Age-structured model

The compartmental models developed in [7] assumed that the movement of animals on and off a herd occurred at constant herd level turnover rate sampled from the Cattle Tracing System (CTS). As a consequence of this approximation, individuals spend an exponentially distributed duration of time on herds. In practice the distribution of residence times on herds can vary considerably between different business models impacting on the herd level rates of removal of residual infection from herds. Implementing these models within an individual based framework allows us to model more realistic residency times of individuals on herds and more accurately capture the variation in turnover rates between herds. An additional benefit of the individual based model framework is that we can also incorporate new evidence for the relative risk of infection with age and probability of reactor animals demonstrating visible lesions recently estimated by [21] (Fig. 1). After adjusting for testing patterns, we found that young beef and dairy animals experience a similar infection risk that peaks at 36 months before falling and plateauing for animals older than five years (Fig. 1A, Table 1). Although the infection risk is lowest in cattle under 12 months, the highest proportion of skin test positive animals is found to have visible lesions when they are examined at slaughter (Fig. 1B, Table 2).

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Table 1. Relative Risk of Infection RR(a).

https://doi.org/10.1371/journal.pcbi.1004038.t001

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Table 2. Age stratified probability of reactors with visible lesions/culture positive (P_VL(ɑ)).

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We estimate two alternative within-herd transmission (Susceptible-Occult-Reactive-Infectious: SORI, Susceptible-Occult-Reactive: SOR) models that differ in terms of the assumed timing of the onset of infectiousness. The SORI model is the more traditional view of bTB progression in cattle [22–24] where susceptible animals (S) must progress through a series of latent classes where they are first undetectable (or occult O), detectable (or reactive R) before finally becoming infectious (I). The SOR model accounts for evidence for the potential ‘early’ transmission of bTB [25] and assumes all infected animals are potentially infectious, but still differ in their detectability.

Following [7], we use a Sequential Monte Carlo implementation of Approximate Bayesian Computation (ABC-SMC) [26] for estimation of our models. Within this methodology, inference of model parameters is based on a set of goodness-of-fit metrics, stratified here by herd size, parish testing interval (PTI) and whether bTB has been confirmed by culture (OTF-S or OTF-W status). Until recently, the frequency of routine testing for herds was determined by the historical herd-level incidence within a parish. As such, for our study population, the frequency at which herds were tested is also a proxy measure for the background risk of infection.

We achieve a comparable fit to our previously published models with respect to the proportion of prolonged and recurrent breakdowns, both indirect measures of the within-herd persistence of infection (Fig. 2). In common with our earlier study [7], both models underestimate the proportion of OTF-W breakdowns in high incidence (PTI 1) areas and overestimate the same proportion in low incidence (PTI 4) areas. However, this discrepancy is far smaller than before with the majority of target values lying within the envelope of the 95% predictive intervals.

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Fig 2. Persistence and surveillance metrics for bTB in GB herds (2003–2011).

Within-herd measures of persistence and surveillance used as target metrics for ABC and to assess model fit. We present four key measures, from left to right: the proportion of prolonged (restrictions of greater duration than 240 days) and recurrent breakdowns, the proportion of herds with evidence of visible lesions and the total number of reactors per breakdown. Breakdowns are classified as either OTF-S (officially TB free suspended), where no reactors are found to have visible lesions (lime green circles), or OTF-W (officially TB free withdrawn) where at least one reactor was found to have evidence of visible lesions or be culture positive (magenta squares). The proportion of such OTF-W breakdowns is shown along with the proportion of these that were initiated by a slaughterhouse case (black circles). The relationship of each measure with herd size is plotted, with breakdowns further stratified by the historical parish testing interval (A, PTI1; B, PTI 2; C PTI 4) and breakdown status. Mean target observations are plotted with uncertainty estimated as ±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 [34].

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Likewise, both models still underestimate the mean number of reactors, in particular for breakdowns with no evidence of visible lesions (OTF-S) and for confirmed breakdowns (OTF-W) in PTI 1. Herd level incidence, as measured by the number of reactor animals removed during a breakdown, is remarkably consistent across testing intervals (Fig. 2). Although the predictive distributions are more variable, our new models still struggle to capture this pattern. These patterns arise as incidence in high-risk (PTI 1) herds is strongly constrained by the requirement to fit the incidence rate in low-risk PTI 4 herds where infectious animals can potentially remain within a herd for a longer period of time between routine testing. Classification of herds purely by testing interval is a crude approximation given that reservoirs of bTB in local wildlife is likely to generate considerably heterogeneity in the risk of background infection down to the herd level. Further heterogeneities not accountable within our modeling framework such as geographic variation in the efficiency of surveillance in slaughterhouses [27] or during routine testing [28] are also likely to contribute to this lack of fit.

The model captures the broad characteristics of the age distribution of reactor animals, slaughterhouse cases and visibly lesioned animals (Fig. 3). However, the assumption that animals are immediately replaced on removal from herds does introduce a small bias in the instantaneous age-distribution of herds with a consequently higher proportion of young (< 2 years) animals and reactors (Fig. 3A,B). There is also a notable discrepancy between the empirical estimates for the proportion of animals with confirmed M. bovis and model predictions (Fig. 3D). This is the consequence of approximating the age-dependent probability of confirmation of reactors using empirical estimates from reactor animals (Table 2). Laboratory confirmation of lesions is assumed to be 100% specific, so logically we must only simulate the confirmation process for reactors from infected compartments. As a consequence, false positive reactors reduce the proportion of reactors with visible lesions in simulated output, with the greatest discrepancy in younger reactors that are less likely to be infected.

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Fig 3. SORI model fit to age-distributions of reactors.

SORI model predictive distributions for the age of reactors (A). Age of “confirmed” reactors with evidence of visible lesions (B). Slaughterhouse cases (C) and the proportion of animals with visible lesions stratified by age (D). Solid points and lines indicate empirical target distributions, model predictive distributions are once again overplotted as shaded density strips where the intensity of color is proportional to the probability density at that point [34].

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Estimates of model parameters are more uncertain than in [7] as a consequence of improved mixing of parameters in the ABC-SMC procedure and a more realistic representation of inter-herd variability (S1 Fig.). Several parameters are poorly identified, in particular the reactive period, occult period, slaughterhouse detection parameter and density dependence parameter. This is a consequence of strong trade-offs, in particular between transmission and surveillance parameters. These trade-offs lead to, in the terminology of Gutenkunst et al. [29], ‘sloppy’ approximate posterior distributions where a large degree of variability has only a small impact on model predictions.

Once again we find no clear evidence to choose between the two alternative models. However, as we shall see, for the purposes of exploring strategies for vaccination it is DIVA test characteristics that are of primary importance, and interest. For simplicity we only present the SORI model results, but include equivalent simulations of the SOR model as supplementary information (S2–S6, S10 Figs.).

Vaccination scenarios

Vaccination is modeled by tracking vaccinated animals, recording the epidemiological status of each (S7 Fig.). Vaccinates are assumed to have the same rates of disease progression as unvaccinated animals, but differ only in their reaction to diagnostic tests and in having a reduced rate of infection by a factor of ε = (1—individual animal vaccine efficacy). We consider a set of three vaccination scenarios using different combinations of tuberculin and DIVA testing motivated by discussions with UK government policy teams. All scenarios are based upon an annual re-vaccination of herds in concert with annual herd tests. The DIVA Negate scenario adheres most closely to the current regulatory regime where all animals are tuberculin tested, with tuberculin positive vaccinates subject to an additional DIVA test to attempt to negate false positive reactors. For the DIVA Replacement scenario tuberculin testing is only used for unvaccinated animals, with vaccinates tested only using a DIVA test. Finally, we consider a strategy where restrictions are lifted based on the number of animals with confirmed M. bovis lesions rather than DIVA positivity. Under the VLend scenario testing is carried out as under DIVA Replacement. However for VLend, short interval testing can be suspended after two clear tests or two successive tests where DIVA reactors are found to have no confirmed lesions.

We compare each of these scenarios, by challenging newly vaccinated herds with a single infected animal onto the herd. Benefits of vaccination will only be manifested if the vaccinal protection is sufficient to offset any increase in the number of animal tests, and false positive reactors, generated by either sensitization to tuberculin or the incomplete specificity of DIVA testing. We use four key measures of the epidemiological and economic costs associated with bTB and testing to assess the benefit of vaccination at the herd level: the number of animals condemned as reactors (R); the number of tests (tuberculin and DIVA) needed to clear restrictions (T); the number of infected animals left in herds after restrictions are lifted (burden of infection missed by testing, B) and finally the number of herds that experience a breakdown before the herd clears the singleton challenge (N).

Vaccine efficacy and herd level benefit using γ-interferon DIVA test

Although proof-of-concept experiments have been carried out for a DIVA skin test [9] at the current time the only viable DIVA test for use in cattle is based on the γ-interferon blood test platform [8]. This test is similar to comparable tests used to diagnose human TB, such as the Quantiferon Gold or TSpot assays and with comparable or better performance characteristics [30]. In common with the SICCT, the interpretation of the γ-interferon DIVA test can be adjusted to trade off sensitivity and specificity of the test. The current candidate γ-interferon DIVA test depends on a combination of response to three antigens: ESAT-6, CFP-10 and Rv3615c. Data to characterise the response of these antigens have been collected from experimentally M. bovis infected animals (107 for ESAT-6/CFP-10, 109 for Rv3615c), non-infected controls (874 for ESAT-6/CFP-10 and 481 for Rv3615c) and a smaller data set of BCG vaccinated/experimentally infected animals (75) and BCG vaccinated non-infected controls (214). We initially selected cut-off values for the three antigens that maximize the DIVA specificity in the larger data set of unvaccinated animals. Applying these cut-off values to the smaller data set of BCG vaccinates provides an estimated DIVA sensitivity of 64.4% (95%CI: 48.8, 78.1%) and 99.4% specificity (95%CI: 96.9–100% CI). Based upon these DIVA test characteristics we simulated our estimated model over the range of individual protective efficacies ε~[0,1] (Fig. 4 and alternative version with linear scale S9 Fig.).

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Fig 4. Break-even points for vaccine efficacy under alternative testing scenarios using γ-DIVA test.

We estimate the break-even point for a protective benefit of BCG vaccination at the herd level under three alternative testing scenarios. We model DIVA testing using parameter estimates that optimize DIVA specificity of 99.4% under the constraint of maintaining a DIVA sensitivity comparable to tuberculin testing of 64.4%. We consider four key measures of the epidemiological, and economic, costs associated with bTB testing: A the number of animals condemned as reactors; B the number of tests (tuberculin and DIVA) needed to clear restrictions; C The number of infected animals left in herds after restrictions are lifted (burden of infection missed by testing) D The number of herds that experience a breakdown before the herd clears the singleton challenge. For all panels, solid black lines indicate the median break-even point for the baseline scenario with no vaccination. Dashed lines indicate the 95% quantiles of the baseline scenario. The distribution for each measure is calculated from 100 simulations with parameters drawn from the (approximate) posterior distributions of our estimated model, with each parameter set simulated once for each herd within our representative study population (of 6,601 herds).

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Across the scenarios considered, vaccination provides a clear protective benefit only in terms of the residual infection remaining on herds that clear movement restrictions (Fig. 4C). This marginal benefit comes at a considerable cost in terms of the number of tests necessary to clear restrictions on herds and the number of animals condemned as reactors under DIVA testing (Fig. 4A,B). Even if we assume that vaccination has 100% efficacy, we fail to see a herd level benefit of vaccination with over a three-fold increase in the number of animals condemned as reactors, with a median estimate of 8,663 reactors under the DIVA negate strategy (red) compared to 2,392 under the baseline, no vaccination scenario. Under this same comparison, DIVA replace is by far the most inefficient strategy with a 32-fold increase in the number of tests (median estimate of 51,554,010 compared to 1,582,048) and 144-fold increase in the number of reactors (median estimate of 345,775 compared to 2,392), despite the assumption of 100% efficacy. This difference is driven almost completely by a high rate of false positive reactors due to the lower DIVA specificity. These testing costs are mitigated through the VLend strategy, although the number of animals removed as reactors is still higher than in the absence of vaccination (median estimate of 10,277 compared to 2,392).

The relative impact of vaccination within these scenarios is driven almost completely by the specified test characteristics of the DIVA test, in particular the impact that the relatively low DIVA specificity compared to SICCT testing has when used within the intensive testing regime used for GB herds. As such, we expect these results to be largely insensitive to model choice for within-herd transmission, and indeed we see qualitatively comparable patterns for the alternative SOR model (see Supplementary Information). This simulation study demonstrates the key importance of DIVA test performance, rather than individual vaccine efficacy, in determining the cost-effective use of BCG vaccination in cattle. To explore this question in more detail we quantify the break-even points for seeing a protective herd level benefit of vaccination as a function of DIVA test characteristics.

Break-even points for DIVA sensitivity and specificity

To quantify the expected break-even point for DIVA test characteristics we performed a broad parameter sweep of assumed values of DIVA sensitivity and specificity under our three alternative testing scenarios. For this comparison we fix efficacy at ε = (1–0.61), corresponding to an individual level efficacy of 61%. We focus on three of our proxy measures relating to costs of testing: the number of breakdowns (N), number of tests required to clear restrictions (T) and burden of infection remaining (B). We calculate the probability of seeing a protective benefit by comparing the distribution of each proxy measure to the baseline distribution for tuberculin testing alone. These distributions are approximated by 100 posterior draws from our estimated model and under the vaccination scenario. The probability of benefit is calculated as the proportion of independent samples where the value from the vaccination scenario is less than the sample from the baseline scenario.

This probabilistic measure captures the uncertainty and variability in both the parameter estimates of our model and due to demographic stochasticity. We consider the break-even point to be when the probability (proportion) of benefit relative to the baseline of tuberculin testing only is 0.5.

DIVA negation. Although DIVA negation provides a benefit when DIVA specificity takes the estimated values used above (Fig. 4) the DIVA replacement and VLend scenarios are clearly more efficient over a wider parameter range than DIVA negation provided the DIVA specificity can be raised to a sufficiently high value (Fig. 5). Under DIVA negation the additional tests needed to negate tuberculin positive vaccinates overwhelms any protective benefit of vaccination in terms of the number of tests (Fig. 5A) and probability of breakdown (Fig. 5B), even for a DIVA specificity of 100%. It should however be noted that in terms of the number of tests carried out the maximal probability of benefit under DIVA negation occurs when the sensitivity of testing is zero and no animals are removed under testing. In this extreme scenario the protection afforded by vaccination is sufficient to reduce the burden of infection to a comparable level as tuberculin testing (Fig. 5C) with the increase in duration (and frequency) of breakdowns driven entirely by false positive tuberculin reactions.

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Fig 5. Probability of a protective herd level benefit of vaccination for alternative DIVA testing strategies.

We explore how the probability of seeing a protective benefit of vaccination depends on the assumed sensitivity and specificity of DIVA testing. The probability of benefit is calculated for a singleton challenge of infection and relative to the current statutory regime of tuberculin testing and slaughterhouse surveillance. Benefit is estimated from 100 simulations of our study population (6,601 herds) for three key measures (across columns): the total number of tests required to clear restrictions (A,D,G), the probability of restrictions being applied before the herd clears infection (B,E,H) and the probability of infection remaining in a herd when restrictions are lifted (C,F,I). We define the break-even point as 50% of herds demonstrating a protective benefit illustrated by the white band in the color map with red values worse this threshold and grey points better. We compare the three strategies described in the main text (across rows): (A,B,C) Under the DIVA negation scenario, the break-even point is limited by the considerable overhead in testing, with an increased probability of restrictions being applied before the herd clears infection (B) and an increase in testing (A) even for a 100% sensitive and specific DIVA test. (D,E,F) Under DIVA replacement, a protective benefit of vaccination can be achieved for DIVA specificities > 99.90% (D). The break-even point also depends on DIVA sensitivity, with a sensitivity of at least 40% being necessary to avoid increased risk of leaving infection in the herd after restrictions are lifted (F). (G,H,I) Under the VLend scenario, linking the maintenance of restrictions to detection of lesioned reactor animals mitigates the addition costs of testing under other scenarios (G). However, a specificity of greater than 99.85% is still required to see no increase in the number of breakdowns with vaccination (H), with the break-even point depending again on a DIVA sensitivity of greater than 40% (I).

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DIVA replacement. Under DIVA replacement, a DIVA specificity of above 99.90% in combination with an absolute sensitivity of at least 40% can provide a protective benefit of vaccination relative to tuberculin testing alone (Fig. 5 D,E,F). This required DIVA specificity is comparable to the lower bound we place on the specificity of the severe interpretation of the SICCT test for our model estimates. Once again it is important to note that the relationship between the probability of benefit and expected costs with DIVA sensitivity is non-linear, with highly sensitive tests potentially increasing the costs associated with testing at the herd level (Fig. 5D).

VLend: Changing the endpoint of breakdowns. Changing the endpoint of breakdowns to depend on evidence of visible lesions in reactor animals can demonstrate a protective benefit across all three cost measures (Fig. 5 G,H,I) for comparably lower values of DIVA specificity (although still very high at >99.85%) and sensitivity than under DIVA negation or DIVA replacement. Although the negative impacts of DIVA specificity are mitigated under this scenario, as a consequence DIVA sensitivity is more important; a break-even sensitivity of ~40% is constrained by the risk of leaving infection within the herd (Fig. 5I). Finally, it should be noted that the magnitude of the benefit under the VLend scenario compared to tuberculin testing would be considerably less if we used the same end-point definition (i.e. in terms of animals with VLs) for tuberculin testing in the absence of vaccination.

Study population

Our within-herd modeling framework estimates rates of transmission and removal of infection from herds based on the strict timescales imposed by the regulatory structure of the testing regime in Great Britain. The sequence of tests following disclosure of reactor animals places strict bounds on the duration of time that infection can remain undisclosed within herds. This is not necessarily true for breakdowns initiated by tracing tests, contiguous testing, inconclusive reactors or follow-up tests following a breakdown. To control for this extra source of variation in the time-to-detection we restrict our study population to “new” breakdowns that were disclosed by routine surveillance tests (classified as VE-WHT, VE-WHT2,VE-RHT,VE-SLH). To limit the impact of disruptions to testing during the Foot and Mouth Epidemic of 2001 and to allow enough follow up time to estimate the probability of breakdowns recurring we further limit our study population to breakdowns with start dates after 1/1/2002 and end dates before 1/9/2009. In a departure from our previous study we place no upper bound on the size of herds, but do require that herds had a minimum size of 10 animals on the start date of the breakdown and at least 30 CTS records for the associated CPH. Finally, we excluded any breakdowns where there was discretionary use of γ-interferon testing. This provides us with a study population of 6,601 herds containing 1,170,541 cattle on the start date of their breakdown.

Target metrics for ABC

We estimate the parameters of our within-herd models using an Approximate Bayesian Computation (ABC) method as described in [7]. ABC is a systematic framework for parameter inference when the likelihood function is intractable or computationally expensive [31]. Parameter estimation is performed through approximating a likelihood function through the probability of matching model simulations to the observed data using a set of goodness-of-fit metrics. For our within-herd models, these metrics consist of a set of within-herd persistence measures related to the duration and probability of recurrence of breakdowns stratified by the historical parish testing interval and herd size (Table 1).

For the purpose of model checking we consider an additional set of age-stratified metrics: the age-distribution of reactor animals, the age-distribution of reactor animals with evidence of visible lesions, the age-distribution of slaughterhouse cases and the probability of visible lesions with respect to age (Fig. 1B, Table 2). For the purpose of reproducibility, all target metrics and anonymised data for each of the study herds are provided as supplementary data tables (S1 Dataset).

ABC-SMC methodology

As in [7] we use the ABC-SMC algorithm of [26]. We sampled a set of 1,500 sets of parameters or particles (Table 3), from a set of uniform prior distributions (Table 4). For each set of parameters we simulate the model for a single replicate for each of the 6,601 herds in our study population and calculate the discrepancy between simulations and our set of target metrics (Table 5). This is a departure from [7], where we simulated multiple (500) replicates of the model at the median value of the herd-size used to stratify our persistence metrics. The new method generates more variable simulated output that is more representative of the variability intrinsic to the size and characteristics of the data set. We then simulate successive rounds where we accept and reject proposed particles according to a set of tolerances set on our summary metrics (described above). Newly proposed particles are sampled from the previous round and perturbed using a multivariate normal kernel with twice the sample variance estimated from the previous round. Convergence of the method is assessed through comparison of the predictive distributions simulated from the model to our set of target metrics (Figs. 2, 3) after 30 rounds of ABC-SMC, reducing the tolerance at each step to the 90th percentile of the particles in the previous round.

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Table 3. Model parameters.

https://doi.org/10.1371/journal.pcbi.1004038.t003

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Table 4. Prior distributions.

https://doi.org/10.1371/journal.pcbi.1004038.t004

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Table 5. Epidemiological target measures for ABC.

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Simulation algorithm

Our epidemiological models are implemented in an individual based framework where we track information on each animal within the population (Table 6), rather than the number of individuals within given epidemiological compartments (S,O,R,I…). Epidemiological events are modeled as a continuous-time Markov process [32] defined by the list of events and rates for the SORI and SOR models detailed in Tables 7 and 8. The demographic events of birth, death and movement off a herd are simulated as a non-Markov process. The time of each of demographic events is sampled from an extract of the CTS database for each individual animal added to the model. During each step of the model we simulate the time for the next Markov event (t_MARKOV) and compare to the time of the next non-Markov (demographic) events (t_{NON MARKOV}). If t_{NON MARKOV} < t_MARKOV, we carry out the demographic event first and recalculate a new t_MARKOV. Otherwise a Markov (epidemiological) event is simulated and the model time updated.

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Table 6. Individual animal variables.

https://doi.org/10.1371/journal.pcbi.1004038.t006

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Table 7. Markov events for SORI(V) stochastic transmission model.

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Table 8. Markov events for SOR(V) stochastic transmission model.

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Demographic events

When the herd is initialized, the birth, death and off-movement times for each individual animal are sampled using an extract from the CTS database (Table 9). This extract contains four pieces of information for each animal alive on the start-date of the corresponding breakdown for that herd within our study population: HerdId links the animal record to a unique herd within our study population: OccupancyTime is the number of days the animal remained on the herd after its first on-movement; AgeOn is the age of the animal when it was moved onto the herd (0 for births); LifeTime is the total number of days the animal lived (on any herd) and BreakAge is the age of the animal on the disclosing test of the breakdown associated with that herd in the study population. This information allows us to sample the timing of all of the demographic events occurring to an individual over its lifetime: time of birth, time of movement off herd, time of death.

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Table 9. Individual animal demographic data extract from cattle Tracing System (CTSTable).

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For each animal added to a herd at the start of a simulation we sample a row (i.e. a set of values of OccupancyTime, AgeOn, LifeTime and BreakAge) from Table 9 and calculate the birth, death and off times for that animal:

Birth_time = (t-BreakAge) + unif(0,0.001)

Death_time = Birth_time + LifeTime + unif(0,0.001)

Off_time = Birth_time + OccupancyTime + unif(0,0.001)

Where t is the current time and unif(0,0.001) is a uniformly distributed random number in the range [0,0.001] added to ensure that each individual has a unique age, death and off movement time.

Herd size is initialized to the number of animals present on the herd at the beginning of breakdown associated with that herd. A constant population size is maintained by immediately replacing animals that are removed from the herd (through either demographic processes or testing) with a new animal. The birth, death and off times for each replacement animal are calculated in a similar way by sampling a row from Table 9:

Birth_time = (t-AgeOn) + unif(0,0.001)

Death_time = Birth_time + LifeTime + unif(0,0.001)

Off_time = Birth_time + OccupancyTime + unif(0,0.001)

In this way we model both births and cattle movements onto the herd, with the relative proportion of replacement animals through births and on-movements determined by the CTS extract for that herd and the value of AgeOn. The CTS extract for all herds in the study population is included as a supplementary data table (S1 Dataset).

SICCT testing model

SICCT testing, and the sequence of tests before, during and after a TB breakdown is modeled as described previously in [7]. 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.

The model is initialised and 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 S8 Fig.

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 corresponding to the historical parish testing interval (PTI) for that herd. 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 (S1 Dataset). 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 (S1 Dataset).

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. This variability in the number of animals tested is the consequence of different eligibility criteria for animals based on their age and use. In our original models we described this variability with empirical distributions. Within the individual based model we can incorporate these eligibility criteria explicitly using the age of animals on the date of a test and their scheduled exit date from the herd (which is pre-calculated as described above). For whole herd tests (WHT) all animals older than 6 weeks are eligible for testing, whereas for routine herd tests (RHT) animals must be older than 2 years to be eligible.

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.

Age-stratified model of confirmation and slaughterhouse surveillance

As before, we simulate switching to the severe interpretation of the SICCT test used in OTF-W breakdowns after the detection of visible lesions (VLs) within reactor animals. However, our earlier models assumed that the probability of VLs being detected was constant per reactor—clearly inconsistent with the pattern of age-dependence in reactor rates and presentation of lesions (Fig. 1). Our current model uses this empirical pattern to simulate the number of lesioned animals in a test through a look-up table based on the animal’s age (Table 2). The lesion status of each individual reactor is then simulated as a Bernoulli trial.

Slaughterhouse surveillance also depends on the detection of visible lesions, or culture confirmation carried out as part of routine carcass inspection. As such, Fig. 1 implies that the efficiency of slaughterhouse surveillance should also depend on the age of the animal. We therefore model the efficiency of slaughterhouse surveillance as the conditional probability of detecting infected animals given that they have signs of visible lesionsP_SL(ɑ). We define the relative efficiency of slaughterhouse surveillance P_RI compared to inspection of reactor animals such that:

Vaccination and DIVA testing, assumptions and model parameters

Modelling the impact of vaccination requires additional model parameters that describe the individual level impact of vaccination and test characteristics of vaccinated animals (Table 10). For all vaccination challenge scenarios, the herd is initialized with a whole herd vaccination and a single infectious individual. The herd is then re-vaccinated on a strict annual cycle after any scheduled whole herd test.

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Table 10. Vaccination model parameters.

https://doi.org/10.1371/journal.pcbi.1004038.t010

Our understanding of the mode of action of BCG through which animals are protected is still incomplete. Our best estimates of vaccine efficacy come from natural transmission studies [4], [5]. In these studies vaccinated animals have been found to be free of disease suggesting that sterilizing immunity is possible. However, given the necessarily limited timescale of these trials it is also possible that BCG is simply acting to slow the rate of progression to detectable disease. Challenge experiments have demonstrated such an effect of BCG with a significant reduction in pathology in inoculated vaccinates, but no sterilizing immunity [2]. However, given that the effective dose under natural transmission may be lower than under artificial challenge these data do not rule out the possibility that BCG also reduces the susceptibility of individual cattle. Given that there are no data to inform the magnitude of the impact that BCG may have on rates of progression we choose to model the individual level protective effect of vaccination through a single parameter (ε) that describes the per-capita reduction in the risk of vaccinated animals acquiring infection. This choice of parameterisation also has the advantage of corresponding closely to the definition of vaccine efficacy as estimated from natural transmission studies.

Given the relative paucity of evidence described for reduction in the severity of disease for vaccinates, we assumed that rates of progression for infected vaccinates were unchanged. Loss of protection of vaccinates is modeled by introducing two vaccinate statuses (V₁,O_V1,V₂,O_V2) that are assumed to have the same basic test characteristics but differ only in their relative risk of infection (S7 Fig., Tables 7 and 8). Protection is assumed to be lost at a constant rate with the average duration of protection fixed at 1 year [2], [33]. Data on the effect of re-vaccination are lacking. In the absence of this important information we treat re-vaccinated animals in exactly the same way as newly vaccinated animals. As a consequence, our model may overestimate both the individual level protection of re-vaccinated animals and their sensitivity to tuberculin testing (as described below).

DIVA testing is modeled by an assumed DIVA sensitivity p_Dand specificity 1-p_DFP defined relative to the true infection and vaccination status of animals (Table 10). An important data gap should be highlighted, in that as with all bTB tests, the empirical estimates of current generation DIVA tests are estimated relative to the presence or absence of visible lesions. The potential misclassification of infected individuals by this imperfect gold standard measurement complicates the translation of empirical estimates of test characteristics to model parameters. In the absence of a true gold-standard test, the relationship between true test characteristics and relative measures cannot be modeled a priori and care must be taken in comparing between the absolute values of these parameters used within the model and relative values that would be estimated relative to visible lesions or culture.

Tuberculin testing of vaccinates

Although the sensitizing effect of BCG vaccination on tuberculin testing is well known, quantitative data on the impact of BCG on test status are limited to a single challenge study carried out by AHVLA [6]. BCG vaccinates were SICCT tested at 90, 180, 270, 450 and 720 days post vaccination. Skin test measurements were then interpreted at the standard and severe interpretation and the probability of animals being classified as a reactor calculated (Table 11). We use these empirical data within our model to define the specificity of SICCT vaccinated animals. As a consequence of the sampling frequency of this experiment our model will underestimate the reactivity within the first 90 days post-inoculation (which we define as 0). There is a further data gap with respect to the sensitization after 2 years and on re-vaccination. We assume that the specificity of vaccinates takes a constant value post 720 days, and that re-vaccination leads to the same time-dependent pattern of sensitization relative to the time of revaccination. As a consequence of these assumptions our model will likely underestimate the number of false positive reactor animals in the first 90 days post-vaccination.

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Table 11. Time-dependent sensitisation of vaccinates to SICCT [6].

https://doi.org/10.1371/journal.pcbi.1004038.t011

We model the sensitization of BCG vaccinates to tuberculin using a time-dependent probability of an animal being classified as a reactor estimated from challenge studies carried out by AHVLA [6]. The probability of being classified as a reactor is assumed to be constant with coarse-grained 90-day intervals and take the same constant value for all animals older than 720 days.