The authors have declared that no competing interests exist.
Conceived and designed the experiments: AJKC TJM APM AVG RSCH JLNW. Performed the experiments: AJKC TJM. Analyzed the data: AJKC TJM KK EBP. Contributed reagents/materials/analysis tools: AVG APM CPDB RSCH. Wrote the paper: AJKC TJM KK EBP AVG APM CPDB RSCH JLNW.
The number of cattle herds placed under movement restrictions in Great Britain (GB) due to the suspected presence of bovine tuberculosis (bTB) has progressively increased over the past 25 years despite an intensive and costly test-and-slaughter control program. Around 38% of herds that clear movement restrictions experience a recurrent incident (breakdown) within 24 months, suggesting that infection may be persisting within herds. Reactivity to tuberculin, the basis of diagnostic testing, is dependent on the time from infection. Thus, testing efficiency varies between outbreaks, depending on weight of transmission and cannot be directly estimated. In this paper, we use Approximate Bayesian Computation (ABC) to parameterize two within-herd transmission models within a rigorous inferential framework. Previous within-herd models of bTB have relied on ad-hoc methods of parameterization and used a single model structure (SORI) where animals are assumed to become detectable by testing before they become infectious. We study such a conventional within-herd model of bTB and an alternative model, motivated by recent animal challenge studies, where there is no period of epidemiological latency before animals become infectious (SOR). Under both models we estimate that cattle-to-cattle transmission rates are non-linearly density dependent. The basic reproductive ratio for our conventional within-herd model, estimated for scenarios with no statutory controls, increases from 1.5 (0.26–4.9; 95% CI) in a herd of 30 cattle up to 4.9 (0.99–14.0) in a herd of 400. Under this model we estimate that 50% (33–67) of recurrent breakdowns in Britain can be attributed to infection missed by tuberculin testing. However this figure falls to 24% (11–42) of recurrent breakdowns under our alternative model. Under both models the estimated extrinsic force of infection increases with the burden of missed infection. Hence, improved herd-level testing is unlikely to reduce recurrence unless this extrinsic infectious pressure is simultaneously addressed.
Epidemic models are commonly used to assess the impact of alternative management strategies. The efficacy of controls is typically assumed from “expert opinion” rather than estimated from data. Managed endemic diseases such as bovine tuberculosis offer the potential to estimate the efficiency of control directly from epidemiological data. Our methodology constitutes a shift in the level of statistical rigor applied to “policy” models and offers insights into the epidemiology of Bovine tuberculosis in Great Britain. bTB continues to persist and spread relentlessly in Britain, despite extensive testing and control programs. Cattle farmers question the efficacy of cattle controls, blaming the badger wildlife reservoir. Contrary to much public perception, we demonstrate the importance of cattle-to-cattle transmission, especially in larger herds. We estimate that in the worst case scenario up to 21% of herds may be harboring infection after they clear restrictions. However, we also estimate that there is a high rate of re-introduction of infection into herds, particularly in high incidence areas. Eliminating the hidden burden of infection alone is unlikely to be sufficient to prevent recurrent breakdowns. Rather, the high rate of external infection, both through cattle movements and environmental sources, must be addressed if recurrence is to be reduced.
The number of cattle herds in Great Britain (GB) placed under movement restrictions due to the suspected presence of bovine tuberculosis (bTB) has progressively increased over the past 25 years
This high rate of recurrence suggests that infection may be persisting within herds in the face of repeated testing. In GB and internationally, detection and clearance of herds is dependent on variants of the imperfect tuberculin skin test. In GB and Ireland this takes the form of a single intra-dermal comparative cervical tuberculin (SICCT)
Within-herd models of bTB have been developed to address this problem with a view to informing government policy
Persistence measures have proven to be a powerful probe on which to parameterize models of childhood infectious diseases
For chronic diseases, such as bTB, demographic turnover of the population is the only natural mechanism acting to clear infection from populations. In this context persistence can be used as an indirect measure of the efficiency of diagnostic testing. In this study we model the within-herd persistence of bTB as a balance between three key processes: the infectious pressure acting to introduce infection into the herd from extrinsic sources, the rate of cattle-to-cattle transmission within the herd and the rate of removal of infection through testing and demographic turnover. Herds are considered as isolated populations loosely connected to a reservoir of infection modeled as an infectious pressure. We are therefore not concerned with modeling the routes of introduction to the herd – which may be through movements of infected animals or contact with wildlife reservoir populations. Instead we focus on the processes of transmission within a herd with relation to the detection and resolution of breakdowns. We do so using two mechanistic models of within-herd transmission that we parameterize using routinely collected epidemiological data. We finally apply our parameterized models to estimate the hidden burden of infection and its implications for control of bTB in Great Britain.
The probability of extinction within epidemic models is dependent on the past history of infection within the population
Bovine tuberculosis is a statutory infectious disease. Incidence and testing data are routinely collected by the Animal Health and Veterinary Laboratories Agency (AHVLA) and collated within the
We choose to restrict our study to the period 2003–2005 due to systematic changes to the testing system surrounding the 2001 foot-and-mouth disease epidemic
The cessation of testing during the 2001 foot-and-mouth epidemic artificially increased the duration of time that herds were kept under movement restrictions, delayed the scheduling of routine surveillance tests and was associated with an increase in incidence and spread of bTB to new areas
Of 10,174 breakdowns recorded within our study period, 3,456 (34%) breakdowns match our criteria for inclusion. Restricting our analyses to this sub-population has an important advantage. The scheduling of surveillance tests in GB is based on the local incidence (
Routine surveillance for bTB in GB is based upon the regular (SICCT) testing of herds at a frequency determined by the local incidence of affected premises. Panel (A) maps the shortest recorded PTI for each parish over our study period of 2003–2005. High incidence areas are spatially clustered with the greatest incidence, and thus intensity of testing, in the south-west of England and south Wales. PTI therefore offers a crude categorization of herds according to epidemiological risk, past history of testing and to a lesser extent, geographical location. In contrast to surveillance testing, the sequence of tests (B) following a breakdown are dependent only on the outcome of tests on the affected premises. A failed surveillance test leads to a sequence of short interval tests (SI) at intervals of at least 60 days. Confirmation of infection, through isolation of
Of the remaining breakdowns the majority are either recurrent breakdowns (2,102; 21%) initiated by a follow-up ‘VE-6M’ or ‘VE-12M’ test or breakdowns that started with a so-called “inconclusive” reactor (2,032; 20%). Inconclusive reactors (IRs) demonstrate a response to the SICCT that is close to the cut-off value defining a reactor. IRs do not necessarily trigger a breakdown but require the animal, rather than the herd, to be retested at an interval of 60 days. The population of IRs will be composed of both false reactor and truly infected animals and cannot be rationally treated within our model framework, requiring us to omit these herds from our analysis. The remaining 25% of breakdowns were initiated through a mixture of contiguous testing of affected premises and contact tracing.
The persistence of bTB has previously been demonstrated to scale with herd size
We further stratify these herds by the parish testing interval (PTI) and confirmation status of breakdowns to produce empirical distributions of persistence (
The within-herd persistence of bTB in GB as measured by the probability of all GB breakdowns from our study population being prolonged (duration of greater than 240 days, top panel) or recurrent within 24 months (middle panel). The relationship of each measure is plotted against herd size, with breakdowns further stratified by parish testing interval (PTI 1, 2 and 4, left to right) and confirmation status (unconfirmed breakdowns: lime green, circles, confirmed breakdowns: magenta squares). Uncertainty in each (mean) target observation (thick lines) is illustrated by an envelope (thin lines) of ±1.96 standard errors around the mean. Predictive distributions from our within-herd (SORI) model for each of these measures are plotted as shaded density strips where the intensity of color is proportional to the probability density at that point
The proportion of prolonged and recurrent breakdowns both scale with herd size, but demonstrate distinct relationships with respect to both confirmation status and the local background risk of infection as measured by PTI. These empirical relationships are consistent with previous analyses suggesting that confirmation is associated with an increase in the duration of breakdowns
We consider the persistence of bTB to be a product of the non-linear interaction of both the disease and testing dynamics. Heuristically, our model can therefore be considered as having two interacting dynamic components: an epidemic model that describes transmission within and into the herd and a testing model that models the sequence of tests and removal of reactors. We estimate the parameters of our model (
Parameter | Description |
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The period of latency between infection and infectiousness is a key epidemiological parameter that sets the time-scale between subsequent epidemic generations. Given the chronic, progressive nature of bTB, models have conventionally assumed long epidemiological latent periods of ∼6–20 months
Parameter | Prior Constraints | Initial sampling distribution |
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Uniform [0.05,1] |
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Uniform [0.05,1-0.9997] |
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Uniform [0.4,1] |
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Uniform [0,1-0.9990] |
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Uniform [0.0,0.5] |
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Uniform [0.0,0.5] |
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Uniform [0.0,1.5] |
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Uniform [0.0,0.35] |
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Uniform [0.0,1.5] |
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Uniform [0,2.0] |
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Uniform [0,1] |
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Uniform [0,3e-4] |
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Uniform [0, 3e-4] |
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Uniform [0, 3e-5] |
Event | Effect | Probability per unit time |
Move susceptible animal onto herd |
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Remove animal from herd |
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Transmission |
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Emergence (Occult) |
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Emergence (Reactive) |
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Move susceptible animal into herd |
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Remove animal from herd |
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Transmission |
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Emergence |
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Both models provide comparable fits to the empirical target distributions (
Both models estimate that the rate of cattle-to-cattle transmission within a herd increases, non-linearly, with herd size. The potential for transmission within a herd can be characterized by the basic reproductive ratio R0, defined as the expected number of secondary cases within a herd of size N on the introduction of a single infectious individual. Within the range of our study population our (median) point estimate of R0 from the SORI model increases from 1.5 (0.26–4.9; 95% CI) in a herd of size 30 up to 4.9 (0.99–14.0; 95% CI) in a herd of 400 cattle (
(
The SOR and SORI models provide contrasting estimates of the efficiency of SICCT testing in Great Britain. The SOR model estimates a true median SICCT test sensitivity of 66% (52–80%, 95% CI) at the standard interpretation, rising to 72% (56–88%, 95% CI) under the severe interpretation. Estimates of true sensitivity from the more traditional SORI model are far lower, at 36% (24–51%, 95% CI) for the standard interpretation rising to 48% (34–69%, 95% CI) for the severe interpretation (
In order to quantify the efficiency of control we introduce a new measure - the infectious burden. We define infectious burden as the probability that
We apply our fitted models to predict how different herd-level interventions may affect the resolution of breakdowns (
Change in the probability of a herd experiencing a recurrent breakdown after application of a ‘perfect’ test (left column) or perfect isolation (right column). The perfect test is assumed to have 100% sensitivity and specificity and no occult period. Perfect isolation corresponds to setting the extrinsic infectious pressure to zero at the end of a breakdown (
Under the SORI model there is a similar relationship in the response to ‘perfect isolation’, except that a greater proportion of recurrence is attributable to persistence of infection. At the national level, averaging over our study population of herds once again, we estimate that 50% (33–67, 95% CI) of recurrent breakdowns are attributable to persistence within the SORI model, compared to 24% (11–42, 95% CI) under the SOR model.
However, eliminating this hidden burden of infection is not sufficient to eliminate recurrence if the extrinsic infectious pressure acting on herds is not simultaneously addressed. Under both models a ‘perfect test’ with 100% sensitivity, specificity and no occult period fails to improve the probability of recurrence in high incidence areas (
This counter-intuitive result demonstrates an important limitation of our approach. Our herd-level model does not distinguish between movements to slaughter or to other herds, so the infectious burden output from our model may potentially be contributing to the extrinsic rate of transmission that drives recurrence in our herd-level model. Both of our within-herd models can equally well fit the empirical patterns of persistence of bTB despite very different predictions for the level of the infectious burden. However, such a difference would place very different weights on the importance of cattle movements in network models of herd-to-herd transmission. Recent analyses of the between-herd transmission of the disease in GB have simplified, or ignored these within-herd dynamics of transmission
A fundamental challenge in epidemiological modeling concerns identifying the appropriate level of model complexity required to understand the dynamics of transmission and form a rational basis for policy development. Tuberculosis has been described as an infectious disease with a period of latency ranging from one day to a lifetime
Both the SOR and SORI models are equally well supported by the population level data used in this study, despite very different estimates for the efficiency of testing. This suggests that persistence measures alone are insufficient to distinguish the true burden of infection and points to experimental studies that could resolve this uncertainty. Neither model identifies, without the support of informative priors, an occult period within the range observed from animal challenge studies
Both models estimate that the rate of cattle-to-cattle transmission in GB herds is non-linearly density dependent. This result has immediate importance for the formulation of bTB policy at the herd level, suggesting that additional controls may need to be targeted towards larger herds. Our models suggest that the key to addressing the ongoing spread of bTB lies with reducing the rate of transmission into herds. The central question remains as to whether this requires management of the reservoir of infection in wildlife populations, or simply improved surveillance and diagnostic testing to reduce the movement of undisclosed infection between herds.
We have shown that stochastic persistence measures can provide insights into the efficiency of control measures for managed populations. However, the interpretation of these patterns of persistence requires a modeling approach that simultaneously accounts for the dynamics of control as well as the intrinsic dynamics of disease transmission. In the case of bTB, the dynamics of infection at the individual level have a profound impact on the estimated burden of infection missed by testing. It is therefore imperative to improve our understanding of the, still mysterious, life history of infection of bTB in individual cattle.
Within-herd transmission of bTB is modeled using the standard compartmental approach where animals are classified only by their epidemiological status. We consider two alternative models (
Both epidemic models are implemented as stochastic Markov chains in continuous time and can be defined by the allowed transitions between the four state variables: Susceptible (
The sequence of tests before, during and after a breakdown is simulated by a model where the timing of tests and number of animals to be tested changes dynamically according to the state-variables of the epidemic model and the outcome of individual animal tests.
Model simulations are initialised with the entire herd in the susceptible compartment (S,O,R,I) = (N, 0, 0, 0). The model is then simulated forward, piecewise, between the dynamically scheduled tests before, during and for 5 years following the end of the first breakdown, or until a recurrent breakdown is triggered. The sequence of decisions following the outcome of herd tests is summarized in
Simulations begin with the herd undergoing routine surveillance through slaughterhouse inspection and whole herd tests (classified as RHT or WHT) at 1, 2 or 4 yearly intervals (described below). Detection of a reactor animal triggers a breakdown. The herd then enters a sequence of short interval tests (SIT). Unconfirmed breakdowns end after a single clear test at the standard interpretation, while confirmed breakdowns must clear two tests – one at severe interpretation and the second at standard interpretation. Two follow-up tests, one six months after the end of a breakdown (VE-6M) and one 12 months later (VE-12M) are then scheduled. The time between all tests associated with a breakdown (SIT, VE-6M, VE-12M) are sampled from empirical distributions (
Breakdowns are triggered by the detection of a reactor, either due to the presence of infected animals in the herd or the generation of a false positive test result. Nominally, we simulate the full sequence of tests until either of these events occurs with the proportion of false-positive breakdowns determined by the relative values of the specificity (
The application of herd tests in GB can be modeled by simulating three basic processes 1) the number of animals to test 2) the number of reactor animals detected at the standard and severe interpretations of the skin test and 3) the confirmation process.
For tests associated directly with a breakdown (SIT, VE-6M, VE-12M) the whole herd is tested. However, there is more variation in the type of test, and numbers of animals tested, in PTI 2 and 4 herds. We simulate this process by choosing the test type – either a whole herd test or a routine herd test – at random according to the proportion of tests recorded within the parish testing interval of the simulated herd (
Whole herd tests specify that all bovines older than 6 weeks should be tested. We simulate this requirement by approximating the instantaneous proportion of the herd ineligible for testing to be (6/52) μ/N, where μ is the per-capita turnover of the herd. The number of animals tested with a WHT (X) is then sampled from a binomial distribution:
There is greater variability in which non-breeding animals are tested during a routine herd test (RHT), and therefore in the proportion of the herd tested. In order to account for this we sample the proportion from a Cauchy distribution fitted to the empirical distribution from VetNet data by maximum likelihood (
The outcome of diagnostic tests within our model is determined by the set of parameters defining the sensitivity and specificity of the SICCT test at both the standard and severe interpretations (
Given X animals to test we sample them randomly (and uniformly) from each of the model compartments (S,O,R,I) to generate the number of animals from each compartment that are tested (XS,XO,XR,XI). For each (XS,XO,XR,XI) we sample a uniform random number and use the value to simulate the number of reactor animals at the standard (Standard Reactors) and severe (Severe Reactors) interpretations:
For each XS:
if (
if (
For each Xo:
if (
if (
For each XR:
if (
if (
For each XI:
if (
if (
We must also keep track of the number of true reactors (Z) in order to simulate the number of confirmed reactors (C):
Provided that the breakdown has not been previously confirmed and C = 0, then all reactors at the standard interpretation are removed from the herd. Otherwise, if the number of confirmed reactors
We use the ABC-SMC algorithm described in Toni
The algorithm begins by generating 10,000
At each successive round the threshold was reduced semi-automatically to the median value of the metric from the previous round. Heuristically the ABC-SMC procedure can be thought of as using goodness-of-fit criteria to inform the shape of the approximate posterior distributions, rather than the likelihood function.
Uniform prior distributions are applied to individual parameters and combinations of parameters to constrain their values to biologically relevant ranges. Probabilities are constrained to be in the interval [0,1] and rates are constrained to be positive. The sensitivity and specificity of the SICCT test are constrained to increase and decrease respectively under the severe interpretation and the probability of confirmation of reactors under routine slaughterhouse surveillance is assumed to be less than the probability of confirmation of reactors. All prior assumptions are intended to be uninformative, apart from the occult period for the SORI model and the upper bound (0.0003) placed on pFP. This value, equivalent to a lower bound on the specificity of the skin test at the standard definition of 99.97%, was obtained by calculating the value of pFP required to explain
Description | Type of Measure | Number of bins per target distribution | Weighting ( |
Breakdown Length | Distribution (Days) [100,200,300,400,500,1000,2000] | 7 | 1/7 |
Reactors at first test | Distribution (Reactors) [1,2,3,4,5,10,47] | 7 | 1/7 |
Reactors at VE-6M | Distribution (Reactors) [1,2,3,4,5,10,47] | 7 | 1/7 |
Reactors at VE-12M | Distribution (Reactors) [1,2,3,4,5,10,47] | 7 | 1/7 |
Total reactors removed within breakdown (until movement restrictions are lifted) | Distribution (Reactors) [2,4,6,8,10,12,14,16,18,20,47] | 11 | 1/11 |
Probability of recurrence within 6 months | Probability | 1 | 1 |
Probability of recurrence within 12 months | Probability | 1 | 1 |
Probability of recurrence within 24 months | Probability | 1 | 1 |
All of the target epidemiological measures for our final ABC-SMC scheme can be expressed either as probabilities or as (binned) probability distributions. This motivated the choice of an ABC metric based on the relative entropy, also known as the Kullback-Leibler divergence
Two properties of the relative entropy should be noted: firstly, the relative entropy is asymmetric to the choice of reference distribution, with
Secondly the relative entropy is undefined if any of the elements of the reference distribution qi = 0. We numerically approximate the distribution of each of our target measures through histograms, with bin-sizes chosen to capture the range of observed values within VetNet data. Where we are free to choose appropriate bin sizes for the empirical distributions (q) such that we avoid any empty bins, we cannot ensure the same for the proposed distributions (p) generated from model simulations. To ensure that our metric is always defined, we add 1 to every bin of our empirical and simulated histograms.
For each proposed set of parameters (particle) we simulated a fixed number of realizations of the model (500) at the midpoint of each of the 6 herd-size histogram bins [30,90,150,210,270,330] for PTI 1,2 and 4 and generate a set of j proposed distributions (
Target and auxiliary distributions necessary for simulation and parameterization of models using ABC-SMC.
(ZIP)
Distribution of times between scheduled whole herd tests in GB (2003–2005). Farmers are responsible for scheduling tests as close as possible to the statutory intervals. Historically, this has lead to variation in the time between tests that we quantify for our study period (2003–2005). The frequency of routine herd tests is determined by the current parish-testing interval (PTI) for a herd. However, the time since the previous whole herd test is also determined by the historical testing intervals for the parish and other epidemiological factors. In practice the time since the previous surveillance test for breakdown herds in PTI 1, 2 and 4 is distributed with the greatest variation seen in PTI 2 (left). Short interval tests (SIT) must be carried out at least 60 days after the last whole herd test leading to a skewed distribution where test intervals are more likely to be late than early (middle). Likewise the follow up tests after a breakdown, that must be scheduled at intervals of at least 6 and 12 months respectively (VE-6 M, VE-12 M) are skewed to be late (right).
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Proportion of animals tested in routine surveillance tests (2003–2005). The number of animals within a herd that are tested during routine surveillance varies depending on the demographic structure of the herd and the perceived epidemiological risk. PTI 1 herds should receive a whole herd test (WHT) where all bovines older than 6 weeks are tested. In PTI 2, 3 and 4 a routine herd test (RHT) may be carried out where there is greater discretion as to which animals are tested based on perceived epidemiological risk. As a consequence the proportion of animals tested is smaller and more variable for RHTs (Right) as compared to WHTs (Middle). The proportion of breakdowns reported as being disclosed by WHTs and RHTs also varies by PTI (Left table). The small proportion of breakdowns in PTI 1 initiated by a RHT, despite WHTs being mandated in these herds, stem from herds whose PTI was updated retrospectively after disclosure. Likewise despite the majority of tests in PTI 4 being RHTs, a higher proportion of
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Annual per bovine rate of turnover in breakdown herds. We define turnover as the time-averaged rate at which animals move into and are removed from a herd. A representative distribution of turnover rates for breakdown herds was calculated from CTS data from 1st January 2003 – 1st January 2005 for all breakdown herds with start dates in 2004. Note that since the CTS data only records movements at the holding (CPH) rather than the herd (CPHH) level, this is an indirect measure corresponding to the annual per capita rate of movement of bovines through the CPH associated with a breakdown herd. Turnover was calculated three ways: using movements into a CPH (“On Movements”, red line), movements out of a CPH (“Off Movements”, green line) and the combined rate of both types of movements (black line, points). The median number of “Off” movements is slightly smaller with than for on-movements consistent with the increase in herd size nationally over the period. The “All movements” estimate is used as the empirical distribution for the within-herd model.
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Distribution of Breakdown Herd Sizes. Smoothed density of the (maximum) herd size during a breakdown for our study population. There is some variation in the size of herds with PTI, with a longer tail of herds beyond our cutoff value of 360 (vertical dashed line) for PTI 4 herds.
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Estimated Parameter Distributions for SORI model. Distributions of parameters consistent with the persistence measures and reactor distributions estimated from VetNet data (
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Target measures for the within-herd persistence of bTB (2003–2005) and predictive distributions for SORI model. The within-herd persistence of bTB in GB as measured by the probability of breakdowns being prolonged (duration of greater than 240 days) or recurrent within a 6, 12 and 24 month horizon. The relationship of each target measure is plotted against herd size, with breakdowns further stratified by parish testing interval (PTI 1 top row, PTI 2 middle row, PTI 4 bottom row) and confirmation status (confirmed breakdowns: green, circles, unconfirmed breakdowns: magenta squares). Target measures are calculated from breakdowns trigged within 2003–2005 by a routine surveillance test (VE-WHT, VE-WHT2, VE-RHT, VE-SLH). The probability of confirmation varies between PTI, as does the proportion of confirmed breakdowns initiated by a slaughterhouse case (white diamonds) and the mean number of reactors reported at the disclosing test. Uncertainty in each (mean) target observation (thick lines) is illustrated by an envelope (thin lines) of ±1.96 standard errors around the mean. Predictive distributions for each of these target measures from the finalized within-herd transmission model are plotted as shaded density strips where the intensity of color is proportional to the probability density at that point.
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Target measures for the within-herd persistence of bTB (2006–2008) and predictive distributions for SORI model. The within-herd persistence of bTB in GB as measured by the probability of breakdowns being prolonged (duration of greater than 240 days) or recurrent within a 6, 12 and 24 month horizon. The relationship of each target measure is plotted against herd size, with breakdowns further stratified by parish testing interval (PTI 1 top row, PTI 2 middle row, PTI 4 bottom row) and confirmation status (confirmed breakdowns: green, circles, unconfirmed breakdowns: magenta squares). Target measures are calculated from breakdowns trigged within 2003–2005 by a routine surveillance test (VE-WHT, VE-WHT2, VE-RHT, VE-SLH). The probability of confirmation varies between PTI, as does the proportion of confirmed breakdowns initiated by a slaughterhouse case (white diamonds) and the mean number of reactors reported at the disclosing test. Uncertainty in each (mean) target observation (thick lines) is illustrated by an envelope (thin lines) of ±1.96 standard errors around the mean. Predictive distributions for each of these target measures from the finalized within-herd transmission model are plotted as shaded density strips where the intensity of color is proportional to the probability density at that point.
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Burden remaining after resolution of a breakdown using SORI model. redictive distributions for the probability of at least one infectious bovine remaining within a herd after a breakdown is resolved as a function of herd size, classified by PTI (1,2,4 left to right) and confirmation status (Green circles confirmed, magenta squares unconfirmed). Predictive distributions are plotted as shaded density strips where the intensity of shading is proportional to the probability density at that point. Solid lines, and points for each herd-size category, indicate the median of the predictive distribution to aid comparison between confirmed and unconfirmed breakdowns.
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Estimated Parameter Distributions from SOR model. Distributions of parameters consistent with the persistence measures and reactor distributions estimated from VetNet data (
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Target measures for the within-herd persistence of bTB (2003–2005) and predictive distributions for within-herd transmission model using SOR model. The within-herd persistence of bTB in GB as measured by the probability of breakdowns being prolonged (duration of greater than 240 days) or recurrent within a 6, 12 and 24 month horizon. The relationship of each target measure is plotted against herd size, with breakdowns further stratified by parish testing interval (PTI 1 top row, PTI 2 middle row, PTI 4 bottom row) and confirmation status (confirmed breakdowns: green, circles, unconfirmed breakdowns: magenta squares). Target measures are calculated from breakdowns trigged within 2003–2005 by a routine surveillance test (VE-WHT, VE-WHT2, VE-RHT, VE-SLH). The probability of confirmation varies between PTI, as does the proportion of confirmed breakdowns initiated by a slaughterhouse case (white diamonds) and the mean number of reactors reported at the disclosing test. Uncertainty in each (mean) target observation (thick lines) is illustrated by an envelope (thin lines) of ±1.96 standard errors around the mean. Predictive distributions for each of these target measures from the finalized within-herd transmission model are plotted as shaded density strips where the intensity of color is proportional to the probability density at that point.
(PDF)
Target measures for the within-herd persistence of bTB (2006–2008) and predictive distributions for within-herd transmission model using SOR model. The within-herd persistence of bTB in GB as measured by the probability of breakdowns being prolonged (duration of greater than 240 days) or recurrent within a 6, 12 and 24 month horizon. The relationship of each target measure is plotted against herd size, with breakdowns further stratified by parish testing interval (PTI 1 top row, PTI 2 middle row, PTI 4 bottom row) and confirmation status (confirmed breakdowns: green, circles, unconfirmed breakdowns: magenta squares). Target measures are calculated from breakdowns trigged within 2003–2005 by a routine surveillance test (VE-WHT, VE-WHT2, VE-RHT, VE-SLH). The probability of confirmation varies between PTI, as does the proportion of confirmed breakdowns initiated by a slaughterhouse case (white diamonds) and the mean number of reactors reported at the disclosing test. Uncertainty in each (mean) target observation (thick lines) is illustrated by an envelope (thin lines) of ±1.96 standard errors around the mean. Predictive distributions for each of these target measures from the finalized within-herd transmission model are plotted as shaded density strips where the intensity of color is proportional to the probability density at that point.
(PDF)
Burden remaining after resolution of a breakdown using SOR model. Predictive distributions for the probability of at least one infectious bovine remaining within a herd after a breakdown is resolved as a function of herd size, classified by PTI (1,2,4 left to right) and confirmation status (Green circles confirmed, magenta squares unconfirmed). Predictive distributions are plotted as shaded density strips where the intensity of shading is proportional to the probability density at that point. Solid lines, and points for each herd-size category indicate the median of predictive distribution to aid comparison between confirmed and unconfirmed breakdowns.
(PDF)
Impact of herd-level interventions on probability of recurrence within 24 months. Change in the probability of a herd experiencing a recurrent breakdown after application of a ‘perfect’ test (left column) or perfect isolation (right column). The perfect test is assumed to have 100% sensitivity and specificity and no occult period. Perfect isolation corresponds to setting the extrinsic infectious pressure to zero at the end of a breakdown (
(PDF)
We thank Chris Jewell for suggesting a parameter transformation to the force of infection to improve convergence. We would also like to thank the anonymous reviewers for their contributions during the peer-review process.