denotes the natural logarithm ( base e ) . from equation 
 ( 2 ) ,
log( ) can be 
 estimated from the transmission experiment data by using a generalized linear model ( glm ) 
 .
equation ( 2 ) was extended into a covariate effects model to control for the 
 effect of covariates on log( ) as follows:(3)the considered covariates were strain , st 
 ( st1 or st2 ; term 1 ) , 
 experimental group , g ( g1 or g2 ; term 2 ) , 
 and the strain- and group - specific environmental contamination level on the preceding 
 sampling day ( e ; term 3 ) .
the level of 
 environmental contamination during the immediately preceding sampling day was used because 
 contamination level on the same day of sampling is unlikely to generate a new case on that 
 very day .
lag times longer than 2 days ( i.e. the preceding sampling date ) were deemed 
 biologically irrelevant because it has been estimated   that shedding occurs at the latest 2 days after successful inoculation .
the 
 overall level of environmental contamination for a given sampling day was determined by 
 log10 transformation of the sum of the eco157 counts from all positive 
 environmental samples for a given strain and group on that day among the collected samples 
 of animal hides , feed troughs , drinking water , water - cup run - offs and pen floor .
the 
 considered environmental contamination covariate was a proxy for some true , but impossible 
 to measure , total environmental contamination on a particular day .
however , because the 
 measurements were consistently estimated for all strains , experimental groups and days , 
 they were comparable .
the above model [ equation ( 3 ) ] was 
 implemented in r version 2.13.1 ( r development core team , 2011 ) using glm function with a 
 complementary log - log link .
the glm version of the model equation is:(4)where c represents the number of new cases , 
 s defines the number of trials of a binomial distribution , 
 st is the strain of eco157 ( with st1  =  0 and 
 st2  =  1 ) , g is the experimental group ( with g1  =  0 and 
 g2  =  1 ) , e is the pathogen load in the environment during the immediately 
 previous sampling day ( continuous on log10 scale ) and 
 offset  =  log[(i / n)*t ] . in the offset term , note that if i  =  0 , this will produce an 
 indeterminate value preventing the glm from computing the transmission rate . on several 
 sampling days , there were no infectious individuals ( i.e. i  =  0 ) for 
 st2 in g1 . for those days , in order to facilitate the computation , we 
 added one infectious animal to the state i , and subtracted one from the 
 state s ( i.e. we used i+1 and s    1 ) . 

the implications of this assumption were assessed by comparing the model results from the 
 full dataset with those produced for a subset of dataset after eliminating observations 
 for st2 in g1 . in the model shown in equation ( 4 )
the 
 coefficient 0 can be interpreted as the transmission rate on 
 the log scale ( log( ) ) for st1 in g1 when 
 e  =  0 .
the coefficient 1 is the average 
 difference in log( ) between the two strains of eco157 after controlling 
 for group and e , 2 is the average difference in 
 log( ) between the two groups after controlling for strain and 
 e , and 3 is the average increase in 
 log( ) for a 1-unit increase in e after controlling 
 for group and strain differences . for the specific combination of the group , strain and 
 contamination load in e , log( ) was estimated , the 
 exponentiation of which gives transmission rate , . the intercept - only 
 form of the model in equation ( 4 ) was run 
 on the subsets of data for the individual strains to estimate the actual strain - specific 
 transmission rates in the conducted experiment .
it is important to note that 
  , as defined in this study , is frequency dependent and therefore , the 
 term 1/n is absorbed into its parameterization .
the model in equation ( 4 ) was used to 
 test the hypotheses that ( i ) transmission rates differ for two different eco157 strains 
 ( st1 , st2 ) and ( ii ) environmental contamination level influences the 
 transmission rate of these two eco157 strains in cattle .
these hypotheses were tested by 
 running several glms , including models with one covariate at a time ( univariate analysis ) 
 and models with multiple covariates considered simultaneously ( multivariable analysis ) . in 
 these analyses we considered environmental contamination as a continuous variable ( i.e. 
 log10-transformed total eco157 load ) or dichotomized variable ( representing 
 whether the environment was contaminated or not with a particular strain on a particular 
 day ) .
when using environmental contamination as a continuous covariate , the validity of 
 the linearity assumption was assessed graphically by plotting , and lowess smoothing , of 
 complementary log - log probability of the outcome variable against the explanatory variable 
 [ 33 , 34 ] .
brown - forsythe  levene 's test supported the validity of the assumption of 
 homogeneity of variances between the strain - specific data ( p  =  008 ) .
the 
 best - fitting model was selected using akaike 's information criterion ( aic  =  7726 ) .
model 
 fit was further evaluated by checking the over - dispersion parameter , which is the ratio of 
 the deviance over the degrees of freedom .
the over - dispersion parameter was slightly 
 < 1 for the final covariate model and 1 for the two strain - specific intercept 
 models ; it was therefore concluded that the final models did not have the over- or 
 under - dispersion problem . to compare survival of the three eco157 strains in bovine faeces ,
a repeated - measures 
 anova was performed on the natural log ( base e)-transformed counts of eco157 for the three 
 strains and the strain - specific decay rates were calculated using the standard exponential 
 growth / decline equation : where r  =  decay rate , 
 n(t )  =  log(c.f.u .
eco157 ) at time zero , and 
 t  =  time ( in days ) . time ( t ) was the length of time 
 between the first and the last sampling day in this experiment ( i.e. days 0 and 28 ) .
the sisl system in figure 1 was solved 
 analytically to obtain an expression for the basic reproduction number 
 ( r0 ) .
we used the next - generation matrix ( ngm ) method   to derive r0 .
the ngm 
 can be derived from the transmission matrix f and transition matrix 
 v : the ngm , h , was obtained by taking the product of matrix 
 f and the inverse of matrix v : from the spectral radius of matrix h , r0 was 
 determined to be /f . in the derived r0 
 expression 1/
represents the length of the infectious period before 
 moving into the s compartment ( indicating recovery ) or into the 
 l compartment ( indicating temporary cessation of infectiousness ) .
the 
 term f can be interpreted as the weighting variable to account for the 
 fact that only a fraction , f , of animals leaving state i 
 enter into state s while the fraction ( 1f ) temporarily 
 stops shedding and is thus considered latent ( l ) . because 
 f reduces the recovery rate , it extends the total duration of infectious 
 period ( i.e. 1/f ) .
previously , we estimated 1/ for 
 st1 to be 43 [ 95% confidence interval ( ci ) 04172 ] days and for 
 st2 to be 53 ( 95% ci 09128 ) days .
we also estimated f for st1 to be 025 
 and for st2 to be 05 .
these estimates indicate that compared to 
 st2 , st1 has on average larger  ( i.e. shorter single 
 episode of shedding ) but smaller f ( i.e. higher probability of extending 
 infection through the mechanism of intermittent shedding ) . for an infected individual ,
the total duration of effective 
 infectious period after discounting for the time spent in l 
 ( 1/f ) , was estimated as 172 ( 95% ci 16688 ) days for 
 st1 and 106 ( 95% ci 18256 ) days for st2 .
the 
 strain - specific r0 was then calculated using the derived 
 expression r0  =  /f .
none of the inoculated and contact animals developed clinical symptoms during the 
 experiments . all inoculated animals in g1 and four inoculated animals in g2 were shedding 
 at least one of the three strains of eco157 on day 1 p.i . in one of the inoculated steers , 

shedding was not detected until day 11 p.i . and this animal was considered susceptible 
 until it was first detected as positive ( when it was considered a new case ) .
four 
 inoculated steers in g1 and three inoculated steers in g2 were excreting 
 st1 on day 1 p.i .
, while only two inoculated steers were shedding 
 st2 in both groups on day 1 p.i . only one inoculated steer from g1 
 tested positive for st3 during the entire study period .
that steer 
 excreted st3 on days 1 , 11 , 13 and 15 p.i . at the average shedding level 
 in positive rams of 095 log10 c.f.u./ml .
none of the contact animals in either 
 experimental group excreted st3 during the study period . overall , average 
 numbers of positive rams between the two experimental replicates for st1 , 
 st2 and st3 were 565 , 185 and 25 , respectively .
the average 
 ( standard deviation , median ) shedding level in positive rams for st1 was 
 212 ( 132 , 191 ) log10 c.f.u./ml in g1 and 237 ( 156 , 221 ) log10 
 c.f.u./ml in g2 .
the average ( standard deviation , median ) shedding level in positive rams 
 for st2 was 177 ( 058 , 164 ) log10 c.f.u./ml in g1 and 177 
 ( 112 , 176 ) log10 c.f.u./ml in g2 .
the number of steers testing positive and 
 negative for st1 and st2 in the two experimental groups 
 for any given day is given in table 1 . 

table 1.experimental infection transmission data for the two strains of eco157 in each of 
 the two experimental groups ( g1 and g2 ) .
inoculated steers were joined with the 
 susceptible group on day 1 post - inoculationsddg1 ( n  =  10)g2 ( n  =  10)eco157 positivemodel input dataeco157 positivemodel input dataiccciscldtsteiccciscldtste014/50/546 
 st1 
 3/50/537 
 st1 
 233/50/546001 
 st1 
 3/50/5357101 
 st1 
 453/50/537002 
 st1 
 202/50/536012 
 st1 
 0673/50/537002 
 st1 
 322/52/536222 
 st1 
 6893/51/547202 
 st1 
 264/53/5454122 
 st1 
 4810112/51/546002 
 st1 

352/50/5753102 
 st1 
 2812132/51/536012 
 st1 
 04/50/526022 
 st1 
 2914152/52/546112 
 st1 
 323/50/546002 
 st1 
 016173/51/545022 
 st1 
 03/50/537002 
 st1 
 018193/51/545012 
 st1 
 03/50/537002 
 st1 
 020214/50/545012 
 st1 
 191/52/547202 
 st1 
 022234/51/545012 
 st1 
 01/53/5356112 
 st1 
 324253/50/555002 
 st1 
 01/52/545012 
 st1 
 026273/51/536012 
 st1 
 02/53/535022 
 st1 
 028291/51/546002 
 st1 
 01/53/555002 
 st1 
 030313/50/536122 
 st1 
 02/53/5455112 
 st1 
 18012/50/5280 
 st2 
 2/50/528 
 st2 
 230/50/528001 
 st2 
 1/51/5258101 
 st2 
 450/50/5010002 
 st2 
 01/52/5258102 
 st2 
 0670/50/5010002 
 st2 
 01/50/537002 
 st2 
 0890/50/5010002 
 st2 
 01/50/518012 
 s2 
 3710110/50/5010002 
 st2 
 02/53/5258312 
 st2 
 4112130/50/5010002 
 st2 
 02/50/5555102 
 st2 
 2714150/50/5010002 
 st2 
 02/51/526022 
 st2 
 016171/50/5.510102 
 st2 
 02/50/535022 
 st2 
 018190/50/519002 
 st2 
 02/52/5256122 
 st2 
 020210/50/5010002 
 st2 
 01/50/545012 
 st2 
 022230/50/5010002 
 st2 
 02/50/518012 
 st2 
 024251/50/5.510102 
 st2 
 01/50/528002 
 st2 
 026270/50/519002 
 st2 
 00/51/5159102 
 st2 
 028290/50/5010002 
 st2 
 01/51/518012 
 st2 
 030310/50/5010002 
 st2 
 01/50/527012 
 st2 
 12 sampling day ;   days post - inoculation ; 
 inoculated steers ;   contact steers ;   average number of 
 infectious steers during the time interval before sampling .
new cases were assumed 
 to be infectious in between the time interval ;   number of susceptible 
 steers at the beginning of the time interval prior to sampling ; 
 number of new cases per time interval ;   number of intermittent 
 non - shedding steers at the beginning of the time interval preceding sampling ; 
  time interval between two samplings ;   strain of eco157 ; 
  number of eco157 in the environmental sample during the preceding 
 sampling time in log10 scale .
experimental infection transmission data for the two strains of eco157 in each of 
 the two experimental groups ( g1 and g2 ) .
inoculated steers were joined with the 
 susceptible group on day 1 post - inoculation   sampling day ;   days post - inoculation ; 
 inoculated steers ;   contact steers ;   average number of 
 infectious steers during the time interval before sampling .
new cases were assumed 
 to be infectious in between the time interval ;   number of susceptible 
 steers at the beginning of the time interval prior to sampling ; 
 number of new cases per time interval ;   number of intermittent 
 non - shedding steers at the beginning of the time interval preceding sampling ; 
  time interval between two samplings ;   strain of eco157 ; 
  number of eco157 in the environmental sample during the preceding 
 sampling time in log10 scale .
the environmental samples were collected on 15 sampling days from each of the two groups 
 ( g1 and g2 ) of animals following the mixing of infectious and susceptible steers ( table 2 ) . in g1 ,
st1 and 
 st3 were recovered , respectively , on six and two out of 15 sampling 
 occasions and st2 was never detected in any of the environmental samples . 
 in g2 ,
environmental samples were positive on seven , five and zero sampling occasions for 
 st1 , st2 and st3 , respectively .
for 
 st1 , the average load ( standard deviation , median ) of eco157 in 
 positive environmental samples was 274 ( 067 , 293 ) log10 c.f.u./ml in g1 and 
 334 ( 152 , 292 ) log10 c.f.u./ml in g2 ; for st2 , the average 
 load ( standard deviation , median ) was 238 ( 110 , 268 ) log10 c.f.u./ml in g2 
 ( no samples were positive in g1 ) ; and for st3 , the average load ( standard 
 deviation , median ) was 273 ( 030 , 273 ) log10 c.f.u./ml in g1 ( no samples were 
 positive in g2 ) . table 2.eco157 load ( expressed as log10-transformed c.f.u./ml ) in the 
 environment during the infection transmission experiment for the two strains ( st1 
 and st2 ) in each of the two experimental groups by sampling day post - inoculationgroupenv .
1970001650000002840000001820000000000000000001feed 
 st1 
 0000001860000000000000000000000000000000000001water 
 st1 
 0002420000000000000000000000000000000000000001pen 
 st1 
 000317246348000288000000070000000000n.a.0000001w.cup 
 st1 
 090000000000000000000000090000000000n.a.0000002hide 
 st1 
 0002874681812910000000000000000000000001180002feed 
 st1 
 0000002510000000000000000000000000000000000002water 
 st1 
 0000000000000000000000000000000000000000000002pen 
 st1 
 000600417273000000000n.a.000300000n.a.000n.a.1592w.cup 
 st1 
 000000361000000000000000000000000n.a.0001711341hide 
 st2 
 0000000000000000000000000000000000000000000001feed 
 st2 
 0000000000000000000000000000000000000000000001water 
 st2 
 0000000000000000000000000000000000000000000001pen 
 st2 
 000000000000000000000000000000000000n.a.0000001w.cup 
 st2 
 000000000000000000000000000000000000n.a.0000002hide 
 st2 
 0000000004120000000000000000000000000001180002feed 
 st2 
 0000000000000000000000000000000000000000000002water 
 st2 
 0000000000000000000000000000000000000000000002pen 
 st2 
 000000372273268000000n.a.000000000n.a.000n.a.0002w.cup 
 st2 
 000000000000000000000000000000000n.a.000000085 feed trough sample ;   pen floor sample ; 
 water - cup run - off sample.n.a .
sample not collected because the rope was eaten by the steers ; 
 st3 was only detected from the environment in group 1 on one 
 occasion from the hide ( day 7 post - inoculation ) and on two occasions from the pen 
 floor surface ( days 3 and 7 post - inoculation ) and is not shown in the table .
eco157 load ( expressed as log10-transformed c.f.u./ml ) in the 
 environment during the infection transmission experiment for the two strains ( st1 
 and st2 ) in each of the two experimental groups by sampling day post - inoculation   feed trough sample ;   pen floor sample ; 
 water - cup run - off sample .
. sample not collected because the rope was eaten by the steers ; 
 st3 was only detected from the environment in group 1 on one 
 occasion from the hide ( day 7 post - inoculation ) and on two occasions from the pen 
 floor surface ( days 3 and 7 post - inoculation ) and is not shown in the table . in the univariate analysis , the effect of environmental contamination level significantly 
 influenced the transmission rate ( p  =  00002 ) , the group effect was 
 marginally significant ( p  =  0052 ) and the strain effect was not 
 significant .
all three covariates were used in the multivariable glm to assess the effect 
 of strain on transmission rate .
the average transmission rate per animal per day for 
 st1 in experimental group g1 in the absence of bacterial contamination 
 of the environment was 0038 ( table 3 ) .
the 
 transmission rate for st2 was on average 169 times greater than that for 
 st1 , albeit not statistically significantly different after controlling 
 for the experimental group and environmental contamination .
table 3.transmission rate (  ) with 95% confidence interval ( ci ) estimated 
 using the generalized linear model with covariates ( strain , group , environment)variables 
  
 95% cip valuebaseline*003800133009strain  st2169065437027  st1group  g215605846104  g1  e151191900006*corresponds to estimate for st1 in group 1 at log10 
 ( env )  =  0.eco157 load in the environment during the preceding sampling time ( i.e. 2 days 
 prior ) in log10 scale .
transmission rate (  ) with 95% confidence interval ( ci ) estimated 
 using the generalized linear model with covariates ( strain , group , environment ) corresponds to estimate for st1 in group 1 at log10 
 ( env )  =  0 .
eco157 load in the environment during the preceding sampling time ( i.e. 2 days 
 prior ) in log10 scale . after controlling for the strain and group factors , contamination of the environment 
 during the immediately preceding sampling day significantly increased the transmission 
 rate . on average ,
the transmission rate increased 15 times for every 1-unit ( on 
 log10 scale ) increase in the environmental contamination .
table 4 shows the increase in the mean transmission 
 rate  and the corresponding r0 for 
 st1 and st2 for increasing levels of environmental 
 contamination as predicted by the model .
table 5 
 shows the transmission rate and the corresponding r0 for the 
 two strains describing the overall dynamics in the conducted experiments that accounts for 
 the strain - specific levels of environmental contamination over time implicitly .
the 
 transmission rate estimated for st2 after eliminating observations from 
 g1 slightly increased the estimated value , but did not alter the result significantly . 

this confirmed that adding an infectious and subtracting a susceptible animal for 
 st2 on days when there were no detected infectious animals in g1 did 
 not affect the conclusions of the study .
table 4.transmission rate (  ) and basic reproduction number 
 ( r0 ) with 95% confidence intervals ( ci ) for different levels of 
 environmental contamination ( e ) represented in log10 scalestraingroupe  =  0e  =  1e  =  3e  =  5 ( 95% ci)r0 ( 95% ci ) 
  

 r 
 0 

  

 r 
 0 

  

 r 
 0 

 st1 
 g10038 ( 0013009)065 ( 022155)005709801712940285490g20060 ( 0008042)103 ( 014722)009155027464045774all0045 ( 00180097)077 ( 031167)006811702033490338581 
 st2 
 g10064 ( 0009039)068 ( 010413)00961020288242048510g20096 ( 0005182)102 ( 0051929)01441210432458072763all0086 ( 0013046)091 ( 014488)012913703874100645684 
 table 5.transmission rate (  ) and basic reproduction number 
 ( r0 ) with 95% confidence intervals ( ci ) for the two strains of eco157 
 estimated using the intercept - only generalized linear modelstrainmean  ( 95% ci)mean r0 
 ( 95% ci ) 
 st1 
 011 ( 006018)189 ( 103310 ) 
 st2 
 014 ( 007024)148 ( 074254 ) transmission rate (  ) and basic reproduction number 
 ( r0 ) with 95% confidence intervals ( ci ) for different levels of 
 environmental contamination ( e ) represented in log10 scale transmission rate (  ) and basic reproduction number 
 ( r0 ) with 95% confidence intervals ( ci ) for the two strains of eco157 
 estimated using the intercept - only generalized linear model the average number of c.f.u.s of st1 , st2 and st3 in 
 faeces over a 28-day storage period is shown in table 
 6 and the percent survival of each strain over time is presented in figure 2 .
the growth of the three strains in lb was 
 similar which resulted in essentially equal starting numbers of c.f.u.s ( viable counts ) at 
 day 0 , suggesting that the three strains have similar growth rates in the conditions 
 tested . during the first 24  h post - inoculation in faeces , all three strains displayed 
 around a 1-log reduction in viable counts with an average percent survival of 22% , 13% and 
 2% , respectively for st1 , st2 and st3 .
after this 
 initial decrease , the viable numbers of st1 remained relatively constant 
 over the 28 days of incubation ( 254    10 c.f.u./g , 10% survivors ) . by 
 contrast , st3 had the initial 1-log reduction followed by an additional 
 3-log reduction in viable counts during the 28 days of incubation ( 743    10 
 c.f.u./g , 001% survivors ) .
the survival curve of st2 was in between 
 those of st1 ( best survival ) and st3 ( poorest survival ) 
 and had a 3-log reduction during the 28 days of incubation ( 279    10 
 c.f.u./g , 008% survivors ) .
the mean decay rates estimated for st1 , st2 
 and st3 were 021 , 026 , 039 , respectively .
nevertheless , the results of 
 the repeated - measures anova and comparison of decay rates did not confirm existence of a 
 significantly different survival in the three strains .
2.comparison of the percent survival of the three eco157 strains ( st1 , st2 , 
 st3 ) in sterilized bovine faeces over time . 

count with the standard deviation ( s.d . ) , expressed per 
 million ( 10 ) , for three eco157 strains , st1 , st2 and st3 , in bovine 
 faeces during the survivability assayday 
 st1 

 st2 

 st3 
 mean 
 s.d . 

038401740351093139502410166142445509211715835786531330320330427444546064025018024103053920680240160261419025004701201001517342476040012012017211512110100030020032420929401000400100228254359003002001001 comparison of the percent survival of the three eco157 strains ( st1 , st2 , 
 st3 ) in sterilized bovine faeces over time .
count with the standard deviation ( s.d . ) , expressed per 
 million ( 10 ) , for three eco157 strains , st1 , st2 and st3 , in bovine 
 faeces during the survivability assay
the aim of this study was to quantify and compare the transmission rates of different 
 strains of eco157 in steers through a combination of an infection transmission experiment 
 and mathematical modelling .
the main finding of the study strongly supports the hypothesis 
 that the transmission rate significantly increases with increasing levels of environmental 
 contamination .
two of the three tested strains had similar transmission rates , but the third 
 did not transmit at all , supporting the hypothesis that eco157 strains are characterized by 
 different transmission rates in the cattle population . in the following sections , we will 
 describe these findings in the context of existing information and discuss important 
 implications , strengths and limitations . previously , laegreid & keen   estimated 
 r0 for eco157 in beef calves in a cow - calf operation to be 
 525 ( 95% ci 387664 ) based on time to seroconversion after birth , using final size of the 
 infected population .
this means that one calf could contribute to at most one case when it 
 seroconverted for eco157 and could not account for re - infection . in our study , we allowed 
 the animals to contribute to more than one case by permitting them to join the susceptible 
 group immediately after recovery from infection . later , another group   estimated r0 of eco157 in dairy calves 
 to be 73 , based on the transmission experiment data under field conditions ( i.e. the calves 
 were raised in outside pasture ) with a sampling interval of 1 day , and in dairy cattle to be 
 07 , based on the shedding prevalence with a sampling interval of 1 month .
the sampling 
 interval of 1 month that they used in dairy cattle is longer than the average duration of 
 infectiousness for two strains of eco157 we estimated in a previous study   ( 172 days for st1 and 106 days 
 for st2 ) , which may have resulted in the r0 
 estimate of < 1 in dairy cattle .
furthermore , those studies only considered the 
 infectious animals in the transmission model and did not consider the influence of eco157 
 load in the environment ; neither did they consider the intermittent shedding pattern 
 explicitly in the model . in the current study we have included the effect of environmental 
 contamination in the estimation of transmission rate ( and showed how eco157 transmission in 
 cattle is affected by the level of bacterial contamination in the barn environment ) and 
 explicitly represented the intermittent shedding pattern in the model .
if the duration of 
 infectiousness is not corrected for the intermittent shedding pattern ( i.e. by discounting 
 the period of non - shedding ) , it will lead to overestimation of 
 r0 .
the differences between our and their estimated values of 
 r0 could be partly due to the differences in the level of 
 environmental contamination with the bacterium , due to strain differences and/or the 
 experimental setting .
regarding intermittent shedding as modelled in our study , it is 
 possible that the recorded intermittent shedding actually represented shedding that 
 alternated below and above the detection level .
however , the detection level in our study 
 was relatively low ( 2 c.f.u./ml ) . therefore , even if an animal recorded as negative was 
 actually shedding at a level of < 2 c.f.u./ml , we believe that such an animal was less 
 infectious than the animals that tested positive and that it is appropriate to consider such 
 an animal as non - infectious .
although not significantly different , the mean transmission rate for st1 
 was smaller than that estimated for st2 .
however , due to a substantially 
 longer duration of infectiousness of st1 , the mean 
 r0 values computed for this strain for several different fixed 
 values of environmental contamination were similar to those estimated for 
 st2 ( table 4 ) .
furthermore , the 
 overall r0 estimated for st1 was higher than 
 that estimated for st2 ( table 5 ) , 
 which may be explained by a higher average load of st1 in positive 
 environmental samples ( 274 log10 c.f.u./ml in g1 and 334 log10 
 c.f.u./ml in g2 ) compared to st2 ( no positives in g1 and 238 
 log10 c.f.u . in g2 ) . according to velthuis et al . , our study had a very low power to detect a 
 difference between st1 and st2 even if such a difference 
 exists , but would have had a reasonable power ( up to 80% ) to detect a difference between 
 st3 and either of the strains st1 or 
 st2 should the data for st3 have allowed statistical 
 comparison .
that said , detecting a small difference in strains , such as that between 
 st1 and st2 , would have a limited practical value from 
 the control point of view and would not be of interest .
the estimate of the transmission rate for the two strains when the environment is 
 completely clean may represent the contribution of direct transmission from an infectious to 
 susceptible animal , or somewhat less likely although not impossible , indirect transmission 
 through environmental locations not represented in our sampling plan . when 
 e  =  0 , the corresponding r0 values for the 
 strains were < 1 suggesting that infection would die out if there is only direct 
 transmission present . with an increase in the contamination level , 

r0 quickly exceeds 1 , indicating the critical role of bacterial 
 concentration in the environment in causing an outbreak and sustaining transmission . 

provided that our results are generalizable to field conditions , the identified influence of 
 environmental contamination in the spread of eco157 indicates the importance of control 
 strategies which either aim to decrease the frequency or rate of eco157 faecal shedding , 
 such as vaccination   or promote elimination of 
 the pathogen from the environment such as through barn cleaning .
moreover , the results indicate a major role of environmental 
 transmission and only a minimal role of direct transmission in the epidemiology of eco157 in 
 cattle .
these results have implications for the current practice of mathematical modelling 
 in epidemiology of eco157 in cattle .
assuming that the results obtained for the eco157 
 strains and experimental conditions evaluated in this study hold for all eco157 strains and 
 in field conditions , the results suggest that the infection spread should be modelled with a 
 predominant rate of environmental transmission ( i.e. occurring through the contaminated 
 environment ) while the rate of direct transmission should be negligible .
this is important 
 because mathematical models of eco157 in cattle have largely used assumed arbitrary values 
 for the rate of direct and environmental transmission [ 12 , 18 , 38 ] . from previous studies [ 22 , 24 ] we know that host - to - host variation plays an important role in 
 eco157 colonization and shedding
accordingly , it was important to control for the 
 confounding effect of host factors in the infection transmission experiment . however , it is 
 also important to understand whether there could be any between - strain interactions ( e.g. 
 competition ) that would mask the true colonization or transmission characteristics of the 
 strains represented in this study . while we did not have the means to verify
whether 
 transmission could have been different if the steers were infected with a single strain , we 
 did have the data from a separate single strain inoculation experiment [ 22 , 24 ] to 
 compare colonization and shedding patterns of these strains on the same experimental 
 animals .
the shedding and colonization pattern for the three strains in steers inoculated 
 with a mixture of strains compared closely with the shedding and colonization pattern when 
 steers were inoculated with a single strain .
for example , st3 was not shed 
 by the inoculated steers during the single strain inoculation experiment   and it was not shed by the steers when inoculated 
 with a mixture of strains .
st1 showed better colonization ability with more 
 episodes of intermittent shedding than st2 in the single strain experiment 
  and a similar pattern was observed in the 
 steers inoculated with the mixture of strains in the transmission experiment .
based on these 
 similarities , we feel comfortable assuming that transmission characteristics would have been 
 similar had the transmission experiment been conducted separately for st1 , 
 st2 and st3 on these same animals ( which would have been flawed 
 because of the effect of age of the steers on eco157 colonization and shedding patterns 
 [ 39 , 40 ] ) .
we used a cut - off of four sampling days to determine whether a steer was latent or 
 recovered , very similar to what has been described by previous studies [ 21 , 41 ] .
it is 
 possible , but not likely , that the cut - off choice was incorrect to the extent that it would 
 significantly alter the results .
all animals were rigorously tested to ensure they were free 
 of eco157 at the beginning of the experiment .
considering that the test used could detect 
 eco157 at a concentration of 10 c.f.u./rams , it is highly unlikely that any steer would 
 continue to shed below this level for three consecutive sampling days ( 6 days ) without 
 clearing from infection .
false - negative results , if any , would therefore be minimal and 
 unlikely to have affected the findings of the experiment . in an attempt to explain the results of the infection transmission experiment described 
 here we conducted assays of survivability of the three eco157 strains in bovine faeces .
the 
 observed trend suggested that st1 survived better than st2 
 and even more so than st3 ( fig .
2 ) , 
 which would explain why st1 was isolated more often than 
 st2 ( and substantially more often than st3 ) from the 
 environmental samples during the transmission experiment .
however , despite the trends , no 
 statistically significant difference was found in the strains which may have been due to the 
 low number of replicates or because there truly is no difference . in summary ,
the results indicate that one of the three tested strains did not transmit at 
 all in cattle while the other two strains had considerable , but indistinguishable , 
 transmission rates .
for the two transmitted strains , the main finding is that the level of 
 environmental contamination strongly , positively influences the rate of infection 
 transmission in animals .
one of the two strains ( st1 ) had on average higher 
 r0 values compared to the other strain ( st2 ) , 
 which was attributed to its longer duration of infectiousness and the ability of this strain 
 to maintain a higher load of the pathogen in the environment .
this implies that the on - farm 
 measures to reduce shedding duration and decrease the pathogen load in the environment are 
 important in the transmission and control of eco157 in cattle .
it also has implications on 
 the practice of mathematical modelling of eco157 spread and the underlying understanding of 
 the contribution of the direct and environmental transmission to the overall infection 
 spread .
 summarya pen infection - transmission experiment was conducted to elucidate the role of pathogen 
 strain and environmental contamination in transmission of escherichia 
 coli o157:h7 ( eco157 ) in cattle . 
 five steers were inoculated with a three - strain 
 mixture of eco157 and joined with five susceptible steers in each of two experimental 
 replicates . 
 faecal and environmental samples were monitored for eco157 presence over 30 
 days . 
 one eco157 strain did not spread . 
 transmission rates for the other two strains were 
 estimated using a generalized linear model developed based on a modified 
  
 susceptible  infectious  
 susceptible mathematical model . 
 transmission rates estimated for 
 the two strains ( 011 and 014 ) were similar . however , the rates significantly 
 ( p  =  00006 ) increased 15 times for every 1-unit increase in the level 
 of environmental contamination measured as log10 c.f.u . 
 depending on the level 
 of environmental contamination , the estimated basic reproduction numbers varied from 
 < 1 to 8 . 
 the findings indicate the importance of on - farm measures to reduce 
 environmental contamination for eco157 control in cattle that should be validated under 
 field conditions . 
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION