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Statistical Communications in

Infectious Diseases

Volume 2, Issue 1 2010 Article 3

Is There an Association between Levels of

Bovine Tuberculosis in Cattle Herds and

Badgers?

Christl A. Donnelly

∗

Jim Hone

†

∗

MRC Centre for Outbreak Analysis and Modelling, Imperial College London,

c.donnelly@imperial.ac.uk

†

Institute for Applied Ecology, University of Canberra, jim.hone@canberra.edu.au

Copyright

c

2010 The Berkeley Electronic Press. All rights reserved.

Is There an Association between Levels of

Bovine Tuberculosis in Cattle Herds and

Badgers?

∗

Christl A. Donnelly and Jim Hone

Abstract

Wildlife diseases can have undesirable effects on wildlife, on livestock and people. Bovine

tuberculosis (TB) is such a disease. This study derives and then evaluates relationships between

the proportion of cattle herds with newly detected TB infection in a year and data on badgers, in

parts of Britain.

The relationships are examined using data from 10 sites which were randomly selected to be

proactive culling sites in the UK Randomized Badger Culling Trial. The badger data are from the

initial cull only and the cattle incidence data pre-date the initial badger cull.

The analysis of the proportion of cattle herds with newly detected TB infection in a year, showed

strong support for the model including signiﬁcant frequency-dependent transmission between cat-

tle herds and signiﬁcant badger-to-herd transmission proportional to the proportion of M. bovis-

infected badgers. Based on the model best ﬁtting all the data, 3.4% of herds (95% CI: 0 – 6.7%)

would be expected to have TB infection newly detected (i.e. to experience a TB herd breakdown)

in a year, in the absence of transmission from badgers. Thus, the null hypothesis that at equi-

librium herd-to-herd transmission is not sufﬁcient to sustain TB in the cattle population, in the

absence of transmission from badgers cannot be rejected (p=0.18). Omitting data from three sites

in which badger carcase storage may have affected data quality; the estimate dropped to 1.3% of

herds (95% CI: 0 – 6.5%) with p=0.76.

The results demonstrate close positive relationships between bovine TB in cattle herds and bad-

gers infectious with M. bovis. The results indicate that TB in cattle herds could be substantially

∗

The Randomized Badger Culling Trial (RBCT) in Britain was designed, overseen and analysed

by the Independent Scientiﬁc Group on Cattle TB (John Bourne, Christl Donnelly, David Cox,

George Gettinby, John McInerney, Ivan Morrison and Rosie Woodroffe). The RBCT was funded

by the Department of Environment, Food and Rural Affairs (Defra) with the cooperation of the

many farmers and land occupiers in the trial areas who allowed the experimental treatments to

operate on their land. JH acknowledges support from the University of Canberra and CAD ac-

knowledges the MRC for Centre funding support. D. Pedersen is thanked for statistical advice.

reduced, possibly even eliminated, in the absence of transmission from badgers to cattle. The re-

sults are based on observational data and a small data set to provide weaker inference than from a

large experimental study.

KEYWORDS: badger, bovine tuberculosis, host-disease model, model averaged prediction, vac-

cination

Introduction

Wildlife have a variety of diseases that includes rabies and bovine tuberculosis

(TB) (Keeling and Rohani 2008; Hone 2007; Krebs 2009; Delahay, Smith and

Hutchings 2009). Some diseases such as bovine TB, caused by Mycobacterium

bovis, are a focus for wildlife control because of effects of the disease on livestock

production (Anderson and Trewhella 1985; Barlow 1991, 2000; Donnelly et al.

2003, 2006, 2007; Jenkins et al. 2007, 2008, 2010). Simulation studies, such as

those by Roberts (1999) and Smith et al. (2001), have suggested vaccination of

wildlife may be useful for control of TB. Vaccination of foxes (Vulpes vulpes) has

reduced rabies incidence in parts of Europe (Blancou et al. 2009).

Cattle and badgers (Meles meles) are both known hosts of, and subject to

control to limit the spread of, bovine TB in cattle herds in the U.K. and Ireland.

Cattle herds in the UK are regularly tested for TB in accordance with EU

legislation. The testing interval is parish based and ranges from 1 year to 4 years,

with lowest incidence parishes receiving 4-yearly routine herd tests and highest

parishes receiving annual whole-herd tests. Additional herd tests, for example in

response to TB being detected in a herd linked through geographic proximity or

through trade, are also undertaken, as well as slaughterhouse checks of all cattle

slaughtered for consumption. A herd is said to experience a TB ‘‘breakdown’’ if

one or more members of a cattle herd fail the conventional TB skin test or show

evidence of TB lesions at slaughterhouse inspection that are positive to M. bovis

on culture.

This paper evaluates evidence for bovine TB association between cattle

herds and badgers in an observational study in ten 100km

2

areas of England.

Alternative hypotheses, as epidemiological models, of the association are

assessed. We also estimate the proportion of herds detected with TB in the

absence of transmission from badgers, such as could occur with completely

effective vaccination.

Modelling

A model of bovine TB in cattle herds in a part of New Zealand (Barlow et al.

1998; their equation 6) assumed that the rate of change of the number of herds

with TB (and hence on movement control) was related to the rate of change from

uninfected to infected herd status as modified by the duration of the time being

infectious. It was assumed in a second (separate, but linked) area that wildlife, for

example brushtail possums (Trichosurus vulpecula), could transmit TB to cattle

herds, at a rate k. Reinfection of wildlife from cattle was considered to be rare in

regularly tested herds, so the model did not include such infection.

1

Donnelly and Hone: Bovine Tuberculosis in Cattle Herds and Badgers

Published by The Berkeley Electronic Press, 2010

We consider the analogous model for a single area with density-dependent

transmission between cattle herds subjected to wildlife transmission risk such that

eqn 1

eqn 2

eqn 3

where cattle herds move between states U (uninfected), I (infected, and

equivalently infectious, but undiagnosed) and M (under movement controls and

thus not infectious to other herds). U, I and M are the numbers of herds, rather

than cattle, in each of these states and N is the total number of herds (N=U+I+M).

The transmission coefficient β represents the between-herd risk per annum while

k is the rate of infection from wildlife (and is equivalent to the force of infection)

per annum. The per-annum rate at which infected herds go on to movement

controls is represented by c and p is the average time on movement control in

years. We, like Barlow et al. (1998), assume no reinfection of wildlife (in our

case, badgers) from cattle herds. Such an assumption is one possibility and the

inferences made here are conditional on any such reinfections being negligible.

At equilibrium

eqn 4

where the superscript * denotes that I* and M* are at their equilibrium values.

Similarly,

eqn 5

eqn 6

and N = U* + I* + M*.

Using substitution, it can be shown that the equilibrium value I* can be

obtained from the solution of this quadratic equation:

eqn 7

2

Statistical Communications in Infectious Diseases, Vol. 2 [2010], Iss. 1, Art. 3

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DOI: 10.2202/1948-4690.1000

In the special case of no risk from wildlife (k=0) and β > 0, the equilibrium

solution is given by:

,

, and

. eqn 8

whereas if there is no herd-to-herd transmission (β=0) and k > 0, the equilibrium

solution is given by:

,

, and

eqn 9

We also consider the analogous model with frequency-dependent

transmission:

eqn 10

eqn 11

eqn 12

At equilibrium

eqn 13

(as before) where the superscript * denotes that I* and M* are at their equilibrium

values, whereas

eqn 14

eqn 15

Using substitution, it can be shown that the equilibrium value I* can be obtained

from the solution of this quadratic equation:

eqn 16

3

Donnelly and Hone: Bovine Tuberculosis in Cattle Herds and Badgers

Published by The Berkeley Electronic Press, 2010

In the special case of no risk from wildlife (k=0) and β > 0, the

equilibrium solution is given by:

,

,

and

. eqn 17

We consider four alternatives for k, that it equals 0 (i.e. no transmission

from wildlife), that, it is proportional to the total number of badgers culled in the

area in question (N

w

), that it is proportional to the number of infected badgers

culled in the area in question (I

w

), and it is proportional to the ratio of infected

culled badgers to all culled badgers (I

w

/N

w

). Thus, when k is related to badgers,

k=αN

w,

k=αI

w

or k =α(I

w

/N

w

) where α is the proportionality constant assumed to

be non-negative. We recognize that there may be other sources of infection of

British cattle herds, for example deer. However, studies of farmland wildlife

found very little evidence of infectiousness from wildlife other than badgers

(Mathews et al. 2006).

A herd scale has been used previously to model disease dynamics, such as

the farm being the unit of study and transmission in models of foot-and-mouth

disease dynamics in the U.K. (Ferguson, Donnelly and Anderson 2001; Keeling et

al. 2001). The additive nature of transmission between cattle and between an

external agent (wildlife or environment) reflects the additive assumptions in two-

host disease models such as described by Barlow et al. (1998) and Hone and

Donnelly (2008). The models considered (Table 1) represent alternative

hypotheses, in the sense of Chamberlin (1965), of the determinants of the

proportion of cattle herds with TB.

Methods

Data on bovine TB in cattle herds and badgers at 10 sites in Britain are from the

Randomized Badger Culling Trial (RBCT), which has been described in detail

previously (Bourne et al. 2007; Donnelly et al. 2003, 2006; Hone and Donnelly

2008). The data on cattle herds and TB in cattle herds are from Donnelly et al.

(2006). The badger data are from the initial cull of badgers in the proactive badger

culling treatment sites as used by Hone and Donnelly (2008). TB diagnosis was

based on skin test for cattle and culture tests for badgers as used by Hone and

Donnelly (2008). The number of cattle herds varied between sites from 63 to 245;

data are presented in the Appendix.

The data from three sites (triplets A, C and E) may have been influenced

by the freezing of badger carcases (Hone and Donnelly 2008) so the analyses

4

Statistical Communications in Infectious Diseases, Vol. 2 [2010], Iss. 1, Art. 3

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DOI: 10.2202/1948-4690.1000

were repeated after deleting data from those three sites. For disease modelling and

management it was assumed that cattle infection as shown by reaction on skin test

was equivalent to the animal being infectious, and that there is no carrier state in

cattle or badgers.

For both the density-dependent and the frequency-dependent models, the

number of herd breakdowns in a one-year period, B, among N herds, is on

average, at equilibrium, equal to I*c where c is the rate at which infected herds are

detected and put under movement controls. In other words, 1/c is the average time

in years that a herd is infected before it is detected. In a single year the proportion

of herds in which infection is newly detected (i.e. which experience TB herd

breakdowns) is thus:

eqn 18

The binomial log likelihood is therefore given by:

eqn 19

ignoring an additive constant.

The rate at which infected herds are detected and put onto movement

controls, c, is derived to incorporate detection of infected herds at routine herd

testing (following Cox et al., 2005) as well as slaughterhouse detection. With

routine testing every b years and the assumption that repeated tests on the same

herd are independent with the same herd test sensitivity, s, each time, the average

time between infection and detection is given by:

eqn 20

assuming that infection of herds starts at a random time between tests. The b(1-

s)/s term arises from the geometric distributions of retests needed when a test with

imperfect sensitivity is used (i.e. s<1) (Cox et al. 2005). Of course, herd test

sensitivity is greater than the test sensitivity for a single infected animal whenever

there is more than one infected animal to be tested within the herd. (The

formulation given by Barlow et al. (1998, equation 8), µ

R

=b/s, is not correct.)

The average time to detection at slaughterhouse, in the absence of routine

herd testing, would depend not just on the age distribution of routinely

slaughtered cattle, but also on the number of infected cattle within the herd. We

make the simplifying approximation that c, the overall rate at which infected

herds are detected and put onto movement controls includes a component due to

slaughterhouse detection, a, such that:

5

Donnelly and Hone: Bovine Tuberculosis in Cattle Herds and Badgers

Published by The Berkeley Electronic Press, 2010

eqn 21

Estimates for β and α were obtained using maximum likelihood, with

confidence intervals obtained from profile likelihoods. We assume values for the

remaining parameters: p (the average time on movement control in years); a/c (the

proportion of infected herds detected and put onto movement controls which are

detected through slaughterhouse surveillance); b (the interval between routine

herd tests) and s (the herd test sensitivity, that is the proportion of infected herds

that are successfully detected by a routine herd test).

The average time that a herd remains under movement controls due to a

confirmed TB breakdown rose from 215 days to 292 days between 1997 and 2002

(the period in which the initial proactive culls of the RBCT were undertaken)

(Defra, 2004). We approximate and assume that p equals 0.7 years (255 days) for

all areas analysed.

In 2005, 14% of confirmed TB herd breakdowns were detected through

slaughterhouse surveillance (Bourne et al., 2007), so we approximate c by setting

a/c=0.14 and solving we obtain

eqn 22

Because RBCT areas were selected to be in areas of highest cattle TB risk, we

assume that all herds under analysis were subjected to annual routine herd testing;

thus, b equals 1 year.

We consider herd test sensitivity (s) values between 0.9 and 1.

Akaike weights based on the Akaike information criterion, corrected for

sample size (AICc), (Anderson, 2008) were used to assess the relative support of

the data for a particular model across the range of models considered.

Results

The analysis of the proportion of cattle herds with newly detected TB infection in

a year, including data from all ten areas, showed that the best fitting model

included frequency-dependent transmission between cattle herds (β=1.98, 95%

CI: 1.84 – 2.07) and badger-to-herd transmission proportional to the proportion of

badgers infectious for M. bovis (α=0.047, 95% CI: 0.013 – 0.119) (Figure 1). This

model achieved an Akaike weight of 0.966 (Table 1). Based on this model, 3.4%

of herds (95% CI: 0 – 6.7%) would be expected to have TB infection newly

detected (i.e. to experience a TB herd breakdown) in a year, in the absence of

transmission from badgers (calculated assuming from the maximum likelihood

estimate of β, 1.98, and its 95% confidence interval, and setting k=0). Thus, the

6

Statistical Communications in Infectious Diseases, Vol. 2 [2010], Iss. 1, Art. 3

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DOI: 10.2202/1948-4690.1000

null hypothesis that at equilibrium herd-to-herd transmission is not sufficient to

sustain TB in the cattle population, in the absence of transmission from badgers

cannot be rejected (p=0.18). Other models received very little support from the

data analysed with Akaike weights being close to 0 (Table 1).

Similar results were obtained when data from triplets A, C and E were

omitted due to concern about their data quality. The analysis of the proportion of

cattle herds with newly detected TB in a year showed that the best fitting model

included frequency-dependent transmission between cattle herds (β=1.93, 95%

CI: 1.59 – 2.06) and badger-to-herd transmission proportional to the proportion of

badgers infectious for M. bovis (α=0.065, 95% CI: 0.015 – 0.203) (Figure 1). This

model achieved an Akaike weight of 0.923 (Table 2). Based on this model, 1.3%

of herds (95% CI: 0 – 6.5%) would be expected to have TB infection newly

detected (i.e. to experience a TB herd breakdown) in a year, in the absence of

transmission from badgers (calculated assuming from the maximum likelihood

estimate of β, 1.93, and its 95% confidence interval, and setting k=0). Thus, the

null hypothesis that at equilibrium herd-to-herd transmission is not sufficient to

sustain TB in the cattle population, in the absence of transmission from badgers

cannot be rejected (p=0.76). Other models received very little support from the

data analysed (Table 2).

These results were obtained assuming a herd test sensitivity of 0.9.

However, similar results were obtained assuming a herd test sensitivity of 1.

The best model fits imply that a completely infected (100% prevalence)

badger population would be associated with roughly 20% of the cattle herds being

newly detected with TB each year (Figure 1). While incomplete identification of

M. bovis infection in badgers at necropsy (i.e. diagnostic sensitivity less than

100%) does not affect the model fits obtained, it does affect the interpretation of

the x-axis in Figure 1 (the observed prevalence of M. bovis infection in badgers).

Crawshaw et al. (2008) estimated, on the basis of a study comparing standard and

detailed necropsy protocols for badgers, that the overall sensitivity of the standard

protocol, to which RBCT badgers were subjected, was only 54·6 per cent (95%

CI: 44·9 – 69·8%), relative to the more detailed protocol. The observed prevalence

in badgers could then be corrected by this parameter, denoted s

B

, and used to plot

the observed data with the best-fitting models now interpreted as having k

proportional to the true M. bovis infection prevalence in badgers with slope αs

B

(Figure 2). With the correction for incomplete sensitivity of the badger testing, the

best model fits imply that a completely infected badger population would be

associated with roughly 15% of the cattle herds being newly detected with TB

each year (Figure 2). The correction has no effect on the estimated proportion of

herds with TB infection newly detected (i.e. to experience a TB herd breakdown)

in a year, in the absence of transmission from badgers.

7

Donnelly and Hone: Bovine Tuberculosis in Cattle Herds and Badgers

Published by The Berkeley Electronic Press, 2010

Table 1. Estimates and log likelihood values associated with density-dependent (DD) and frequency-dependent (FD)

transmission models fitted to the data on TB in cattle and badgers including data from all ten triplets. β is a measure

of herd-to-herd transmission while k, such that k=αN

w

, k=αI

w

or k =α(I

w

/N

w

), where N

w

equals the number of badgers

culled in the area and I

w

equals the number of infectious badgers culled in the area, represents the transmission risk

from badgers to cattle. Each of the models has one (α or β) or two fitted parameters, β and α. Throughout herd test

sensitivity is assumed to equal 0.9. The model with most support (highest Akaike weight) is shown in bold.

Between-

herd

transmission

Transmission

from

wildlife

1

Num.

of

param

β

p-value

H

0

: β=0

α

p-value

H

0

:

α=0

Log

likelihood

AICc Akaike

weight

None pt N

w

1 --

2

--

2

0.00025 N/A

3

-353.79 710

0.000

None pt I

w

1 --

2

--

2

0.0026 N/A

3

-349.77 702

0.000

None pt I

w

/N

w

1 --

2

--

2

0.80 N/A

3

-329.18 661

0.000

DD None 1 0.031 N/A

3

--

2

--

2

-739.78 1482

0.000

DD pt N

w

2 0 1 0.00025 <0.001 -353.79 713

0.000

DD pt I

w

2 0 1 0.0026 <0.001 -349.77 705

0.000

DD pt I

w

/N

w

2 0 1 0.80 <0.001 -329.18 664

0.000

FD None 1 2.09 N/A

3

--

2

--

2

-322.25 647

0.019

FD pt N

w

2 2.09 <0.001 0 1 -322.25 650

0.004

FD pt I

w

2 2.06 <0.001 0.000040 0.16 -321.24 648

0.011

FD pt

I

w

/N

w

2 1.98 <0.001 0.047 <0.001 -316.74 639

0.966

1

pt =proportional to;

2

When α or β is assumed to be zero, the parameter estimate is omitted from the table and no p-value is calculable.

3

When

only one parameter (α or β) is fitted and the other is assumed to equal zero, the calculation of a p-value for the null hypothesis that the single

fitted parameter is also equal to zero is not applicable (N/A), as that null model would have no disease transmission and thus at equilibrium no

disease. Alternatively, one could think of such p-values as equalling zero, because the model with no disease has a log likelihood of negative

infinity.

8

Statistical Communications in Infectious Diseases, Vol. 2 [2010], Iss. 1, Art. 3

http://www.bepress.com/scid/vol2/iss1/art3

DOI: 10.2202/1948-4690.1000

Table 2. Estimates and log likelihood values associated with density-dependent (DD) and frequency-dependent (FD)

transmission models fitted to the data on TB in cattle and badgers excluding triplets A, C and E. β is a measure of

herd-to-herd transmission while k, such that k=αN

w

, k=αI

w

or k =α(I

w

/N

w

), where N

w

equals the number of badgers

culled in the area and I

w

equals the number of infectious badgers culled in the area, represents the transmission risk

from badgers to cattle. Each of the models has one (α or β) or two fitted parameters, β and α. Throughout herd test

sensitivity is assumed to equal 0.9. The model with most support (highest Akaike weight) is shown in bold.

Between-

herd

transmission

Transmission

from

wildlife

1

Num.

of

param

β

p-value

H

0

: β=0

α

p-value

H

0

:

α=0

Log

likelihood

AICc Akaike

weight

None pt N

w

1 --

2

--

2

0.00026 N/A

3

-266.39 536 0.000

None pt I

w

1 --

2

--

2

0.0023 N/A

3

-260.37 524 0.000

None pt I

w

/N

w

1 --

2

--

2

0.71 N/A

3

-250.25 503

0.013

DD None 1 0.031 N/A

3

--

2

--

2

-608.71 1220 0.000

DD pt N

w

2 0 1 0.00026 <0.001 -266.39 540 0.000

DD pt I

w

2 0 1 0.0023 <0.001 -260.37 528 0.000

DD pt I

w

/N

w

2 0 1 0.71 <0.001 -250.25 508 0.002

FD None 1 2.10 N/A

3

--

2

--

2

-249.18 501 0.038

FD pt N

w

2 2.10 <0.001 0 1 -249.18 505 0.005

FD pt I

w

2 2.04 <0.001 0.000064 0.084 -247.69 502 0.020

FD pt I

w

/N

w

2 1.92 <0.001 0.065 0.001 -243.88 495 0.923

1

pt =proportional to;

2

When α or β is assumed to be zero, the parameter estimate is omitted from the table and no p-value is calculable.

3

When

only one parameter (α or β) is fitted and the other is assumed to equal zero, the calculation of a p-value for the null hypothesis that the single

fitted parameter is also equal to zero is not applicable (N/A), as that null model would have no disease transmission and thus at equilibrium no

disease.

9

Donnelly and Hone: Bovine Tuberculosis in Cattle Herds and Badgers

Published by The Berkeley Electronic Press, 2010

Figure 1. The observed proportions of herds in which infection is newly detected

(i.e. which experience TB herd breakdowns) in a year (filled symbols represent

triplets A, C and E) and fitted models (solid line fit includes all data and dotted

line fit omits triplets A, C and E) of the proportion of herds in which infection is

newly detected (i.e. which experience TB herd breakdowns), (I*c/N, equation 18)

as a function of the observed proportion (I

w

/N

w

) of badgers infectious with M.

bovis in parts of Britain. The parameter estimates used are from the models with

the lowest AICc. (The graph is plotted over the entire possible range of I

w

/N

w

(i.e.

from 0 to 1) to demonstrate the fit of the model to the observed data as well as the

implications of the model for cattle in the presence of badger populations with

high observed M. bovis prevalence levels.)

Discussion

The evaluation of the association between TB in cattle herds and badgers showed

evidence of a strong positive relationship, similar to the results of Hone and

Donnelly (2008), although in this study the important badger variable was the

proportion of badgers infectious with M. bovis implying much stronger support

for frequency-dependent badger-to-cattle transmission than density-dependent

badger-to-cattle transmission. The analyses were based on epidemiological

models derived from the TB model of Barlow et al. (1998) which examined

transmission between cattle herds and from brushtail possums to cattle herds in

New Zealand.

If the reported associations between bovine TB in cattle herds and badgers

in parts of Britain reflect causal relationships, then the results imply that reducing

the prevalence of M. bovis infection in badgers, such as by effective vaccination

of badgers, may be important in reducing TB incidence in cattle herds. However,

0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8 1

Proportion of herds in which infection is

newly detected in a year

Observed proportion of badgers infectious with M. bovis (I

w

/N

w

)

10

Statistical Communications in Infectious Diseases, Vol. 2 [2010], Iss. 1, Art. 3

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DOI: 10.2202/1948-4690.1000

Figure 2. The observed proportions of herds in which infection is newly detected

(i.e. which experience TB herd breakdowns) in a year (filled symbols represent

triplets A, C and E) and fitted models (solid line fit includes all data and dotted

line fit omits triplets A, C and E) of the proportion of herds in which infection is

newly detected (i.e. which experience TB herd breakdowns), (I*c/N, equation 18)

as a function of the corrected, or true underlying, proportion (I

w

/N

w

× 1/s

B

) of

badgers infectious with M. bovis in parts of Britain. The parameter estimates used

are from the models with the lowest AICc. (The graph is plotted over the entire

possible range of badger infection prevalence (i.e. from 0 to 1) to demonstrate the

fit of the model to the observed data as well as the implications of the model for

cattle in the presence of badger populations with high observed M. bovis

prevalence levels.)

stronger inference (Platt 1964; McArdle 1996) would be possible from an

experimental study. Such an experiment might take the form of monitoring TB

incidence among cattle herds in areas randomised to receiving and not receiving

badger vaccination, where the magnitude would need to be similar to that of the

RBCT (i.e. ten 100km

2

areas per randomised ‘treatment’ monitored for 5 years) in

order to achieve comparably precise estimates of the effects of badger vaccination

on TB incidence in cattle herds. Vaccination experiments would help

interpretation and application of previous simulation studies, such as by Smith et

al. (2001), of vaccination. Vaccination has been successful for rabies control

(Blancou et al. 2009) and is an area of active research for TB control.

Experimental evidence suggests reduction in badger density can have

positive and negative effects on the incidence of TB in cattle herds (Donnelly et

0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8 1

Proportion of herds in which infection is

newly detected in a year

Corrected, or true underlying, proportion of

badgers infectious with M. bovis (I

w

/N

w

× 1/s

B

)

11

Donnelly and Hone: Bovine Tuberculosis in Cattle Herds and Badgers

Published by The Berkeley Electronic Press, 2010

al. 2006). The present study makes no inferences about any effects on TB in cattle

herds in surrounding areas, and hence about whether negative effects may occur.

The analysis of the proportion of cattle herds with newly detected TB in a

year showed that the Akaike weights of the best models were close to 1.0 (Tables

1, 2). While the estimation of the equilibrium disease state in the absence of

transmission from badgers (k=0) involved some extrapolation beyond the range of

the observed data, examination of Figure 1 shows the extrapolation was quite

limited as the lowest value of the linear predictor of k, prevalence of M. bovis

infection in badgers, was 1.6%. The conclusions may have been influenced by the

small sample sizes of the data sets studied. For example, a small data set may

generate wider 95%CI than a much larger data set, and so a 95%CI may include a

particular value, 0 for example, due to the sample being limited in size. However,

it is difficult to foresee a larger dataset becoming available while accurate

diagnosis of M. bovis infection still requires badgers to be killed and subjected to

a detailed necropsy.

Mathematical models have a long history of effective use in infectious

disease epidemiology. Models such as those presented here are, of course, highly

idealized while aiming to describe the key features of an epidemic. Those utilising

the results of this and similar modelling studies need to understand the limitations

of any model of interest, its structure and the details of the data used to estimate

model parameters. In this case the data were observational, despite being collected

as baseline data for the experimental study known as the Randomised Badger

Culling Trial.

12

Statistical Communications in Infectious Diseases, Vol. 2 [2010], Iss. 1, Art. 3

http://www.bepress.com/scid/vol2/iss1/art3

DOI: 10.2202/1948-4690.1000

Appendix. Data used in the analysis of association of bovine TB in cattle herds

and badgers.

Triplet Herd breakdowns

detected in 12 months

preceding initial

proactive cull

1

Total herds

1

(N)

Badgers

culled

2

(N

w

)

Infectious

badgers

culled

3

(I

w

)

A 8 71 55 8

B 15 152 238 13

C 8 105 243 4

D 11 97 293 102

E 4 116 602 29

F 4 138 446 13

G 7 245 422 29

H 11 63 161 12

I 15 100 218 82

J 8 114 442 65

1

Based on the numbers of total herds and TB-affected herds in the 12-month periods preceding the

initial proactive badger culls, as published by Donnelly et al. (2006) in the form of Supplementary

Data based on location data as recorded in the VetNet database.

2

Based on the numbers of badgers

culled in initial proactive culls (excluding 19 with incomplete data), as published by Woodroffe et

al. (2005).

3

Based on the numbers of badgers culled in initial proactive culls found to be M. bovis

infected, as published by Woodroffe et al. (2005).

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Statistical Communications in Infectious Diseases, Vol. 2 [2010], Iss. 1, Art. 3

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DOI: 10.2202/1948-4690.1000