Estimating the Hidden Burden of Bovine Tuberculosis in Great Britain
[['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 [1] .', 'This increase in the rate of so-called “breakdown” herds is despite an intensive and costly test-and-slaughter control program [2] .', 'Recent studies have focused on estimating the contributions of cattle movements and wildlife transmission to incidence [1] , [3]–[8] as measured by the rate of new breakdowns .', 'However , less attention has been paid to quantifying the dynamics of transmission within herds , even though this is arguably the most data-rich unit within the wider ecology of M . bovis .', 'Previous history of disease within a herd is an important predictor of breakdown [5] , [8] , [9] , with 38% of herds that clear movement restrictions experiencing a recurrent incident within 24 months [10] .', '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 ) [11] test .', 'Infection missed by SICCT testing is likely to be contributing to recurrence within herds .', 'However , the lack of a gold-standard diagnostic test for bovine tuberculosis means that the efficiency of the SICCT test is poorly characterized and the contribution of missing infection to recurrence cannot be easily assessed .', 'Furthermore , reactivity to the SICCT test is dependent on the time-from-infection [12] , most often characterized [13] , [14] as an occult period where animals are infected but not yet detectable .', 'As a consequence , the efficiency of testing within a herd depends not only on the characteristics of the diagnostic test , but also on the competing timescales of transmission and the frequency of testing .', 'Within-herd models of bTB have been developed to address this problem with a view to informing government policy [13] , [14] .', 'However , extant models have been based on ad-hoc parameterizations informed by disparate experimental studies and expert opinion .', 'There exists considerable uncertainty in the assumed values of key parameters , in particular the occult period , the scaling of transmission rates with herd size [15] , [16] and the duration of latency between infection and infectiousness .', 'To address this uncertainty , we propose a novel basis for parameterization of within-herd models using measures of stochastic persistence [17] as a metric for Approximate Bayesian Computation ( ABC ) [18]–[19] .', 'Persistence measures have proven to be a powerful probe on which to parameterize models of childhood infectious diseases [20]–[23] .', 'A successful approach has been to assume that the intrinsic rate of transmission within a population is rapid compared to the combined rate of transmission from sources extrinsic to the local population .', 'This time-scale separation allows us to model local populations independently .', 'Extrinsic routes of transmission are modeled through a generalized infectious pressure [20]–[22] .', 'Comparatively less theoretical attention has been paid to modeling the persistence of managed endemic 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 [24] .', 'Alternative empirical measures of persistence , that capture different aspects of the transmission dynamics , can be constructed depending on how we condition on the past history of infection [21] .', 'For bTB , infection missed during a given test is likely to contribute to the probability of the herd failing subsequent tests .', 'Contingent on the natural time-scale of transmission and the scheduling of testing , missing infection may act to prolong the duration of breakdowns and/or increase the probability of a recurrent breakdown .', 'We therefore quantify within-herd persistence through two competing measures related to the duration and the rate of recurrence of breakdowns .', 'The duration of breakdowns is captured by the probability that breakdowns are prolonged [25] , defined as lasting longer than 240 days .', 'Recurrence is captured through the probability of a breakdown recurring [10] within a fixed time horizon of 6 , 12 and 24 months after the end of a breakdown .', '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 VetNet database .', 'It is not feasible or desirable to model the full complexity of the British testing regime within a herd level model .', 'In addition to the schedule of statutory surveillance testing , there exists a diverse range of auxiliary tests including pre-movement testing , contiguous tests and tests trigged by epidemiological investigations of “at risk” premises .', 'As a consequence there is considerable variability in the duration of time that infection can spread unobserved within herds before detection .', 'In an attempt to control for this uncertainty we restrict our current analysis to new breakdowns with start dates between 2003–2005 that were detected through routine surveillance , either through the slaughterhouse or by the detection of reactors at a routine or whole herd test ( tests classified as ‘VE-WHT’ , ‘VE-WHT2’ , ‘VE-RHT’ or ‘VE-SLH’ ) .', '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 [5] and a later increase in use of the gamma-interferon test [26] .', 'Although discretionary use of the gamma interferon test increased after the end of our study period , this does not appear to have impacted upon persistence and our model still provides an equally good fit to target measures taken from more recent data ( Figures S7 , S11 ) .', '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 [5] .', 'Given the slow rate of transmission of bTB , the perturbative effect of this disruption to testing is likely to have continued for many years .', 'However , our interest is primarily in the sequence of transmission and testing after the disclosure of a breakdown .', 'Disruptions to testing prior to the disclosure of infection will increase the duration of time that infection was able to transmit silently within our study herds .', 'However , as this variation is included within the empirical testing distributions used within our model ( Figure S1 , Dataset S1 ) we do not expect it to affect our results .', '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 ( Figure 1 ) , that determines the so-called parish testing interval ( PTI ) .', "The duration of time that infection may have remained undisclosed within our sub-population of herds is strongly constrained by the herd's local PTI .", 'After detection of infection , regardless of the disclosing test type , all herds must undergo the same statutory sequence of testing .', 'We therefore do not believe that our inclusion criteria impacts upon the generality of our inference for rates of within-herd transmission and the efficiency of surveillance .', '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 [27]; a known risk factor for both prolongation [25] of breakdowns in GB and recurrence in Irish herds [28] .', 'We extend these analyses to quantify the relationship of our two persistence measures with herd size .', 'The size of a cattle herd varies dynamically , even over the course of a breakdown .', 'We therefore define herd size as the maximum herd size over the breakdown .', 'The distribution of herd sizes is right skewed with 90% of breakdowns having herd sizes less than or equal to 360 cattle ( Figure S4 ) .', 'The scarcity of herd sizes larger than this limits our ability to measure the relationship with persistence [27] .', 'We therefore finally restrict our study population to breakdowns with a herd size of less than or equal to 360 cattle , leaving us with a final study population of 3 , 094 breakdowns .', 'These 3 , 094 breakdowns were then binned into 6 groups with histogram mid-points of [30 , 90 , 150 , 210 , 270 , 330] .', 'We further stratify these herds by the parish testing interval ( PTI ) and confirmation status of breakdowns to produce empirical distributions of persistence ( Figure 2 , Figures S6 , S10 ) .', 'This classification is motivated by the systematic differences in testing for herds within different PTIs and after confirmation .', 'Confirmed ( recently re-classified as Officially TB-Free Status Withdrawn or OTF-Withdrawn ) breakdowns are required to pass an additional clear test at a more strict ( severe ) interpretation of the SICCT test ( Figure 1B ) .', 'The severe interpretation increases the sensitivity of the SICCT test at the expense of reducing the specificity .', 'Confirmation is triggered by the discovery of reactor animals with visible lesions and/or culture of M . bovis .', '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 [25] , but has negligible impact on recurrence [10] .', 'In contrast to the consistency of the duration of breakdowns across all areas there is a marked increase in the rate of recurrence with local risk as measured by PTI .', 'These differential relationships of persistence with herd size are the basis on which we set out to infer the within-herd transmission dynamics of bTB .', '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 ( Table 1 ) directly from our target measures of persistence using a sequential Monte Carlo implementation of Approximate Bayesian Computation ( ABC-SMC ) [18] , [19] .', 'This framework is designed to bypass the calculation of computationally infeasible likelihood functions and instead generates distributions of parameters for which model outputs are consistent with the data according to a set of pre-defined goodness-of-fit metrics .', '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 [13] , [14] .', 'However , animal challenge studies have suggested that bacterial shedding , and therefore transmission , may occur over shorter time-scales of ∼30 days [29] .', 'In order to explore these two scenarios of latency , we fitted two models using vague ( uniform ) prior assumptions ( Table 2 ) , one based on the conventional model structure assumed for bTB [13] , [14] ( SORI , Table 3 ) and an alternative model allowing for “early” infectiousness ( SOR , Table 4 ) .', 'In the SORI model cattle are assumed to be infectious ( I ) only after passing through two latent stages: an occult stage ( O ) where animals are infected , but not detectable by SICCT testing and a reactive stage ( R ) where animals are ‘reactive’ to the SICCT test but not yet infectious .', 'The SOR model decouples this relationship between epidemiological latency and reactivity to the SICCT test .', 'Animals are assumed to be potentially infectious from both the occult ( O ) and reactive ( R ) classes , dispensing with the infectious class ( I ) .', 'Both models provide comparable fits to the empirical target distributions ( Figure 2 , Figures S6 , S10 ) despite remarkably different estimates for the duration of the occult period and the epidemiological period of latency between infection and infectiousness ( Figures S5 , S9 ) .', 'The occult period is estimated to last ∼1 . 8 days ( 0 . 0–7 . 7 days , 95% CI ) for the SOR model and ∼275 days ( 24–517 , 95% CI ) for the SORI model .', 'Whereas infectiousness is implicitly assumed to begin with infection under the SOR model , the period of epidemiological latency estimated under the SORI model is more than twice that of previously assumed values [13] , [14] with a point estimate of 406 days ( 116–827 , 95% CI ) .', 'The occult period estimated from the SORI model is an order of magnitude larger than the range of 8–65 days observed in animal challenge studies [12] , [30] , [31] .', 'Placing a more informative prior ( uniform on the range 0–128 days ) on the occult period for the SORI model has no appreciable impact on the fidelity of the model fit and reduces the estimated occult period to a median point estimate of ∼28 days ( 1–119 days , 95% CI ) .', 'We therefore select the SORI model fit with the more informative prior for comparison with the alternative SOR model within this paper .', '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 ( Figure 3A ) .', 'Estimates from the SOR model are smaller , but with overlapping credible intervals , increasing from 0 . 52 ( 0 . 1–1 . 6 , 95% CI ) in a herd of size 30 up to 3 . 6 ( 0 . 73–8 . 85 , 95% CI ) in a herd of size 400 ( Figure 3A ) .', 'As a consequence , both models predict that the efficiency of control will also scale with herd size .', '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 ( Figure 3B ) .', 'However , these model estimates are relative to the true infection status of animals .', 'Given the lack of a gold standard diagnostic test for bTB , such information is not available in real populations .', 'Rather , out of necessity , sensitivity of diagnostic tests for bTB is routinely measured relative to the presence of visible lesions and/or culture .', 'The limitations of such comparative measures of sensitivity are aptly illustrated by comparison of our estimates from the SOR and SORI models .', 'Despite the differences in the true sensitivity between the two models , the effective test sensitivities relative to visible lesions are indistinguishable and considerably higher than the true values ( Figure 3B ) .', 'As a consequence the diverse sensitivity estimates from the SOR and SORI models are nonetheless both consistent with published estimates of the sensitivity of SICCT relative to visible lesions of up to 93 . 5% at the severe interpretation [11] .', 'In order to quantify the efficiency of control we introduce a new measure - the infectious burden .', 'We define infectious burden as the probability that at least one infected animal remains within a herd after movement restrictions are lifted .', 'By simulating our within-herd models using the distribution of herd sizes from our study population we can generate predictive distributions for the infectious burden at the national level ( Figure 3 C , D ) .', 'Once more , the SOR and SORI models provide contrasting views of the efficiency of control .', 'Under the SOR model we estimate that 8% ( 3–17%; 95% CI ) of breakdowns will have an infectious burden when they clear restrictions , with a median of 1 ( 1–3; 95% CI ) infectious animal remaining in these herds .', 'Under the SORI model this estimate increases to 21% ( 12–33%; 95% CI ) of breakdowns with an infectious burden when they clear restrictions , with a median of 1 ( 1–4; 95% CI ) infectious animal remaining in these herds .', 'We apply our fitted models to predict how different herd-level interventions may affect the resolution of breakdowns ( Figure 4 ) .', 'Specifically we consider two treatments: application of a ‘perfect test’ and eliminating the extrinsic infectious pressure through ‘perfect isolation’ .', 'In the SOR model , recurrence is driven almost completely by re-introduction , with ‘perfect isolation’ having the potential to eliminate recurrence completely in some herds ( Figure 4B ) .', 'Perfect isolation is predicted to be less effective at reducing recurrence in herds with a low extrinsic rate of re-introduction ( i . e . small herds in low incidence areas ) .', 'Although these herds are predicted to have a lower infectious burden ( Figures S8 , S12 ) , when they do experience a recurrent breakdown it is more likely to be caused by infection missed by SICCT testing than re-introduction .', '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 ( Figure 4 ) .', 'Although the perfect test reduces the duration of breakdowns , it can also detect infection within herds more quickly .', 'In the short term , rates of recurrence will therefore increase in high incidence areas and such a perfect test would only be of benefit for low incidence ( PTI 4 ) breakdowns where the rate of re-introduction is sufficiently low .', '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 [6] , [7] .'], ['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 [32] .', 'However , this uncertainty surrounding the progression of disease in individuals is rarely considered as a part of epidemiological modeling studies .', 'In this study we have demonstrated how assumptions concerning the relative timing of infectiousness and reactivity to tuberculin profoundly impacts upon the estimated efficiency of SICCT testing .', '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 [12] , [30] , [31] .', 'However , if there is a relationship between infectious dose and the duration of latency , estimates from challenge studies must also be treated with caution .', 'Given the importance of this parameter in determining the hidden burden of infection , further research is required to clarify the relationship between infectiousness and sensitivity to diagnostic tests .', 'Our modeling suggests that transmission of bTB ‘early’ in infection necessitates a lower level of persistence of infection than predicted by traditional ( SORI ) transmission models .', 'However , evidence for such ‘early’ transmission comes from animal challenge studies [29] , [33] and has not been verified under natural transmission conditions .', 'Our modeling emphasizes the critical importance of understanding how the pattern of bacterial shedding in naturally infected animals changes over time .', '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 ( SORI and SOR ) corresponding to different assumptions concerning the relationship between latency , transmission and reactivity to the SICCT skin test .', 'In the traditional SORI model for bTB , occult ( O ) and reactive ( R ) animals are infected but not yet infectious , differing only in their response to the SICCT test .', 'Infectious animals ( I ) are assumed to be both infectious and detectable by the SICCT test with the same efficiency as reactive animals .', 'In the SOR model occult ( O ) and reactive ( R ) animals are both assumed to be potentially infectious eliminating the need for the infectious class ( I ) .', '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 ( S ) , Occult ( O ) , Reactive ( R ) and Infectious ( I ) ( Tables 3 , 4 ) .', 'A per capita turnover rate μ is sampled from an empirical distribution for each simulation ( Figure S3 ) .', 'A constant target herd size ( ) is maintained by balancing a constant per-capita removal rate ( ) with a fixed import rate of .', 'Herd size therefore fluctuates , with an instantaneous herd size of .', 'The extrinsic infectious pressure ( ) is the only parameter to vary with the parish testing interval ( PTI ) taking unique values for PTI 1 , 2 and 4 ( , , ) .', '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 Figure 1B .', '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 ( Figure S1 , Dataset S1 ) .', 'The duration of time between routine tests is also sampled from an empirical distribution ( with separate distributions for PTI 1 , 2 and 4 ) to account for the additional variation in the time to detection that is a consequence of delays in testing and the transition of herds between different parish testing intervals ( Figure S1 , Dataset S1 ) .', '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 ( ) and the infectious pressure ( ) .', 'In practice , and to increase the speed of simulations , this can be pre-calculated by explicitly calculating the probability of a false positive breakdown occurring between periods where there are no infectious animals within the herd .', 'Breakdowns can also be triggered by routine slaughterhouse surveillance that is modeled as a fixed probability ( ) that removals from the O , R and I compartments will be detected .', 'Breakdowns triggered by slaughterhouse surveillance are treated as confirmed breakdowns , with the first whole herd test carried out under the severe interpretation .', '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 ( Figure S2 , Dataset S1 ) .', '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 ( Figure S2 ) with scale parameter 0 . 0932 and shift parameter 0 . 494 ( to 3 s . f . ) .', 'The number of animals tested with a RHT ( X ) is then sampled from a binomial distribution as before with: 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 ( Table 1 ) .', 'In the field , the classification of reactors is based on cut-off values for the difference in reaction between avian and bovine tuberculin , with the cut-off value for a reactor changing with the severe and standard interpretation .', 'As a consequence , tests can , and are , re-interpreted at the severe interpretation following the confirmation of a reactor animal after slaughter .', 'In order to model the process of confirmation in a consistent fashion we must simulate the test outcome for each individual animal in the herd s
['Introduction', 'Results', 'Discussion', 'Methods']
['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 .']
['public health and epidemiology', 'veterinary epidemiology', 'epidemiology', 'infectious disease epidemiology', 'population dynamics', 'disease dynamics', 'biology', 'population biology', 'veterinary science']