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Is There an Association between Levels of Bovine Tuberculosis in Cattle Herds and Badgers?

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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 cattle 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 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). 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 badgers infectious with M. bovis. The results indicate that TB in cattle herds could be substantially reduced, possibly even eliminated, in the absence of transmission from badgers to cattle. The results are based on observational data and a small data set to provide weaker inference than from a large experimental study.
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
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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
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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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DOI: 10.2202/1948-4690.1000
... To paraphrase De Jong (1995), the gain of such modeling is not the resulting model, but instead the insight into the population dynamics of infectious agents that is obtained in the process of model building and model analysis on the one hand, and interpreting experimental and observational data on the other. Donnelly and Hone (2010) presented epidemic models for bTB corresponding to areas of the Randomised Badger Culling Trial (RBCT) in S-W England. However, transmission dynamics between badgers and cattle herds may be inherently different in Ireland than in Britain and require separate modeling. ...
... An analogous model was subsequently formulated by Donnelly and Hone (2010) for a single area with both risk of infection from wildlife and density-dependent between-herd risk of infection (i.e. a model which assumes that the rate of contact of one herd with another increases in proportion to the total number of herds in the population). ...
... We also consider a second model which assumes herd-to-herd transmission to be frequency-dependent i.e. the rate of herd-to-herd transmission is completely independent of the total number of herds, N . The model and associated equilibrium values are described in Donnelly and Hone (2010). ...
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Bovine tuberculosis, a disease that affects cattle and badgers in Ireland, was studied via stochastic epidemic modeling using incidence data from the Four Area Project (Griffin et al., 2005). The Four Area Project was a large scale field trial conducted in four diverse farming regions of Ireland over a five-year period (1997-2002) to evaluate the impact of badger culling on bovine tuberculosis incidence in cattle herds. Based on the comparison of several models, the model with no between-herd transmission and badger-to-herd transmission proportional to the total number of infected badgers culled was best supported by the data. Detailed model validation was conducted via model prediction, identifiability checks and sensitivity analysis. The results suggest that badger-to-cattle transmission is of more importance than between-herd transmission and that if there was no badger-to-herd transmission, levels of bovine tuberculosis in cattle herds in Ireland could decrease considerably.
... One potential uncontrolled variable identified here is the disparity in SICCT test frequency in areas surrounding the trial areas before and during the experiment. In the 1990s, districts of England with bTB outbreaks were placed in SICCT testing cycles of between one and four years, according to the level of NHB locally and giving rise to a variable pattern of testing frequency [11,15]. Testing frequency changed throughout the three years prior to and during the RBCT experiment; a period of around ten years. ...
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Science is about discovering new things, about better understanding processes and systems, and generally furthering our knowledge. Deep in science philosophy is the notion of hypotheses and mathematical models to represent these hypotheses. It is partially the quantification of hypotheses that provides the illusive concept of rigor in science. Science is partially an adversarial process; hypotheses battle for primacy aided by observations, data, and models. Science is one of the few human endeavors that is truly progressive. Progress in science is defined as approaching an increased understanding of truth – science evolves in a sense.
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The primary aim of a scientific investigation is to find the most likely model for a situation out of a host of alternative explanations. The strength of evidence provided by anecdote, logical argument, mathematical modelling, observation, and designed studies (manipulative and observational) are discussed and the effectiveness of randomisation and orthogonal designs in separating hypotheses compared. Pseudoreplication is shown to be often misunderstood. It consists of two concepts: the importance of adequate replication and the independence of the sampling units. While replication is necessary to separate out the effects of different factors and to provide an error term for inference, contrary to popular belief independence of sampling units is not necessary. Finally the interpretation of evidence is discussed and the distinction made between formal and informal generalisation to a population.
Article
Summary • Bovine tuberculosis (TB) occurs in cattle and badgers in the UK and control efforts are undertaken to reduce the spread of the disease. • This study evaluates relationships predicted by nine epidemiological two-host models of disease spread generated by various combinations of density-dependent, frequency-dependent and environmental pathogen transmission. The relationships of interest are between measures of TB in cattle and in badgers from 10 sites which were randomly selected to be proactive badger culling sites in the UK Randomized Badger Culling Trial. The data are from the initial badger cull only. • There was most support (Akaike weight = 0·562, R2 = 0·869) for models that predicted a positive linear relationship between density of infectious cattle per square kilometre and the density index of infectious badgers. There was less support (Akaike weight = 0·060) for a model that predicted a positive linear relationship between density of infectious cattle per square kilometre and the proportion of badgers infectious with Mycobacterium bovis. A correction to reduce effects of badger carcase storage and an examination of effects of the 2001 foot-and-mouth disease epidemic had little impact on estimated relationships. • Synthesis and applications. The results provide support for two-host disease models of TB in cattle and wildlife such as badgers, although the form of disease transmission cannot be identified clearly by these analyses. The implication of the results is that the best-fitting models predict that, in the absence of intervention-related changes in badger behaviour, a reduction in density of infectious badgers should reduce the density of infectious cattle. However, analysis of bait-marking data collected following experimental badger culls indicated that culling badgers profoundly alters their spatial organization as well as their population density, potentially influencing contact rates. Effective vaccination of badgers, were it to become available, would be expected to reduce the density of infectious badgers without directly affecting their behaviour.
Article
Summary • An individual-based stochastic simulation model was used to investigate the control of bovine tuberculosis (TB) in the European badger Meles meles. Nearly all population and epidemiological parameters were derived from one study site, and the transmission of TB from badgers to cattle was included. The latter is an essential step if reactive badger control strategies are to be modelled. • The model appeared to underestimate slightly the rate of population recovery following widespread culling. This may have been due to simulating an isolated population with no immigration and no compensatory increase in fecundity. This should not affect the relative efficacy of each control strategy, but does require further investigation. • Of the historical methods of badger control, gassing and the ‘clean ring’ strategies were the most effective at reducing disease prevalence in the badger and cattle herd breakdown rates. These results agree with those of earlier models. • The proactive badger removal operation as part of the current field trial should cause a dramatic decrease in the number of cattle herd breakdowns, but also has the greatest effect on the badger population size. • The proactive use of a live test to detect TB, followed by vaccination, appears to reduce substantially cattle herd breakdowns and disease prevalence in the badger. • Three combined control strategies gave the best initial reduction in cattle herd breakdown rate and disease prevalence in the badger: (i) a proactive cull followed by reactive test and cull; (ii) a continued vaccination and proactive test and cull; and (iii) a continuous proactive test and cull. • The results of simulation models suggest that badger vaccination is a very good method of TB control. This is at odds with simple models and requires further investigation.
Article
Summary • Control of zoonotic disease is difficult to achieve when populations of multiple hosts, particularly wildlife, become persistently infected. Bovine tuberculosis (TB) is one such disease: its causative agent, Mycobacterium bovis, infects cattle, humans and multiple wildlife species including European badgers Meles meles. • In Britain, from 1974 to 1998 various strategies for the control of cattle TB involved culling badgers in the immediate vicinity of TB-affected herds. However, patterns of association between cattle and badgers had not been investigated at a local scale. • Using data from the Randomized Badger Culling Trial, an ongoing large-scale study of TB dynamics and control, we investigated local geographical associations between M. bovis infection in badgers and cattle. • Mycobacterium bovis infections were locally clustered within both badger and cattle populations. • We show, for the first time, that M. bovis infections in badgers and cattle are spatially associated at a scale of 1–2 km. Badgers and cattle infected with the same strain type of M. bovis are particularly closely correlated. These observational data support the hypothesis that transmission occurs between the two host species; however, they cannot be used to evaluate the relative importance of badger-to-cattle and cattle-to-badger transmission. • Synthesis and applications. The close associations between M. bovis infections in cattle and badgers suggest that localized badger culling could reasonably be expected to reduce the risks of cattle TB infection; however, experimental culls have found no such beneficial effects over the time-scale on which they were tested. This demonstrates the difficulty of predicting the outcome of management interventions, and reinforces the need for well-designed empirical assessments of future control strategies. Journal of Applied Ecology (2005) doi: 10.1111/j.1365-2664.2005.01081.x