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Applied and Environmental Microbiology, October 2005, p. 5765-5770, Vol. 71, No. 10
0099-2240/05/$08.00+0 doi:10.1128/AEM.71.10.5765-5770.2005
Copyright © 2005, American Society for Microbiology. All Rights Reserved.
Department of Farm Animal Health, Faculty of Veterinary Medicine, Utrecht University, Yalelaan 7, 3584 CL Utrecht, The Netherlands,1 Animal Sciences Group, P.O. Box 65, 8200 AB Lelystad, The Netherlands2
Received 21 December 2004/ Accepted 3 May 2005
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Several control measures have been implemented to reduce the exposure of humans to Campylobacter spp., either by reducing the incidence of Campylobacter infections in broiler flocks by biosecurity measures at farms or by improving slaughterhouse hygiene. However, these measures are apparently not sufficiently effective, because many broiler flocks still become colonized with Campylobacter spp. (5). Therefore, intervention strategies should be improved or alternatives developed.
Current intervention strategies are based on risk factors identified in field surveys (6, 12, 34). An important disadvantage of these field surveys is that they used associative static models to determine an association between risk factors and the presence of Campylobacter in a flock and were based on qualitative data on the infection status of the flocks at the end of the production period. These studies did not take the dynamic aspects of a Campylobacter infection in a flock into account. Quantitative knowledge of the transmission of Campylobacter is important for the development of control programs for various reasons (8). First, it enables us to determine which measures can reduce transmission, and to what extent (10). Secondly, the transmission rate affects the prevalence of an infection in a population in time, which, in turn, determines the probability of detection. Finally, it may help to determine the moment of introduction of Campylobacter in commercial broiler flocks under field conditions (14, 16, 30). With this knowledge, control measures could focus more on high-risk periods, which might facilitate the maintenance of biosecurity measures at the appropriate level.
Clear quantitative information on Campylobacter transmission is still lacking, although some transmission experiments have been carried out (30, 33). Unfortunately, transmission in these studies was only determined qualitatively. Hartnett et al. (15) analyzed the experiments (30) and did quantify transmission, but their exact method of analysis is unclear. Data from the study of Jacobs-Reitsma (19) were available for further analysis. That group carried out four experiments to determine whether groups of 400 broilers could be colonized after introduction of a few Campylobacter-inoculated seeder birds. This experimental setup, with four seeder birds per group, a high sampling frequency scheme, and relatively large sample sizes, offered the opportunity to quantify transmission. Here, we present the results of a further quantitative analysis of these data (19) and a quantification of the transmission using a mathematical model. These models can be useful in unraveling complex processes at the population level by clarifying some of the factors that determine the speed and scale of transmission of an infectious disease (3, 11, 23). In addition, we show how the transmission parameter could be used to estimate the moment of Campylobacter introduction in the field and how the precision of this estimation is affected by the sampling scheme and sample size.
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Housing.
In each experiment, 400 broilers were accommodated at day of hatch in a separate shed at a density of 20 broilers per m2, which is similar to the housing density under commercial conditions. The broilers were fed commercial broiler feed. They were housed on wood shavings, and the drinking water was supplied by means of a nipple drinking system. Before the start of the experiments, samples were taken from water, feed, and wood shavings in the broiler sheds and tested for Campylobacter. The box liners used in the hatchery were tested for Campylobacter as well.
Inoculation.
The Campylobacter strains and inoculation doses are listed in Table 1. Campylobacter coli strain C136 was isolated from a pig farm in March 1990 (16). Campylobacter jejuni strain C356 was isolated in 1990 from broilers (Penner serotype O2) (18) and registered in the CAMPY-NET reference set as number CN076 (14). The strains are stored in glycerol at 80°C and have often been used by the Animal Sciences Group in Lelystad for infection experiments and as reference control strains (9). C. jejuni strain C4021 (experiment 4) originated from the parent flock of the chicks.
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TABLE 1. Challenge strains and inoculation doses
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Experimental design.
In experiments 1 and 2, four chicks per group were orally inoculated with 0.1 ml of the Campylobacter inoculation suspension at day of hatching. In experiments 3 and 4, four chicks per group were orally inoculated with 0.1 ml of the Campylobacter inoculation suspension 1 day after hatching. The inoculated chicks (seeders) were marked on the head with a black spot, were given an identification wing number, and were placed back into their shed. All experiments lasted 42 days. The use of four seeders increases the probability that a large outbreak will occur, allowing transmission to be quantified more accurately (11). The experiment was approved by the Animal Care and Use Committee (license number 44600).
Sampling.
The chicks were sampled at fixed time points (Table 2), starting 1 day after inoculation. In experiments 1 and 2, the four seeders and 50 chicks, chosen at random, were removed from the groups for sampling for Campylobacter by cloacal swabbing. After sampling, the broilers were put back into their groups. In experiments 3 and 4, the seeders were removed from the groups for the time necessary to obtain a fresh (cecal) dropping. A swab was taken from these droppings. Fifty samples of soft, fresh, wet, and homogeneous cecal droppings were collected from the boiler sheds, which were divided into five sectors (1 by 4 m each). Defecation was stimulated by turning on the lights and making a noise, which ensured the samples were fresh. When all samples appeared to be Campylobacter positive, the sample size was reduced in all four experiments to 10 or 12 per group.
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TABLE 2. Number of contact infections in each experiment
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Quantification of transmission.
A susceptible-infectious (SI)-type model was used to describe the dynamics of transmission with time (3, 11). In such a model all individuals are considered to be identical and each individual can be in one of two stages: susceptible or infectious. The model then describes the changes in the fraction of individuals in the two states, with s(t) being the proportion of susceptible birds at time t and i(t) the proportion of infectious birds. The SI model assumes that once a bird becomes infected, it will remain infectious during the experimental period (16) and that contacts within the population are random. In addition, both classes S and I are assumed to be homogeneous, and the transmission rate is taken to be constant during the entire infectious period and equal for all infectious broilers.
Susceptible birds are assumed to become infected at the rate of ßs(t)i(t). The transmission rate parameter ß can be defined as the average number of secondary cases caused by one infectious bird per time unit in a susceptible population (11). Although transmission between individuals is inherently a chance process, the dynamics in a large enough population can be approximated by a deterministic differential equation. In the case of the SI model we have the following equation: di(t)/dt = ßs(t)i(t), of which the solution is the logistic curve i(t) = ceßt/(1 + ceßt), with c = i(0)/[1 -i(0)], i(0) being the proportion of infectious birds at t = 0. The curve is shown in Fig. 1.
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FIG. 1. Simulated course of Campylobacter infection in a population of 400 broilers, starting at t = 0. The middle curve is the deterministic (logistic) curve; the other two are random simulations. As can be seen, the deterministic and stochastic curves are similar, except for a time shift due to random effects in the initial phase of the outbreak.
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) was added to the model to account for a possible time shift in the start-up of the epidemic process caused by, for example, the experimental setup, the strains used, the inoculation dose, age, or stochastic effects. This resulted in the following model for the log-odds of i(t):
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The model was fitted by a standard logistic regression, with ln[i(0)/(1 i(0)] as offset, t as covariate, and a as intercept. The fit resulted in an estimate for ß and for a, from which the delay
was calculated as
= a/ß.
Separate models were fitted for each experiment, resulting in four ß values and four a values, and shared models were fitted in all possible combinations of these experiments, resulting in common ß values for the different experiments. The Akaikes information criterion (7) was used to decide which model had the best fit and to see whether different values of ß should be adopted for different (sets of) experiments.
As an example of how ß can be used, we investigated the precision with which the moment of Campylobacter introduction can be estimated by regularly sampling the flocks. We simulated 10,000 outbreaks in flocks of 20,000 chicks with ß = 1.04 (the estimation result) and starting at time t = 0. Simulations were carried out using the so-called Sellke construction (4): first, for each bird j a value Qj is drawn from an exponential distribution with mean 1. Then, the epidemic is reconstructed by supposing bird j becomes infected when the cumulative infectiousness ß
0ti(u)du reached Qj, with i(u) being the fraction of infected birds at time u. In this simulation, 10, 20, or 60 birds were sampled every 1, 3, 7, or 14 days, the time of the first sample having been randomly selected from the appropriate uniform distribution, and the number of infected birds at time t was recorded. The resulting proportion of infected birds at each sampling time was then used to carry out a logistic regression analysis, as described above, in which either ß was fixed at 1.04 and only a was estimated (and consequently
) or both ß and a were estimated. Because every simulation started at t = 0, the estimated
is the error made in estimating the time of Campylobacter introduction. Thus, the 10,000 simulations yielded estimation errors for each combination of sample size (10, 20, or 60) and sampling interval (1, 3, 7, or 14 days).
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Quantification of transmission.
The logistic regression model was used to estimate ß for each experiment separately and to estimate shared ß values in all possible combinations. As the simplest model with a single ß for all four experiments had one of the lowest Akaikes information criterion scores, there was no evidence that a more complex model was needed. The joint ß was estimated at 1.04 per day with a standard error of 0.06, which means that after introduction of Campylobacter in a flock, each broiler will infect on average 1.04 new broilers per day. The estimated intercepts c were 2.57 (standard error [SE], 0.47), 2.77 (SE, 0.48), 6.06 (SE, 0.71), and 7.416 (SE, 0.78) for experiments 1, 2, 3, and 4, respectively. This resulted in estimated delay times of 2.4, 2.7, 5.8, and 7.1 days, respectively.
Because only four birds were initially inoculated, it was hypothesized that the observed delay times, and also the differences between the estimated delay times for the four experiments, were due to chance. Therefore, we tested whether the observed delay times were due to stochastic effects of the transmission process by simulating 10,000 transmission experiments with the stochastic version of the SI model, with ß = 1.04, N = 400, and i(0) = 1/400 or 1/100. Simulations were carried out with the Sellke construction (3) as described above. For each simulation, we determined the delay time by comparing the time it took until i(t) = 0.5 with its deterministic expectation. Delay times were obtained for two different initial conditions, namely, four infected chicks, as in the experiment [i(0) = 1/100], and one infected chick, as an example of an extreme case of unsuccessful inoculation [i(0) = 1/400]. The 0.5, 2.5, 5, 50, 95, 97.5, and 99.5 delay time percentiles are shown in Table 3.
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TABLE 3. Expected delay times under two initial conditions: one or four inoculated chicks [I(0) = 1 or 4]a
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Table 4 shows the 90% intervals of the estimation errors when flocks of 20,000 chicks are regularly sampled to estimate the time of Campylobacter introduction. If ß were assumed to be 1.04, then 1-day, 3-day, and 7-day sampling intervals had comparable errors, irrespective of whether 10, 20, or 60 samples were taken. Precision decreased only with a 14-day sampling interval. If there is no information on ß, then more intensive sampling would be needed, in order to generate enough data to estimate ß. Note that even the most precise estimate of the time of introduction may be wrong by 3 days, due to chance effects at the beginning of the infection chain.
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TABLE 4. Precision of determination of the time of Campylobacter introduction into a flock of 20,000 broilers, with different sample sizes and sampling intervalsa
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In contrast to what is assumed to occur in the field, that is, that an infection starts with one infected bird, we started the infection with four seeders. We chose this approach to minimize the risk of an unsuccessful experiment due to a failed inoculation and the variability in the infection course, which would make it impossible to accurately quantify transmission. Starting with more than one seeder does not affect the parameter estimate, because the transmission rate is not related to the number of seeders but only depends on the number of infections and susceptible birds present. The parameter is an estimate on an individual broiler level and can be estimated properly, even when the infection starts with more than one infectious bird, but only given that a major outbreak is observed. Choosing four seeders is a compromise between guaranteeing this and staying close to a natural introduction (colonization of one bird).
Mathematical models are important tools for assessing the best means of containing an outbreak, and they help to clarify some of the associations between epidemiological factors (23). However, the assumptions on which a model is based should be examined carefully. The model we used assumed that the birds mixed randomly, which seems reasonable given the observations of Preston and Murphy (26). However, Hartnett et al. (15) interpreted the same data differently and assumed that broilers stay within a cluster and that clusters move. However, since our simpler mathematical model fit the experimental data well, we see no reason to introduce a more complicated model for contact structure.
The overall estimates of ß did not differ significantly among experiments 1 to 4, indicating that despite various circumstances the infection processes run a similar course, but the delay time (i.e., time between inoculation of the seeders and the occurrence of the first contact infections) did differ. The delay time for experiments 1 and 2 was approximately 2 days and for experiments 3 and 4 about 5 to 7 days. Stochastic simulations with the SI model indicated that this delay time could not be explained by chance alone. In vitro passage and deep frozen storage of strains might have adversely influenced the initial colonization potential of the strains (22, 27, 30, 32, 35), whereas the colonization potential would be stronger after the strain had adapted to the alimentary tract of broilers, especially the seeders. This phenomenon, however, would be observed in all four experiments, as all strains were treated comparably, and so other explanations should be considered.
In experiments 1 and 2 cloacal swabs were analyzed, which might be a less sensitive method than analyzing cecal droppings, as performed in experiments 3 and 4; however, the correlation between the two methods is reported to be high (13). Since the detection limits were equal for individual birds within each experimental group, this difference does not affect the shape of the epidemic curve (Fig. 1) but shifts it to the left or right. If the exact dynamics of Campylobacter colonization and the detection limits are known, it would be possible to correct for this, but unfortunately this was not the case. The consequence of different detection limits would be that the differences in delay time between experiments 1 and 2 and experiments 3 and 4 are even larger than reported here.
Another possible explanation for the differences in delay times between the experiments is the use of different Campylobacter strains, as it is known from other studies that strains differ in their colonization capacities or transmissibilities (1, 8, 20, 35). This hypothesis might be investigated further. Also, the inoculation doses or the presence of maternal antibodies in the broilers of experiments 3 and 4 might explain the differences in delay time (28). However, all inoculation doses were rather high, and most inoculated chicks started shedding only a few days after inoculation. Therefore, it is not likely that the dose or antibodies caused the time delay in transmission. Thus, although there are several possible explanations, the exact cause of the difference in delay times needs to be investigated further. Because the transmission rate parameter ß is not affected by the delay time, this parameter can still be used in further studies to evaluate control measures for their reduction of the transmission of Campylobacter or to determine the within-flock prevalence over time in the field.
As with all laboratory studies, there is the question to what extent findings can be extrapolated to the field situation. However, in this instance, the problem with extrapolation is only relevant for the start of the epidemic, when the first birds become colonized and when the prevalence is still low. In this phase of the epidemic, chance processes play an important role. However, our results suggest that once the infection is spreading, the time taken to go from a prevalence of 5% to 95% will be approximately the same in various situations, allowing extrapolation to the field, which is substantiated with observations in the field (6, 12). Thus, the random mixing model is robust for this phase of an epidemic, and there is no need to use a model with a more complicated contact structure.
A mechanistic model has several advantages: it forces users to identify key parameters, to provide a minimal set of mechanisms necessary to explain the data, and to state underlying biological assumptions. It may also facilitate the generation of new hypotheses (3, 11, 24). We have shown that the mathematical model fit the data of the experiments; we pinpointed the underlying assumptions and created hypotheses for the apparent delay times. Once a suitable model is available, validation of the model for field situations can be performed. Mathematical models have been used extensively to analyze epidemics of infectious diseases (3, 10, 11, 21, 23, 24, 31). The information they generate provides insight into the course of epidemics and can be used in attempts to reduce the incidence of various infectious diseases. Especially in the case of fast-spreading infections like Campylobacter, gathering quantitative information on field infections can be a helpful tool in the evaluation of interventional measures. Knowledge of epidemiological mechanisms and parameters underlying Campylobacter transmission in broiler flocks is important for the evaluation and development of control strategies, because it enables us to determine which measures can reduce transmission and whether the magnitude of the effect is sufficient to reduce transmission or to postpone introduction, which in turn decreases the prevalence in a flock and subsequently the exposure of humans to Campylobacter via contaminated poultry products.
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