A simulation model for the spread of bovine tuberculosis within New Zealand cattle herds

ELSEVIER

PREVENTIVE VETERINARY MEDICINE Preventive Veterinary

Medicine 32 (1997) 57-75

A simulation model for the spread of bovine tuberculosis within New Zealand cattle herds N.D. Barlow a,*, J.M. Kean a, G. Hickling b, P.G. Livingstone A.B. Robson d a.4gResearch, Canterbury Agriculture and Science Centre, PO Box 60, Lincoln, New Zealand ’ Depa&nent of Entomology and Animal Ecology, Lincoln Uniuersity, PO Box 84, Lincoln, New Zealand ’ Animal Health Board, PO Box 4312, Wellington, New Zealand ’ Centre for Computing and Biometrics, Lincoln University, PO Box 84, Lincoln, New Zealand Accepted 3 December

1996

Abstract Bovine tuberculosis, caused by Mycobacterium bouis, presents a major problem to New Zealand agriculture because of the risk that it poses to export-market access. New Zealand research has focused largely on the epidemiology of the disease in wildlife reservoirs, and relatively little is known about the dynamics of the disease in cattle. This study, therefore, investigates bovine tuberculosis (Tb) dynamics within cattle herds, by construction and application of a simple simulation model of disease transmission. The model was designed firstly to estimate rates of disease transmission within herds, and secondly to identify likely consequences of changes in herd %-testing policies. Both deterministic and stochastic versions of the model were used to achieve these aims. The model suggests that within-herd Tb transmission does occur and contributes to the reactor rates observed under annual herd testing regimens. The mass-action disease transmission coefficient (proportion of susceptible animals infected per unit time per infectious animal, i.e. not per diseased animal or per reactor), appears to be in the order of 2.7 X 10m5 per cow per day for a typical herd of around 200 animals, resulting in a contact rate (number of potentially infectious contacts made per infectious cow per day) of about 0.0073. These are average estimates for both beef and dairy herds. ModeI results suggest that improving the sensitivity of the test used to diagnose bovine Tb would improve control in areas where wildlife reservoirs are absent but have little effect where they are present. Reducing the time between tests of herds on Tb-induced movement control from the current 6 months to 2 or 3 months reduces the average time a herd spends on movement

* Corresponding

author. Tel.: 0061-3-325-6900;

Fax: 0061-3-325-2946;

0167-5877/97/$17.00 0 1997 El sevier Science B.V. All rights reserved. PII SO167-5877(97)00002-O

E-mail: [email protected]

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control and hence national Tb prevalence. In the presence of wildlife reservoirs of infection, both the total number of tests and total reactors per unit time increase, but the extent depends on the level of external infection. In all scenarios examined, involving thousands of model runs in total, infection was invariably absent from the modelled herd by the time it was considered clear of Tb based on testing results. This suggests that the caudal fold test is a realistic measure of herd Tb status and that Tb is unlikely to persist in herds under current testing practices in the absence of anergic cattle or an external source of infection. Specificity of the caudal-fold test as used in practice was estimated to be greater than 99%. 0 1997 Elsevier Science B.V. Keywords: Bovine tuberculosis; Mycobacterium bovis; Disease-host model; Cattle

1. Introduction Bovine tuberculosis (Tb) is a bacterial disease caused by Mycobacterium bouis, which infects a wide range of mammals. Of most concern worldwide is its infection of farmed cattle and deer, and its persistence in wildlife populations (Allison, 1992). In New Zealand, current policies to control Tb in livestock include regular herd testing of susceptible stock, with subsequent slaughter of those with a positive reaction to the test. There is also slaughterhouse surveillance of carcases, and a quarantine-like “movement control” period for any herds found to contain infected animals (Livingstone, 1991). In some areas, wildlife-population reduction can help lower the incidence of Tb in nearby herds (Allison, 1992). In New Zealand, Tb control is complicated through re-infection from infected wildlife reservoirs such as the brush-tailed possum (Trichosurus vulpecuZu). As a result, 2.9% of New Zealand’s cattle herds were on movement control in the 1992/1993 testing season, which exceeds the internationally recognised “Tb-free” limit of 0.02% (Anon, 1992). The percentage of herds on movement control is the standard worldwide measure of Tb prevalence. Current Tb-control measures rely heavily on regular herd testing, with slaughter of positive test reactors, and movement control of known infected herds. Unfortunately, no cost-effective screening test approaches both 100% sensitivity and 100% specificity, so some infected animals may remain in post-test herds. Potentially, these could spread infection to herd-mates and their presence dictates that each herd is likely to spend a longer total time on movement control than the sum of the intervals between the two minimum necessary tests. In addition, if the interval between herd tests is too long, then cattle that have been infected since the previous test may become infectious to other members of the herd before being tested again. It is unclear whether the current testing regimen is optimal, given the sensitivity and specificity of the principal test (the caudal-fold (CDF) test). Morris et al. (1994) reviewed the epidemiology of M. bovis and highlighted the lack of recent literature on the basic biology and ecology of the organism. Nevertheless, it is clear that populations of wildlife such as possums make a large contribution to the maintenance of agricultural Tb infections in many areas of New Zealand (Livingstone, 1986). For this reason, bovine Tb models in New Zealand have focused largely on its epidemiology in possum populations (e.g. Barlow, 1991a,b, 1993, 1994; Roberts, 1992).

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In contrast, the role of within-herd transmission in sustaining the Tb problem in cattle herds is largely unknown. The dynamics of bovine Tb in Australian range cattle was modelbd by Stoneham and Johnston (19861, but has limited relevance to the more intensively managed New Zealand situation. Our paper, therefore, describes the formulation and application of a simple simulation model of bovine tuberculosis dynamics within a cattle herd, based on a preliminary model (PG. Livingstone, unpublished MAF report) which structured the problem, collated much existing information and developed some initial estimates of Tb transmission rates. The model described here was used in combination with appropriate data from the literature and from the NZ Ministry of Agriculture and Fisheries (MAF) Tb herd-test database, to achieve the aims: to estimate Tb transmission rates within herds; to assess the likely importance of within-herd Tb transmission in spreading infection in the absence of continued inputs of infection from external sources; to predict the likely effects of increased sensitivity of the test and changing the herd testing and movement control regimens (in the presence and absence of infection from wildlife vectors); and to indicate likely times spent by herds on movement control under different testing regimens-a necessary parameter for proposed future models addressing Tb spread between rather than within herds.

2. Model The model simulated the change in disease state of individual cattle in a herd on a daily basis. The herd was assumed to contain a constant 200 animals, corresponding to the average size of herds in the Hohotaka, North Island data set (see below), and was divided into disease classes representing susceptible (state S), incubating (states U and R), and infectious (state I) animals. The spread of tuberculosis between herd members was assumed to be proportional to the numbers of infectious and susceptible cattle in the herd at any time, with the number of new infections per unit time given by the mass-action term /3SZ, where S and I are the number of susceptible and infectious cattle respectively and /3 is the disease-transmission coefficient (Anderson and May, 1979). Neil1 et al. (1989) found that the density of cattle (and by implication the contact rate between susceptible and infectious individuals) was an important factor in transmission of bovine Tb, supporting the use of the mass-action principle. As in most quantitative epidemiology studies, p is not well quantified. It has been suggested that some genotypes may be relatively immune (Carmichael, 1941), but genetic resistance of hosts to bovine Tb has never been conclusively demonstrated (Morris et al., 1994). Following infection, bovine tuberculosis develops through a number of stages represented by states U, R, and I in the model (Kleeberg, 1960; Blood and Radostits, 1989). State U represents an initial period of latency during which the cattle have not yet mounted: a cell-mediated response to invading A4. bovis bacteria. It takes 8-65 days before infected cattle achieve the maximum immune response (Kleeberg, 1960). The CDF test used, at present, to detect bovine Tb in a herd is based on this response (Kleeberg, 1960; Blood and Radostits, 1989). State U in the model, therefore represents a state of limited responsiveness and low sensitivity to the test. The next state of disease,

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R, represents animals with non-infectious disease but which are responsive to the CDF test so test sensitivity is higher for this state. The total duration of latency is thought to lie within the range 87-226 days (Neil1 et al., 1992, in experimentally infected calves) to 7 years (calculated for Australian range cattle by Stoneham and Johnston, 1986). However, a realistic range for most New Zealand cattle is thought to be 6-20 months (P.G. Livingstone, unpublished MAF report), which corresponds to the sum of the lengths of states U and R in the model. In practice the durations of these states vary between cattle, depending on the route of infection and the initial dose (Neil1 et al., 1992). Stress resulting from pregnancy, lactation, poor nutrition, or other disease depresses the immune response in cattle, thus also affecting the test sensitivities and durations of the states (Kleeberg, 1960). The final state, I, corresponds to infectiousness, and cattle are assumed to remain infectious until detected by the CDF test and removed. Blood and Radostits (1989) suggested that infectious individuals may be infectious only intermittently. This was not considered here because any periodic loss of infectiousness could be accounted for, to a first approximation, by adjusting the value for the disease-transmission coefficient ( /3). If infectious cattle remain in the herd for a long time, they may become so heavily infected that their immune system no longer responds to additional tuberculin extract injected for the herd test (Kleeberg, 1960). These “anergic” cattle may be relatively unresponsive to the standard Tb diagnostic test. Anergic cattle were not considered in the model, as they are thought to be currently of little importance in New Zealand farming situations, where most herds are thoroughly and regularly Tb tested. Anergy was important in the early years of herd testing, and would need to be considered if simulations were to be investigated in which the time between herd tests was greatly extended, or in cases where there may be incomplete mustering of herds as in Australian range cattle (Stoneham and Johnston, 1986). Regular CDF herd testing is the key to current bovine Tb control in agricultural stock. It therefore, forms an important part of the simulation model. Also, herd-test results represent the principal source of data for validation of the model. The current Tb-testing regimen used throughout most of New Zealand involves regular one- or two-yearly testing of herds considered free from infection and termed “accredited”; the testing interval is determined by their geographical location and consequent risk of infection from stock movement or wildlife vectors. Any herd that fails a test (i.e. has positive reactor cattle) is immediately classed as “infected movement control”. It loses this designation on passing two successive tests at intervals of at least 6 months, when it becomes “Tb free”. To become reaccredited, a herd must pass a further two herd tests at intervals of approximately 12 months; failure at any of these tests results in “infected movement control” classification again. This testing regimen was used as the default for the model (although it was modified for many of the simulations). Herd tests were implemented as discrete events at the appropriate time step, with positive reactors (given by the test sensitivity multiplied by the number of cattle in the corresponding model class) being removed and replaced by susceptible cattle in order to keep the total herd size constant. The model and test regimen are summarised in Fig. 1. An additional complication is that the CDF test is not entirely specific to bovine tuberculosis. Sometimes individuals that react positively to the CDF test are not infected

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: Test

1Test

61

i Test

Reactors I

I

Fig. 1. The structure of the model and how the caudal fold (CDF) test is implemented. q is the test specificity and s its sensitivity, and the subscripts denote the stage of disease at which the animal is tested. Disease transmission has two components representing proportions of susceptible animals becoming infected per unit time: p :I from infectious cattle in the herd, and k from external sources such as feral vectors.

with Al. bovis but with a closely related bacterium such as M. avium (Kleeberg, 1960). False-positive reactions tend to be aggregated in space and time, corresponding to the transient presence of other mycobacteria (Blood and Radostits, 1989). It was assumed in the model that “false reactors” resulting from the imperfect CDF-test specificity would contribute to total reactors from a test, but would not affect the testing- regimen classification of the herd. That is, a herd would not be placed on movement control as a result of only false reactors. This is a realistic assumption, as real-world herds are only placed on movement control if CDF test reactors are found to be visibly lesioned at slaughter, or if they also fail a different follow-up test. The model operated with a time step of 1 day and, except where specifically noted, with the default parameter set shown in Table 1. States U and R were subdivided into five and ten sequential subclasses respectively, in order to obtain realistic distributions

Table 1 Parameter

values for the model of within-herd

Tb spread

Name

Default value

Range of values tested

Duration of state U Duration of state R Duration of state I Test sensitivity in state U Test sensitivity in state R Test sensitivity in state I Test specificity

22 days 180 days until removed by testing 0% 80% 80% 100% 3.0x 10-j 0

14-22 days 90-270 days -

P k See Fig. 1 for description

of parameters

O-30% 98-100% o-10-4

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of residence times within these states. That is, animals stayed in these states for the mean time specified in Table 1 with a standard deviation equal to the mean time divided by the square root of the number of subclasses. This is a compromise between the two unlikely extremes of a fixed residence time with no distribution (which would result from a number of day-long subclasses equal to the duration of each state), and a negative exponential distribution (which would result from the use of a single class for each state U and R). The transfer rates between subclasses of U and R were given by: (number of subclasses) divided by (duration of whole stage in days). The deterministic model was compared with a stochastic version, in which proportions of animals failing CDF tests Table 2 Estimated values for the transmission coefficient, p, for bovine tuberculosis spread within cattle herds and the disease contact rate (number of potentially infectious contacts per infectious animal per day), given different assumptions for test sensitivity over the duration of infection, duration of the “responsive” disease state (R, see text and Fig. 1 for explanation), test specificity and herd size Row

Test sensitivity in states U, R, and I

Duration of unresponsive infected state (VI

Duration of responsive infected state (R)

(%I

(days)

(days)

Herd size

Test specificity (%I

Estimate for /3 (x 1om5 per cow

Estimate for contact rate (x10-3 rate per day)

per day)

NZ (Hohotaka, 1988-1993) 22 1 0/80/80 2 O/80/80 14 22 3 30/80/80 4 O/80/80 22 22 5 0/80/80 22 6 O/80/80 22 I O/80/80 22 8 O/80/80 22 9 0/80/80

180 180 180 180 180 90 270 180 180

200 200 200 100 300 200 200 200 200

100 100 100 100 100 100 100 98 98

2.20 2.30 2.39 4.39 1.50 1.70 2.19 _a _a

4.4 4.6 4.8 4.4 4.5 3.4 5.6 _a _b

NZ (1952-1955) 10 0/80/80 11 O/80/80

22 22

180 180

200 a 200 a

100 98

1.72 1.31

3.4 2.6

Canadian 12 O/80/80

22

180

200a

100

0.97

1.9

Egyptian 13 0/80/80

22

180

200 a

100

0.69

1.4

200 200

100 98

4.59 4.52

9.2 9.0

Hypothetical, constant reactor rates at each annual test 14 O/80/80 22 180 15 O/80/80 22 180

Results are based on fitting the model to data for declining reactor rates on annual testing over approximately 5 years at four sites (see text), and for a hypothetical situation in which reactor rates were maintained at 10% rather than caused to decline. a Herd size assumed but unknown. b Impossible values (less than 0).

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and proportions of animals transferring between classes were re-interpreted as probabilities. The outcomes in each time step, in terms of numbers of animals failing a test or passing from one class to another, were chosen from Poisson distributions based on the expected (mean) numbers involved (implemented as suggested by Law and Kelton, 1991, p. 503). The purpose of the stochastic model was to ensure realistic average outcomes, given the likelihood that individual herd status over time would depend strongly on the fates of small numbers of animals and would, therefore, be highly variable. Three different scenarios were assumed for CDF test sensitivity over the course of disease development (Table 2). In practice, test sensitivity overall is around 80% in New Zealand cattle herds and specificity 98% or greater (data from Ryan et al., 1991). In most runs of the model, we assumed that there was no external source of Tb infection from stock purchases, infected wildlife, or neighbouring infected herds. The model was programmed in Turbo Pascal and run on an IBM 486/50 PC.

2.1. E,rtimation of the transmission

coejkient

by applying

the model to herd histories

The deterministic version of the model was used to estimate values for the transmission coefficient, p, under different assumptions about test sensitivity and specificity, duration of the incubating stages (states U and R) and herd size. This was achieved by varying p until predicted outputs of reactor rates under simple annual testing regimens corresponded to those observed in four data sets. These data sets consisted of herds in: New Zealand (Hohotaka, North Island) 1988-1993 (G. Hickling, unpublished data); New Zealand 1952-1955 (Laing, 1955); St Jean County, Canada 1928-1932 (Anon, 1958); and Egypt (Government herd) 1953-1956 (Myers and Steele, 1969) (Fig. 2). In each case, the model was initialised with one animal in state U and 199 in state S. It was then run with repeated “trial” tests but no removal of reactors until a test gave the observed number of reactors corresponding to that in the first test of the data set. The run was then continued with annual tests and removal of reactors at each test, these being compared with numbers observed and the sums of squares of differences calculated and summed for all tests in the data set. The process was repeated for different assumed p values until overall sums of squares were minimised and patterns of reactors generated by the model over all tests resembled that observed. The p value corresponding to this was considered to be the best estimate for that data set. We assumed that the herds experienced negligible input of infection from external sources for the duration of the herd tests; this was reasonable in the Hohotaka data set since a major possum-control operation had been undertaken at the beginning of the period considLered (G. Hickling, unpublished data). Unfortunately, the complexity of current New Zealand testing regimens precludes the use of most recent herd data for estimating p in this way. However, in the absence of infection from external sources or anergic cattle, reactor incidence always declines under annual or more-frequent testing. Therefore, it was possible to estimate an upper limit for p as the largest value that was consistent with a constant reactor incidence (arbitrarily chosen as 10%) over the series of annual tests, using the same model-fitting procedure as above.

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Veterinary Medicine 32 (1997) 57-75

24 3.0 I8 2.0

6

i! z

I

2

3

4

5

6

I

2

3

4

5

-q

Annual Test Fig. 2. Observed (dark bars) and simulated (light bars) percentages

of reactors in successive annual tests: a) New Zealand (Hohotaka) data; b) New Zealand (dairy herd); c) Egyptian; d) Canadian. The solid lines represent simulated patterns of reactors in the successive tests on the assumption of no within-herd transmission ( p = 0).

2.2. Estimation

of the transmission

coeficient

direct from herd histories

Another method for estimating p relies on the knowledge of susceptible, infected, and infectious host numbers at several different times (Hone et al., 1992). Data on herd size, reactor incidence, and test date were available from MAF herd-test histories. However, the only situation in which we could be reasonably sure of the number of infectious cattle in a herd was when a single anergic beast had been implicated by veterinarians as being responsible for a series of infections. In such cases, p may be estimated directly from MAF herd histories, provided that the herd is thought to have contained a single anergic animal. Details of only one such herd history were available. In this example, an infected cow was brought into a herd from a known problem area,

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after successfully passing a number of CDF tests. Over the next two-and-a-half years, individual cattle from its mob reacted positively to routine CDF herd tests, and over half of these had visible lesions at slaughter. Eventually, the animal was killed on the farm and found to be rife with tuberculous lesions (J. Adams, personal communication). Subsequent to the animal’s removal, the herd remained free of Tb and a possum survey carried out during the infection period was unable to identify Tb in any of 800 possums killed locally. Therefore, it is considered likely that this epidemic was due entirely to the single anergic cow brought in from a Tb “endemic area”, where there had been a known wildlife-source of infection (J. Adams, personal communication). Many other herd test histories are available from MAF, but these lack the detailed observations described for the previous herd. However, several herds had persistent Tb breakdowns in non-endemic areas. Their histories provided information on the dates of herd tests, how many were tested, how many reacted positively, and how many of these were lesioned at slaughter. Assuming that the evident Tb problems were due to a single anergic cow in each herd and that all CDF reactors, whether lesioned or not, were actually Tb-infected, it was possible to estimate the highest likely value for p for each of the nine herds for which data were considered adequate. 2.3. Estimation

of test specificity

A very approximate estimate of the specificity of the CDF test could be obtained from MAF herd histories. Herds were first grouped by size, then for each herd-size class the number of tests with no reactors was counted and compared with the number of tests with false reactors (taken to be those cattle giving positive results in accredited herds with either no visible lesions on slaughter or a negative result for a subsequent comparative cervical test). Given x tests with no reactors and y with false reactors in a herd of size n, the test specificity as it relates to an individual animal is calculated as (X/(X + y)) ‘In . Absence of visible lesions does not confirm absence of infection, so this procedure will tend to underestimate specificity. 2.4, The effect of herd test sensitivity The stochastic version of the model, with default parameters, was used to estimate the likely practical advantage in developing a more sensitive test. Herds were assumed to be initially infected, with a composition of 196 S-, zero U-, two R- and two I-state cattle and the model was run 500 times for each regimen tested. Test sensitivity was increased from 880to 90% for states R and I and the result assessed in terms of: the time taken for a herd to become reaccredited; the time it spent on movement control; the total number of tests it underwent; and the total number of reactors produced until reaccreditation. The second criterion is particularly important because the time herds spend on movement control is a key component of the national prevalence of movement-control herds, upon which New Zealand’s international Tb status depends. 2.5. The effect of d@erent herd-testing

regimens

The stochastic model was used to investigate the likely effects of changing the interval between the two movement-control tests. Two sets of criteria were used. In the

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first case, the stochastic model was run for 10 years from an initial state of 196 S, zero U, two R and two I cattle and the effect of changing the movement-control regimen was expressed in terms of the percentage of time that the herd spent on movement control and the number of tests undergone per year (both averaged over 500 simulations). It has been suggested that repeat testing within 7-8 weeks may lower the specificity of the second test owing to non-tuberculous cattle reacting as a result of exposure to tuberculin in the previous test (Kleeberg, 1960). Therefore, the specificity of the herd test was assumed to be 95% for any test carried out within 1 month of a previous test, as a conservative representation of this effect. The model was also modified to include variable levels of infection from a wildlife source. This is because one of the main constraints to reducing the time between tests in movement control herds is the location areas with continued infection from nearby wildlife of these herds in “endemic” vectors. Under these circumstances, reducing the time between tests simply increases the number of tests the herd undergoes without clearing it of infection. Thus, there may be a trade-off between the degree of external infection and the benefits of frequent testing. If the probability of such infection is low, the overall average time that the herd spends on movement control may be minimised by tests at short intervals (e.g. 3 months rather than 6 months) to clear infection rapidly and remove the herd from movement-control status, on the basis that it will take a relatively long time for the herd to be reinfected and test positive again. However, if the probability of external infection is higher, the herd will be on permanent movement control and there will be no advantage in a short interval between tests. In practice, a 12 month interval is common in such areas. In the second case, rather than running the model for 10 years it was run until the herd became reaccredited in a situation free from external infection. In this case the results of the different regimens were expressed as the time to reaccreditation, the time spent on movement control, the total number of reactors and the total number of tests undergone until reaccreditation. The same starting conditions were assumed and the stochastic model run 500 times to generate mean outcomes.

3. Results 3.1. Estimation

of the transmission

coeficient

using the model

Table 2 shows values for the transmission coefficient, /3, estimated by fitting the model to annual testing results from four sites and given different assumptions about the other model parameters. For the default values of these other parameters, as in Table 1, /3 values were 2.3 X 10m5, 1.7 X 10m5, 1.0 X 10e5, and 0.7 X 10M5 per cow per day for New Zealand (1988-19931, New Zealand (1952-1955), Canadian, and Egyptian herds, respectively. Corresponding contact rates (number of potentially infectious contacts per infectious animal per day) were 0.0046, 0.0034, 0.0019 and 0.0014 per cow per day. Table 2 (rows 1-3) shows that varying the profile of CDF-test sensitivity over the period that an animal is infected but not infectious (states U and R) has little effect on the estimate of p. The sensitivity profile was adjusted both by reducing the length of time after infection during which sensitivity is zero (state U, row 2 in Table 21, and by

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increasing the sensitivity from zero to 30% during latency (the previously unresponsive state U, row 3, Table 2). However, herd size has a major effect, as would be expected from the mass-action transmission term in which new infections are proportional to the product of infectious and susceptible animals. Thus, the estimate for p varies in a direct inverse relationship to herd size (rows 4 and 5 in Table 2). The assumed duration of state R, which approximates the latent period for the disease since state U is comparatively short, also has a considerable effect on the estimate of p (rows 6 and 7 in Table 2). Increasing the latent period by increasing the duration of state R from 180 to 270 days (row 7 in Table 2) means that /3 must be increased to compensate for the delay in becoming infectious, while the reverse applies if state R is reduced in length to 90 days. Finally, reducing test specificity from 100 to 98% (rows 8 and 9, Table 2), is inconsistent with the observed data: specificity cannot be this low, because in all the data sets except the New Zealand dairy herd, several of the tests gave reactor rates of less than 2%, even in the likely presence of actual Tb (see Fig. 2). In the New Zealand dairy herd data set, changing specificity to 98% had little effect on the estimate of p (rows 10 and 11, Table 2). The likely upper limit for p, corresponding to maintenance of constant 10% reactor rates in successive tests, was 4.6 X lop5 per cow per day (Table 2). With testing intervals shorter than 1 year (as is now the case for herds in which Tb has been detected), the model suggested that Tb could not be realistically maintained in the absence of anergic animals or infection from external sources; the p value required to do so was far higher than the estimates from this study, and therefore, highly improbable. 3.2. Estimation

of the transmission

coeficient

from herd histories

In the case study in which one cow was highly likely to have been anergic, that individual was strongly implicated in the infection of at least five, and up to eleven, of its 320 herd-mates over a period of around 800 days. This equates to an upper estimate for p of approximately 8/(320 X 800) = 3.12 X 10e5 per cow per day. The mean estimal:e for p from other MAF dairy and beef herd histories, based on numbers of reactors from infection assumed to be caused by single anergic animals, was 7.7 X 10e5. This estimate represents an upper limit, as there may have been more than one infectious animal in the herd at one time, which would reduce the estimate of /3. Table 3 summa&es estimates for p and the contact rate (number of potentially infectious contacts per infectious cow per day equals /3 multiplied by herd size) from this study. The average values for the best available estimates were 2.7 X 10e5 per cow per day for p and 0.0073 per day for the contact rate. Given the likely errors involved, a default value for p of 3 X 10e5 was assumed in subsequent experiments with the model. 3.3. Estimation

of test specificity

The estimate was based on data in which the mean herd size was 186, yielding 246 tests with no reactors and 49 tests with false positive reactors. According to the formula

N.D. Barlow et al./ Preventive

68 Table 3 Summary herds

of estimates for the tuberculosis

Derivation method

Veterinary Medicine 32 (1997) 57-75

transmission

coefficient,

p, and contact rate for New Zealand cattle

Source

p estimate (x10-5 per cow per

1. Field data 2. Field data 3. Fitting model 4. Fitting model 5. Fitting model Best overall estimate

Detailed herd history involving a single anergic animal in the Waikato, NZ 8 less detailed MAF herd histories 3 case studies with herds of unknown size (Canadian, Egyptian, NZ dairy) Case study with herd size known (NZ Hohotaka) Estimated upper limit (to maintain reactor rates constant with annual testing) Average of row 1 and row 4

Contact rate (x10-s per

day)

day)

3.1

10

7.1 1.1

47 2.2

2.3 4.6

4.6 9.2

2.7

1.3

given above (see model), the specificity was, therefore, (49/(246 + 49))(“‘86) = 99.9%. For simplicity, this was rounded to 100% as the default value for the model. 3.4. The efect

of herd test sensitivity

If a herd of size 200 is initially infected (assuming a distribution of: 196 S; zero U; two R; and two I animals), and is subjected to a standard testing regimen (see above) in the absence of infection from wildlife, then changing test sensitivity from 80 to 90% reduced the average time taken for the herd to become reaccredited by 9% (Table 4). There was a more substantial reduction (around 20%) in the average time the herd spent on movement control and in the average total number of reactors and tests undertaken per herd (Table 4). The times spent on movement control and from infection to

Table 4 The predicted effect of increasing herd-test sensitivity for bovine tuberculosis from 80 to 90% on the time taken for a herd in a non-endemic area to be reaccredited, the average time it would spend on movement control, the number of tests it would undergo and the number of reactors which would be found in the herd until reaccreditation Test sensitivity

Default Improved Percentage

scenario

improvement

Average time to reaccreditation

Average time on movement control

(days)

(days)

1296 (111 1185 (7) 9

556 (10) 449 (7) 19

Number of tests to reaccreditation

Number of reactors to reaccrediation

6.1 (0.10) 5.5 (0.04) 6

5.7 (0.21 4.1(0.21 18

The default percentage sensitivities in states U, R and I are 0, 80, and 80, respectively and the corresponding values for the improved scenario are 0, 90, and 90. Other parameters are assumed to take their default values and the initial herd composition is assumed to be S/U/I/R = 196/O/2/2. Figures in parentheses are the standard errors of the means (n = 500 model runs in each case).

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Table 5 The predicted effect of increasing test sensitivity from 80 to 90% on the average percentage of time that an initially infected herd (S/U/R/I = 196/O/2/2) would spend on movement control over a period of 10 years, and the average number of tests it would undergo ka

Outcome

Percentage

time on movement control

Tests per year

Maximum

test sensitivity

80%

90%

0 10-j 10-4

15 (0.28) 55 (0.68) 100 (0.00)

12 (0.18) 51 (0.69) 100 (0.00)

0 10-j 10-4

0.78 (0.004) 1.55 (0.011) 2.10 (0.002)

0.74 (0.002) 1.51 (0.011) 2.10 (0.001)

a Three levels of external infection from wildlife vectors are assumed (k is probability of infection from an external source per susceptible cow per day), as is the current movement-control regimen involving two tests for bovine tuberculosis at six-monthly intervals. Figures mnparentheses are the standard errors of the means (n = 500 model runs in each case).

reaccreditation were 1.5 and 3.5 years, respectively, under the current testing regimen and 1.23 and 3.25 years if test sensitivity was increased to 90%. The model confirmed that, for both levels of test sensitivity, none of the 1000 simulated herds contained residual infection by the time the herd became reaccredited. Where there is continuous infection from wildlife, the effect of a change in test sensitivity was similar to or less than that in the absence of wildlife vectors (Table 5). Criteria different from those in Table 4 were used because herds do not become re-accredited. These criteria were the proportion of time spent on movement control and the number of tests over a 10 year period. Two levels of external infection from wildlife were assumed (the parameter k in Table 51, to give the percentage times on movement control up to the 100% observed for some herds in endemic areas.

3.5. The effect of d@erent herd-testing

regimens

Table 6 addresses the question as to whether the current testing regimen can be improved. In all cases (except at the highest level of external infection when the herd is permanently on movement control), the average time spent on movement control is directly related to the time between tests: the shorter the interval between tests, the less time the herd spends on movement control. Given that the herds are all assumed to be initialky infected, the scenario with no external infection (k = 0) would correspond in practice to episodic and infrequent (rather than continuous) infection (e.g. through purchase of stock). Under this scenario, reducing the interval between the two movement-control tests has little effect on the total number of tests which the herd undergoes. However, with increasing levels of external infection, the long-term average testing rate becomes much higher, as movement control tests are carried out at shorter intervals (columns 5 and 6 of Table 6).

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70

Table 6 The predicted effect of different movement-control testing regimens on the average percentage of time that an initially infected herd (S/U/R/I = 196/O/2/2) would spend on movement control over a period of 10 years, and the average number of tests it would undergo Outcome

% timeon movement control Tests per year

k”

0 10-5 1om4 0 1o-s 10-4

Movement-control

regimen b

12

6

3

2

1

39 (1.08) 87 (0.00) 100 (0.00) 0.74(0.01) 0.98(0.00) 1.00(0.00)

15 (0.28) 55 (0.68) 100 (0.00) 0.78(0.00) 1.55(0.01) 2.10(0.00)

7 (0.11) 31 (0.411 93 (0.00) 0.80(0.00) 1.85(0.02) 3.89(0.01)

5 (0.07) 21 (0.27) 74 (0.00) 0.79(0.01) 1.98(0.02) 4.80(0.02)

2 (0.04) 11 (0.15) 36 (0.25) 0.80(0.01) 2.05(0.02) 5.10(0.03)

a Three levels of external infection from wildlife vectors are assumed (k is probability of infection external source per susceptible cow per day). b Movement-control regimens are given as the number of months between tests. Figures in parentheses are the standard errors of the means (n = 500 model runs in each case).

from an

Where external infection is present, herds only rarely become reaccredited and, if they do so, they rapidly relapse into infected status. In the absence of a continuous external source of infection, the total time an average herd spends on movement control before it becomes reaccredited is directly related to the interval between movement control tests. For movement-control test intervals of less than 12 months, the total time to reaccreditation declines more slowly as the interval between movement control tests is decreased, since the former includes an additional two years of Tb-free tests; the time on movement control is, thus, a small proportion of the total time taken to reaccreditation (Table 7). Reducing the time interval between movement-control tests has little effect on either the number of tests carried out or on the number of reactors detected before the herd is reaccredited (again for intervals less than or equal to 6 months). The large number of tests associated with an interval of 1 month (Table 7) is a consequence

Table 7 The effect of different movement control testing regimens on the average time taken for an initially infected herd (S/U/R/I = 196/O/2/2) to become reaccredited and the average time it spends on movement control Movementcontrol regimen a

Average time to reaccreditation

12 6 3 2 1

Number of tests to reaccreditation

Number of reactors to reaccreditation

(days)

Average time on movement control (days)

2210 (45) 1296 (11) 1011 (5) 928 (5) 839 (4)

1476 (45) 556 (10) 270 (4) 184 (3) 90 (11

7.1 6.1 6.0 6.0 6.0

12.5 (0.8) 5.7 (0.2) 4.8 (0.2) 4.7 (0.1) 34.3 (0.6)

(0.10) (0.10) (0.05) (0.05) (0.05)

a Movement-control regimens are given as the number of months between tests. Figures in parentheses are the standard errors of the means (n = 500 model runs in each case).

N.D. Barlow et al./ Preuentiue Veterinary Medicine 32 (1997) 57-75

71

of the assumed reduction in sensitivity of a test carried out so soon after the previous test. In none of the model runs involved in Tables 6 and 7 (500 herd simulations per scenario, including scenarios with external infection from wildlife), was infection still present in the modelled herd by the time it was reaccredited. In other words, the model shows what cannot be shown in the real world because the tests are not 100% sensitive: that the Tb-testing regimen actually does clear herds of infection.

4. Discussion 4.1. Is it necessary rates?

to invoke within-herd

transmission

to explain

observed

reactor

The question here is whether the observed patterns of reactor rates in the four cases shown in Fig. 2 can be explained simply by an initial burst of infection without invoking subsequent infection within the herd during the time that the tests are carried out. Assuming that the initial infection level was such as to give the observed number of reactors at the first test, in the absence of within-herd transmission ( /3 = O), the followjng tests would yield reactor rates corresponding to the solid lines in Fig. 2; these lines correspond to a relative decline at each test equal to the test sensitivity (approximately 0.8). In practice, this figure is more likely to hold for the third and subsequent tests than for the second, since some initially unresponsive cattle may become responsive by the second test (so the figure for this test could be higher than 80%). However, the fact that the lines underestimate observed reactor rates in later tests strongly suggests that w:ithin-herd transmission does occur. The relative contribution of this within-herd transmission and external infection in herds in endemic areas where wildlife vectors are presem is considered in a further paper. 4.2. What is the Tb transmission

rate within a cattle herd?

The number of new Tb infections in a herd, in units of cattle per day, has been modelled by the mass-action term PSI. Therefore, the mean rate of Tb spread in a herd over the course of an epidemic can be characterised, in general, by the herd size (on which the numbers of cattle in states S and I are mutually dependent) and by j3. For estimates of p based on fitting the model to observed reactor rates, we have assumed typical herd sizes of 200 as at the New Zealand Hohotaka site. In general, the rate of spread of disease will increase with herd size. Therefore, estimates of /3, though not the actual parameter, will vary in inverse proportion to number of animals assumed to be in the herd. However, as herd size increases, the assumption of homogeneous mixing becomes less reasonable, violating the mass action principle which is used to model Tb transmission. Given this caveat, the model suggests that large herds should be managed as a number of smaller sub-herds in order to minimise the rate of Tb spread. Disease transmission will be affected, not only by the total number of animals in the herd, but also by the cattle density or stocking rate (an effect which is subsumed within the value of j? with higher values denoting more intensively managed herds). Thus, although we

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have derived a single estimate for /? averaged over beef and dairy herds and not distinguishing between these in the models, in practice the transmission coefficient is likely to be higher in dairy herds than in beef ones because of their more intensive management (particularly the close aggregation of cattle at milking). No previous estimates of /3 or contact rate (number of potentially infectious contacts per infectious animal per day equal to p multiplied by herd size) were available for Tb in intensively managed cattle herds, although Stoneham and Johnston (1986) estimated p for a group of Australian range cattle at 2.64 X 1O-4 per cow per day. This study indicates a much lower value of 2.7 X lo-’ (Table 3), which is the average for estimates derived from model-fitting and directly from herd history data. The separate estimates covered a range from 1.1 X lop5 to 7.7 X 10m5, and where these are based on fitting the model to patterns of reactor rates in herds of unknown size (N.Z. 1952-1955, Canadian and Egyptian), they rely on the assumption of an average size of 200 animals. The much higher p value in Stoneham and Johnston’s study (Stoneham and Johnston, 1986) may be due to the lower effective group size and greater mobility in the freely ranging cattle. It is also likely to reflect the very long incubation period (around 7 years) calculated for Tb in these cattle. If the incubation period for Stoneham and Johnston’s cattle had been more in accordance with the results of other studies (e.g. Neil1 et al., 19921, then a smaller value for /3 would have matched the observations to which they were calibrating their model. Not surprisingly, p is sensitive to the assumed duration of the latent stage (state R in the model, Table 2), increasing as the latent period increases (Table 2 suggests a relationship of the form p = 1.14 + 0.182 X latent period (months)). Thus, the values presented above are conditional upon the model’s assumption of an average latent period of approximately 6 months, and can be modified given better estimates for this quantity. However, Table 2 also shows that /3 is not affected by minor changes in the assumed pattern of test sensitivity during the initial development of disease within the individual animal. The estimates for the contact rate (0.0073 potentially infectious contacts per infectious cow per day overall; Table 3) were derived independently of herd size, whether using the model or using herd histories. Since herd size was unknown in all cases except Hohotaka, these estimates are more accurate than those of p, in the sense that they did not require the additional assumption about herd size. However, the mass-action assumption for disease transmission implies that the contact rate varies with herd size, and unless this can be shown to be invalid for cattle herds, the contact rate estimates cannot necessarily be applied to other herds whose sizes may be different. Under current testing regimens involving annual or more frequent tests, the model suggests that within-herd transmission is unlikely to maintain infection in the absence of external Tb inputs. The only case in which long-term infection may be maintained in the absence of external inputs, is when an anergic animal is present within a herd. This is probably very rare (T. Ryan, personal communication,) but under such circumstances, within-herd spread may maintain prolonged Tb infection of a herd. There are known cases of anergic cattle but these may be relics of historically laxer testing regimens in which animals had the opportunity to develop to very advanced stages of infection. The regularity of current New Zealand herd-testing regimens means it is unlikely that an infected animal can remain in a herd long enough to become anergic, although small

N.D. Barlow et al./Preventiue

areas with semi-feral or incompletely animals. In addition to providing estimates rate wi.thin herds, this study has also under New Zealand field conditions, 4.3. Can management

practices

Veterinary Medicine 32 (1997) 57-75

13

mustered cattle remain potential sources of anergic for the disease-transmission coefficient and contact yielded a tentative estimate of CDF test specificity which is likely to be well above 99%.

be improved?

All Tb test methods involve a trade-off between sensitivity and specificity (Blood and Radoslits, 1989). It is widely recognised that test specificity is more important economically tlhan test sensitivity in areas where total disease prevalence is low (Meyer, 1990), as is tme for most New Zealand farms. However, the model suggests that control could be improved by increasing test sensitivity in non-endemic areas where there is no continuous external infection. Under these circumstances, where any infection is sporadic and infrequent, increased sensitivity has little effect on the time to reaccreditation for an infected herd (Table 4) but the time spent on movement control is reduced by 20% if improved tests allow sensitivity to increase from 80 to 90% with no loss in specificity. This would reduce the prevalence of herds on movement control and thereby, improve New Zealand’s Tb status. Additionally, the number of tests carried out before the herd is reaccredited would be reduced by 10% and the number of reactors produced by 18%, both of which benefit the farmer (Table 4). However, these benefits cannot be realised in endemic areas where there is continual infection from wildlife (Table 5). There is some evidence (e.g. Kleeberg, 1960; Blood and Radostits, 1989) that testing more frequently than every 7-8 weeks could result in loss of test specificity and sensitivity. However, there appears to be no biological reason why movement-control herds ishould not be tested at two-monthly intervals, other than the fact that the early pathogenesis of M. bouis in cattle is not yet clearly understood (Neil1 et al., 1992). While there may be political reasons for a longer interval between tests, this cannot be justified on epidemiological grounds since it compromises the purpose of the movement-control programme, which is to detect and remove tuberculous animals from a known infected herd. A longer interval increases the chance of additional infection within the herd, as indicated in Table 7: there are more total reactors before reaccreditation with a 6 month interval between tests than with a 3 month interval. Monitoring post-infection herds to ensure that all infected animals have been removed is achieved by the second part of the reaccreditation process, which involves annual testing for two years. Although 80% of New Zealand cattle and deer herds on movement control are in endemic rather than non-endemic areas, the above conclusions imply that where wildlife vectors are absent or controlled, the interval between movement control tests should be reduced from the typical 12 months to 6, 3 or even 2 months, in order to improve national Tb status. In practice, an allowable minimum interval of 2 or 3 months everywhere would allow farmers to judge whether this could be achieved after wildlife control in endemic areas without resulting in excessive numbers of tests as herds became reinfected. The problem is that, at present, there is little incentive for farmers to reduce the interval between movement-control tests (apart from allowing greater freedom in

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N.D. Barlow et al. / Preuentiue Veterinary Medicine 32 11997) 57-75

movement and sale of stock); yet, it is in the national interest that they do so. The model confirmed that whatever movement control regimen was adopted, by the time herds were reaccredited (that is, after they had passed a further two tests at annual intervals), they were indeed clear of infection. It also provided estimates of the average time spent by a herd in a non-endemic area on movement control and prior to reaccreditation (Table 4), as required by further models for between-herd as opposed to within-herd spread of Tb. In conclusion, the model has suggested that within-herd Tb transmission is important, has allowed some tentative estimates to be derived for the disease transmission coefficient and contact rate in intensively managed cattle herds, and has suggested that the percentage of herds on movement control (the accepted measure of national Tb status) could be reduced in non-endemic areas by improvements in CDF-test sensitivity and by reducing the minimum allowable time that a herd spends on movement control.

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Morris, R.S., Pfeiffer, D.U., Jackson, R., 1994. The epidemiology of Mycobacterium bouis infections. Veterinary Microbiology 40, 153-177. Myers, J.A., Steele, J.H., 1969. Bovine Tuberculosis Control in Man and Animals. Warren H. Green Inc., Missouri, USA. Neill, SD., Hanna, J., Mackie, D.P., Bryson, T.G.D., 1992. Isolation of Mycobacterium bouis from the respiratory tracts of skin test negative cattle. Veterinary Record 13 1, 45-47. Neill, S.D., Hanna, J., O’Brien, J.J., McCracken, R.M., 1989. Transmission of tuberculosis from experimentally infected cattle to in-contact calves. Veterinary Record 124, 269-271. Roberts, M.G., 1992. The dynamics and control of bovine tuberculosis in possums. IMA Journal of Mathematics Applied in Medicine and Biology 9, 19-28. Ryan, T J., de Lisle, G.W., Wood, P.R., 1991. The performance of the skin and gamma interferon tests for the diagnosis of tuberculosis infection in cattle in New Zealand. Veterinary Continuing Education, Massey University Publication 132, 143-150. Stoneham, G., Johnston, J., 1986. Report on the brucellosis and tuberculosis eradication campaign. Australian Bureau of Agricultural Economics Occasional Paper No. 97. Canberra.