Bovine tuberculosis: Within-herd transmission models to support and direct the decision-making process

Accepted Manuscript Title: Bovine tuberculosis: within-herd transmission models to support and direct the decision-making process Author: Julio Álvarez, Javier Bezos, Maria Luisa de la Cruz, Carmen Casal, Beatriz Romero, Lucas Domínguez, Lucí,a de Juan, Andrés Pérez PII: DOI: Reference:

S0034-5288(14)00140-4 http://dx.doi.org/doi:10.1016/j.rvsc.2014.04.009 YRVSC 2653

To appear in:

Research in Veterinary Science

Received date: Accepted date:

29-10-2013 24-4-2014

Please cite this article as: Julio Álvarez, Javier Bezos, Maria Luisa de la Cruz, Carmen Casal, Beatriz Romero, Lucas Domínguez, Lucí,a de Juan, Andrés Pérez, Bovine tuberculosis: withinherd transmission models to support and direct the decision-making process, Research in Veterinary Science (2014), http://dx.doi.org/doi:10.1016/j.rvsc.2014.04.009. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

1

Bovine tuberculosis: within-herd transmission models to support and direct the decision-

2

making process

3 4

Julio Álvareza,*, Javier Bezosc, Maria Luisa de la Cruzc, Carmen Casalc, Beatriz Romeroc, Lucas

5

Domínguezc,d, Lucía de Juanc,d, Andrés Pérezb

6 7 8

a

9 10

c

11 12

d

13

*Corresponding autor. Tel.: +1 612-624-9458.

14

E-mail address: [email protected] (J. Alvarez).

Department of Veterinary Population Medicine, College of Veterinary Medicine, University of Minnesota, St. Paul, Minnesota 55108, USA. Centro de Vigilancia Sanitaria Veterinaria (VISAVET). Universidad Complutense Madrid. Avda. Puerta de Hierro S/N, 28040 Madrid, Spain Departamento de Sanidad Animal, Facultad de Veterinaria, Universidad Complutense de Madrid. Avda. Puerta de Hierro S/N, 28040 Madrid, Spain

1 Page 1 of 29

15

Abstract

16

Use of mathematical models to study the transmission dynamics of infectious diseases is

17

becoming increasingly common in veterinary sciences. However, modeling chronic infectious

18

diseases such as bovine tuberculosis (bTB) is particularly challenging due to the substantial

19

uncertainty associated with the epidemiology of the disease. Here, the methodological

20

approaches used to model bTB and published in the peer-reviewed literature in the last

21

decades were reviewed with a focus on the impact that the models’ assumptions may have

22

had on their results, such as the assumption of density vs. frequency-dependent transmission,

23

the existence of non-infectious and non-detectable stages, and the effect of extrinsic sources

24

of infection (usually associated with wildlife reservoirs). Although all studies suggested a

25

relatively low rate of within-herd transmission of bTB when test-and-cull programs are in

26

place, differences in the estimated length of the infection stages, sensitivity and specificity of

27

the tests used and probable type of transmission (density or frequency-dependent) were

28

observed. Additional improvements, such as exploring the usefulness of contact-networks

29

instead of assuming homogeneous mixing of animals, may help to build better models that can

30

help to design, evaluate and monitor control and eradication strategies against bTB.

31

Keywords: bovine tuberculosis; modeling; within-herd transmission; eradication; diagnosis

2 Page 2 of 29

32

1. Introduction

33

Although mathematical models of disease dynamics have been extensively used in human

34

medicine since the eighteenth century and particularly from the 1900’s onwards (Keeling and

35

Rohani, 2008), their use in veterinary medicine has been quite limited until the end of the

36

twentieth century. However, in recent decades, the number of animal disease mathematical

37

models published in the peer-reviewed literature has substantially increased. In the field of

38

animal health, different types of disease models of varying complexity have been useful tools

39

for development of policy, design and evaluation of surveillance systems and the prediction of

40

consequences due to introduction of new diseases and the expected impact of control

41

strategies (Garner and Hamilton, 2011; Willeberg et al., 2011a; Willeberg et al., 2011b). In the

42

case of bovine tuberculosis (bTB), modeling has been used to provide estimates of i) within-

43

and between-herd transmission rates (Alvarez et al., 2012; Barlow et al., 1997; Griffin et al.,

44

2000; Kao et al., 1997; Kean et al., 1999; Perez et al., 2002a), ii) the duration of the period

45

between infection and detection/shedding of the pathogen (commonly referred to as

46

“latency”) (Conlan et al., 2012; Fischer et al., 2005; Kao et al., 1997; Perez et al., 2002a; Smith

47

et al., 2013a), iii) bTB diagnostic techniques reliability (sensitivity and specificity) (Conlan et al.,

48

2012; Fischer et al., 2005; Smith et al., 2013a), iv) disease dynamics in wildlife and contribution

49

of wildlife reservoirs in disease incidence and/or persistence in livestock (Anderson et al.,

50

2013; Barlow, 2000; Delahay et al., 2013; Graham et al., 2013; Kean et al., 1999), and v) the

51

effectiveness of alternative control measures in cattle and wildlife reservoirs (Fischer et al.,

52

2005; Hardstaff et al., 2013; Kao and Roberts, 1999; Perez et al., 2002b; Smith et al., 2013b).

53

Here, we offer a comprehensive review of models assessing bTB within-herd transmission,

54

including a simplified description of the methodologies and assumptions adopted to formulate

55

the models, a summary of the values used to parameterize or obtained from the modeling

56

exercises, and a discussion on the most important conclusions that may be extracted from

3 Page 3 of 29

57

existing knowledge. We emphasize the review of studies published since the last review of the

58

subject was published more than 10 years ago (Goodchild and Clifton-Hadley, 2001).

59 60

2. Modeling within-herd transmission of bTB

61

2.1. Model formulation and basic parameterization

62

Models of bTB within-herd transmission typically assume different mutually exclusive states

63

between which individuals move through transitions with a given probability, which are

64

referred to as “state transition models” (Fig. 1). All models consider a “Susceptible (S)” state

65

(non-infected animals that become infected after an adequate contact) and an “Infectious (I)”

66

state (infected animals shedding the pathogen that, when in contact with susceptible cattle,

67

may infect them). However, certain models also assume a number of intermediate stages

68

between those two states. An infected-but-unreactive state (animals in early stages of

69

infection that do not contribute to new infections and do not respond – or respond poorly – to

70

the in-vivo diagnostic tests), typically referred to as “Unreactive (U)” or “Occult (O)” (of a given

71

duration=λ1), has sometimes been assumed. In addition, other models also considered an

72

infected-and-reactive state (animals in intermediate stages of infection that become

73

detectable by in-vivo diagnostic tests but do not shed the pathogen and therefore do not act

74

as sources of new infections), referred to as “Reactive (R)” period (of duration= λ2) (Fig. 1).

75

Transition between these categories may be dependent on the period of time that a given

76

individual has spent in each of the states, although a constant rate of transition (1/λ1 for

77

animals moving from state O to R

78

sometimes assumed.

79

Parameters λ1 and λ2 have been parameterized using data from experimental studies (Costello

80

et al., 1998; Dean et al., 2005; Neill et al., 1989; Neill et al., 1991) as well as fitting models to

81

field data (Conlan et al., 2012; Kao et al., 1997; Perez et al., 2002a), with the median values

1

and 1/λ2 when the transition is between state R to I) is

4 Page 4 of 29

82

assumed to be 41 days for λ1 and 21 months for λ2, although much higher estimates (> 34

83

months) than those typical values have also been reported (Table 1).

84

A wide variety of field data from bTB outbreaks have been used to validate models. Results of

85

diagnostic tests (usually the tuberculin skin test, performed either in the cervical or the caudal

86

region) are used to approximate the true number of infected animals in the detectable stages,

87

taking into account their limitations in terms of sensitivity and specificity. In addition,

88

assessment of the effectiveness of alternative diagnostic approaches (or improvement of those

89

in place by means of an increase in its frequency/sensitivity) for disease control/surveillance

90

has been pursued using transmission models. In those cases, the uncertainty about the true

91

performance of the diagnostic tests is often included in the models using estimates for the

92

sensitivity and specificity obtained from the literature, typically ranging from 55 to 100% for

93

sensitivity [although recent studies suggest an even lower sensitivity may be possible (Conlan

94

et al., 2012; VLA (Veterinary Laboratories Agency), 2011)] in the case of the skin test (Table 1).

95 96

2.2. Basic model assumptions: density- vs. frequency-dependent models

97

Most bTB within-herd transmission models have assumed homogeneous mixing of individuals

98

(susceptible and infectious) in the population; however, whereas some have assumed that

99

transmission is density-dependent (Anderson and May, 1979), others rely on the principle of

100

frequency-dependent transmission (de Jong, 1995). This difference may have an impact on the

101

model outputs. In the former scenario, the transmission rate will increase if the herd size

102

increases (and the farm size remains constant, thus leading to an increase in animal density) as

103

this will yield an increase in the contact rate. This may be particularly true for smaller farms in

104

which animals are housed in reduced areas, and in which an increase in the number of animals

105

will likely have a strong impact on the transmission patterns. In contrast, in extensively

106

managed herds, a change in the actual number of animals may not affect the animal density.

107

Alternatively, the latter scenario assumes that the number of contacts is independent of the 5 Page 5 of 29

108

population size, and that it is affected by the disease frequency, i.e, its prevalence (Keeling and

109

Rohani, 2008).

110

Depending on whether a density- or frequency-dependent model is fitted, the “transmission

111

term” dI/dt, i.e., the rate per unit of time during which susceptible hosts become infected due

112

to contact with infectious individuals, may be estimated as: dI/dt=βSI/A (density-dependent

113

transmission) or dI/dt=β’SI/N (frequency-dependent transmission), where S and I represent

114

the number of susceptible and infected individuals in a population of size N, A is the area

115

occupied by the population, and β and β’ are the transmission coefficients (the product of the

116

contact rate and the probability that a given contact will end in transmission of disease) for

117

each scenario. Density-dependent transmission models are often expressed as dI/dt= β*SI,

118

with β*= β/A, and therefore being constant only if A is constant (Begon et al., 2002). Thus, β*

119

depends on the area occupied by the population and assumes such area is constant so that any

120

increase in the population size leads to an increase of the density, whereas β’ is a true constant

121

irrespective of the density of the population (Begon et al., 2002; de Jong et al., 1995). However

122

if density is constant for two populations, the larger the population size (N=S+I), the larger the

123

area A in which the population is located, and for that reason the transmission term dI/dt will

124

not be affected by population size for the density-dependent transmission. In contrast, the

125

transmission term will be inversely proportional to the population size in frequency-dependent

126

transmission based models (de Jong et al., 1995). Conversely, the basic reproductive ratio R0,

127

(the average number of new infections resulting from the introduction of an infectious

128

individual in an entirely susceptible population) is directly proportional to the population size

129

for density-dependent transmission models but independent of the population size if

130

frequency-dependent transmission is assumed (de Jong et al., 1995; McCallum et al., 2001). In

131

summary, both approaches have certain factors in common driving the transmission force (the

132

size of the susceptible and infectious population), whereas they are differentially affected by

6 Page 6 of 29

133

other factors, such as size of the population in frequency-dependent models and density –

134

area in which individuals are located – in density-dependent models.

135 136

2.3. Density-dependent models

137

Early models of within-herd bTB transmission assumed that density-dependent transmission

138

occurred based on experimental evidence (Neill et al., 1989). Fitting a SORI (Susceptible →

139

Occult → Reactive → Infectious) model to different sets of data from herds of between 100

140

and 300 animals in New Zealand, Canada and Egypt, Barlow and collaborators estimated that

141

every infected animal could make from 0.0014 to 0.0056 infectious contacts per day

142

depending on the size of the herd, the assumed duration of the occult and reactive periods

143

and the sensitivity and specificity of the test used (thus leading to an annual estimate of

144

between 0.5 and 1.7 new infected animals per infectious cattle and year in a herd of 200

145

animals) (Barlow et al., 1997). However, analysis of the herd histories of bTB outbreak in which

146

the number of susceptible, infected and infectious animals was known, provided a an overall

147

higher estimate of 0.0073 infectious contacts per day per infected animal (2 new infected

148

animals per infectious cattle and year) compared to early estimates, suggesting a relevant

149

effect of within-herd transmission in disease control and a potential expected benefit of

150

increasing test sensitivity and frequency on the time required for releasing movement

151

restrictions (Barlow et al., 1997).

152

In order to assess the contribution of cattle-to-cattle transmission and infection from an

153

external source (infected possums) in the overall infection burden in cattle herds in New

154

Zealand some of the data used by Barlow and collaborators were further analyzed using a SORI

155

model and an alternative “simple analytical model” in which only two status (Susceptible and

156

Infected) were considered, so all infected cattle were assumed to be infectious (Kean et al.,

157

1999). Assumed values for the sensitivity of the diagnostic test used [caudal fold tuberculin

158

(CFT) test] and duration of Occult and Reactive periods were identical to those previously used 7 Page 7 of 29

159

(Barlow et al., 1997), but the inclusion of potential external sources of infection led to a 3 to

160

10-fold decrease in the estimates for the transmission coefficients, compared to the values

161

initially obtained (Table 1). Assuming that the sensitivity of the diagnostic test used in the

162

study was accurate, those findings suggested that within-herd transmission could not be

163

maintained in the absence of re-infections (likely due to contact with infected wildlife) (Kean et

164

al., 1999). Another SORI density-dependent transmission based model considering both a

165

wildlife source of infection (possum) and within-herd transmission was formulated to evaluate

166

the existing disease control methods in New Zealand (Kao et al., 1997). Under the assumption

167

of an external source of infection (wildlife) for most of the new bTB cases, higher estimates for

168

the rate of infection due to wildlife (4.42*10-4 per year) compared to within-herd transmission

169

(7.19*10-5 per year) were obtained, and an insufficient impact of potential measures targeting

170

exclusively cattle-to-cattle transmission (improved herd management and testing, use of

171

therapeutic vaccines) was expected. Prophylactic vaccines for cattle that would decrease the

172

infection rates due to contact with both infected wildlife and cattle were predicted to succeed

173

as long as a 50% of final vaccine efficacy over all animals could be achieved within a period of

174

three months (Kao et al., 1997).

175

No external sources of infection were assumed in the analysis of field data from outbreaks in a

176

limited number (n=20) of Irish herds, carried out using a density-dependent transmission

177

based SORI model that provided low estimates for the transmission coefficient in addition to

178

high estimates for the cervical comparative tuberculin (CCT) test sensitivity and specificity

179

(Table 1) (Griffin et al., 2000).

180

Two SORI and SOR (in which all occult and reactive animals are considered infectious) models

181

were recently formulated using Approximate Bayesian Computation to fit data from 3,094

182

outbreaks occurring in 2003-2005 in the UK (Conlan et al., 2012). In this study a transmission

183

parameter ranging from 0 to 1 was included in the models formulation to measure the

184

strength of density dependence of the transmission: a non-linear dependence of the cattle-to8 Page 8 of 29

185

cattle transmission with the herd size was found with both models suggesting the occurrence

186

of density-dependent transmission, with R0 estimates around 0.5-1.5 for small herds (n=30)

187

and 3.6-4.9 for large herds (n=400) depending on the model used (SOR-SORI).

188 189

2.4. Frequency-dependent models

190

Frequency-dependent models provided, in general, higher estimates for the within-herd

191

transmission coefficient in small-middle size (n<2,000 animals) cattle herds compared to those

192

obtained using density-dependent transmission based models (Table 1). Perez and

193

collaborators estimated a β coefficient of 2.2 using field data from three dairy herds in

194

Argentina. Fitting the same field data to a SRI model that assumed perfect sensitivity and

195

specificity of the diagnostic test used (CFT) yielded a large estimated mean duration of the

196

incubation of the disease (24 months) (Perez et al., 2002a). A SORI model developed to

197

evaluate the usefulness of different surveillance strategies for bTB detection in the

198

Netherlands (Fischer et al., 2005) used a higher estimate of β=5.2 (newly infected animals per

199

infectious cattle and year), obtained from the analysis of field data, and length values for the λ1

200

and λ2 transition rates similar to those used by Barlow and collaborators (Barlow et al., 1997)

201

(Table 1). Analysis of field data from cattle herds located in a region from Spain yielded a β of

202

2.3, although the estimated transmission coefficient varied with the productive type of the

203

herd (from 2-2.6 in extensively managed beef and bullfighting cattle to 4.3 in intensively

204

managed dairy herds) (Alvarez et al., 2012). Recently, comparison of fit of models assuming

205

alternative density and frequency-dependent transmission to field data from bTB outbreaks in

206

10 US dairy herds revealed a significantly higher predictive ability of the latter, although

207

density-dependent transmission based models performed significantly better in the two

208

largest outbreaks (Smith et al., 2013a). The frequency-dependent model provided a basic

209

reproductive number R0 = 4.13 if no test-and-cull strategies were in place and a R0 = 0.02 if this

210

control measure was implemented (assuming a three-month interval and sensitivity values 9 Page 9 of 29

211

>96% for the CCT and CFT tests considered, Table 1). In fact, implementation of constant test-

212

based culling yielded a R0 <1 if testing was performed more frequently than every four years

213

(Smith et al., 2013a). The same frequency-dependent model was used to determine the most

214

cost-efficient strategy to eradicate a bTB outbreak in a dairy herd (Smith et al., 2013b). In this

215

study the diagnostic strategy was based on the combined use of CFT [screening test, with an

216

assumed sensitivity ranging from 63.2 to 100% (with 83.9% as the most likely value)], CCT

217

[applied in serial on CFT-positive cattle once a herd had achieved a number of negative herd-

218

tests assuming a sensitivity between 75-95.5%)] and an enhanced post-mortem investigation

219

(histopathology + culture and PCR of bacilli, with an expected sensitivity of 100%). Two

220

consecutive negative herd tests (i.e., in which no CFT reactors were found, or the post-mortem

221

inspection of the skin test-positive animals was negative) with a 2-month testing interval was

222

identified as the optimal program to consider a herd as free of disease (Smith et al., 2013b).

223

Those results do not support the rationale behind current U.S. and European policies, which

224

require at least two consecutive herd tests in which no reactors are identified separated by at

225

least six months since the removal of the last positive cattle (Anon., 1964; USDA, 2005). That

226

divergence may be explained, at least in part, by the high individual-sensitivity values assumed

227

for the diagnostic techniques considered, in contrast with recent estimates for skin tests

228

performed repeatedly in infected herds (Alvarez et al., 2011; Clegg et al., 2011; EFSA, 2012;

229

Smith et al., 2013a) combined with the possibility of finding animals in the occult stage for

230

longer periods of time (in which the techniques would likely be less sensitive).

231

Using a simplified SI model (in which all infected animals are infectious) and considering

232

external (wildlife) sources of infection and a more limited sensitivity of the diagnostic test

233

considered (CCT) of ≈ 66.7% for fitting data from bTB incidence data from the UK, Cox and

234

collaborators estimated higher R0 values (1.02-1.11). Still, these values were close enough to 1

235

so that a relatively small increase in the test performance would yield R0 values below the 1

236

threshold thus leading to control of the epidemic in the region (Cox et al., 2005). 10 Page 10 of 29

237 238

3. Lessons learned from bTB within-herd transmission modeling

239

Modeling has received criticism in the past, often due to a misunderstanding about the

240

potential benefits that could be gained from modeling disease dynamics in animal populations

241

(de Jong, 1995). As reviewed in the previous sections of the manuscript here, alternative

242

modeling approaches and assumptions may be applied to one single disease and

243

epidemiological setting, eventually leading to a wide range of estimates for a number of

244

parameters, and thus demonstrating the impact that the different assumptions may have in

245

their outcomes (Table 1).

246

However, one conclusion is consistently extracted from the review of all the above mentioned

247

studies; namely, the number of new cases caused by the existence of infectious cattle in a

248

given herd is always estimated using a transmission term that includes (1) the number of

249

infectious cattle, (2) the number of susceptible cattle, and (3) the contact rate between

250

individuals. Because disease control may be obtained by reducing at least one of those three

251

parameters down to values that are not compatible with disease transmission, disease control

252

and eradication may be planned and assessed considering the impact that selected strategies

253

may have on each of those three components through the use of transmission models.

254

Reducing the number of infectious cattle, thus leading to disease control, is the target of “test-

255

and-cull” programs, and their success is highly dependent on the accuracy of the diagnostic

256

tests used to identify infected animals. For that reason, a number of the bTB models published

257

in peer-reviewed literature have tried to measure the impact in bTB control by a theoretical

258

increase of the sensitivity or the frequency of the diagnostic tests in place (Barlow et al., 1997;

259

Conlan et al., 2012; Cox et al., 2005; Fischer et al., 2005; Kean et al., 1999; Perez et al., 2002b).

260

Such a trend is likely related to and consistent with the nature of current bTB-control

261

programs, whose foundation is the implementation of test-and-cull strategies. However, little

262

attention has been paid to the potential effect that the two other components of the equation, 11 Page 11 of 29

263

namely, the reduction of the susceptible population and the reduction of the contact rate

264

between infected and susceptible cattle, may have on bTB control. Only one study found in

265

peer-reviewed literature addressed the impact of a modification in those terms by using a

266

prophylactic vaccine (Kao et al., 1997).

267

Even when similar theoretical compartment models were used a wide range of estimates were

268

obtained for the parameters defining duration of the diseases intermediate stages

269

(occult/reactive) and accuracy of diagnostic tests used (sensitivity and specificity). This may

270

reflect the inherent variability that can be expected in the case of chronic diseases with a long

271

period of incubation such as bTB and may also be the product of changes in the estimates of

272

certain parameters to compensate expected values in others (so an increased transmission

273

rate could compensate a longer latent period, for example). Still, most studies yielded an

274

estimated period between infection and detection of infected animals of between one to eight

275

weeks, while estimates of the duration of the infectious stage were much more variable and

276

ranged between a few months to up to 3 years (Table 1). Assumed diagnostic sensitivity and

277

specificity of skin tests were high (particularly for the sensitivity) considering recent studies

278

that have reported a much more limited sensitivity (with median values <70%) of the skin test

279

at animal level using latent class analysis (Alvarez et al., 2011; Clegg et al., 2011; EFSA, 2012).

280

Interestingly, one of the two studies that also modeled diagnostic performance of the skin test

281

provided values for the diagnostic sensitivity of the skin test in the same range (Conlan et al.,

282

2012), suggesting that overall individual sensitivity in infected herds may be overestimated

283

when values >85% are assumed.

284

Despite different model assumptions, when the effect of an extrinsic infectious pressure was

285

considered, improvements in the performance of the diagnostic strategies evaluated (mostly

286

based on the skin test) were often considered ineffective unless the external source of

287

infection was also addressed (Barlow et al., 1997; Conlan et al., 2012; Kean et al., 1999),

288

although a modest increase in the sensitivity was expected to have an effect in disease control 12 Page 12 of 29

289

in one case (Cox et al., 2005). In contrast, in the absence of a continuous external source of

290

infection an increase in diagnostic sensitivity is expected to improve bTB control effectiveness

291

(Barlow et al., 1997). In this context the gain expected by the use of ancillary diagnostic tests

292

that may increase diagnostic sensitivity such as the IFN-γ would be maximized (Perez et al.,

293

2002b), while its use in areas where there is a high extrinsic infectious pressure would be more

294

limited unless such extrinsic source of infection is adequately addressed (Conlan et al., 2012;

295

Kean et al., 1999).

296 297

4. Knowledge gaps and model limitations.

298

Although tuberculosis is arguably one of the infectious diseases that has been studied more

299

extensively in the history of human and veterinary medicine, many aspects of its pathogenesis

300

are yet to be elucidated, which limits the formulation and parameterization of transmission

301

models. The way those uncertainties are handled in mathematical models, usually in the form

302

of more or less flexible assumptions, may have a critical impact on model outcomes, as

303

recently suggested (Conlan et al., 2012). Still, the use of models may help to at least partially

304

address these uncertainties. Knowledge gaps include:

305

1. The effect of certain factors, such as age, breed, and individual genetic resistance, and co-

306

infection with other pathogens, that may influence the susceptibility to infection and

307

disease and the hosts ability to respond to the diagnostic tests (Allen et al., 2010; Ameni

308

et al., 2007; Claridge et al., 2012; Driscoll et al., 2011; Finlay et al., 2012; Monies, 2000;

309

Sun et al., 2012; Vordermeier et al., 2012) among others].

310

2. Existence of virulence variations depending on the M. bovis strain as demonstrated for M.

311

tuberculosis (Lopez et al., 2003; Palanisamy et al., 2009), although such feature in M. bovis

312

infection remains controversial due to contradictory findings of other studies(Goodchild

313

et al., 2003; Wright et al., 2013). In this sense, the increasing availability of high

314

throughput sequencing techniques will increase the ability to detect genetic signatures 13 Page 13 of 29

315

that may correlate with virulence (given the limited variability of the usual DNA loci

316

targeted by the characterization techniques between M. bovis strains) in areas in which a

317

certain degree of genetic variability may exist.

318

3. Variation in the frequency of cattle-to-cattle transmission events as demonstrated in

319

experimental studies, probably associated with housing conditions, different infected-to-

320

susceptible ratios, and stage of infection in infectious animals, with cattle in advanced

321

stages of disease showing a substantially higher risk of spreading the disease compared to

322

recently infected animals (Ameni et al., 2010b; Costello et al., 1998; Khatri et al., 2012).

323

However, transmission has also been demonstrated in the absence of gross pathology

324

(Khatri et al., 2012), and in fact experimental infections with low and high M. bovis doses

325

induced a similar outcome regardless of the challenge dose (Dean et al., 2005; Johnson et

326

al., 2007), and very low doses of M. bovis may suffice to effectively infect an animal (Neill

327

et al., 1991).

328

4. Accuracy of diagnostic tests: most within and between-herd transmission models are

329

based on the use of in-vivo and post-mortem diagnostic methods for estimation of the

330

true burden of disease; however, accuracy of the most widely used diagnostic methods

331

(skin test, interferon-gamma assay, detection of gross lesions, bacteriology) is

332

considerably variable, leading to wide (and sometimes contradictory) estimates of their

333

sensitivity and specificity (Alvarez et al., 2011; Antognoli et al., 2011; Clegg et al., 2011; de

334

la Rua-Domenech et al., 2006; Gormley et al., 2006, Monaghan et al., 1994; Muller et al.,

335

2009) that may impact the significance of the findings of observational and experimental

336

studies (Szmaragd et al., 2012).

337

5. Contribution of external sources of infection to the within-herd disease burden (usually

338

due to the presence of an infected wildlife reservoir), that may be highly variable and that

339

can lead to differences in model outcomes (Barlow et al., 1997; Kean et al., 1999).

14 Page 14 of 29

340

Some of those unknowns have been brought up by recent investigations, often designed to

341

clarify other aspects of the pathogenesis and epidemiology of bTB. Nevertheless, only

342

experimental studies (that must acknowledge their limitations compared with natural

343

infections) and the thorough assessment of field evidence (sometimes using modeling, which

344

may help to evaluate the reliability of the observations) will provide the answers needed to

345

build robust evidence-based epidemiological models of bTB transmission.

346

In addition, conclusions of the models regarding impact of the herd size differ largely

347

depending on the modeling strategy followed (i.e., density vs. frequency-dependent

348

transmission), with the former yielding higher estimates for larger herds, whereas results of

349

the latter are relatively unaffected by herd size. Despite the methodological advances applied

350

in recent years it still remains unclear which modeling approach may be more accurate or

351

when should either of them be applied, as studies allowing a comparison of both options have

352

provided different results (Conlan et al., 2012; Smith et al., 2013a). In addition all previous

353

models of bTB within-herd transmission have relied on the principle of homogeneous mixing;

354

even though this may be a realistic assumption in certain cases (Kleinlutzum et al., 2013), the

355

potential effect of the degree of mixing in the contact rate estimate (and thus in the estimated

356

rate of transmission) may deserve further attention. In the case of wildlife, homogenous

357

mixing models were found to be ineffective in modeling transmission of tuberculosis (Barlow,

358

2000). Homogeneous mixing-based models may lead to an overestimation of disease spread in

359

a given animal population (Duncan et al., 2012; Schley et al., 2012), whereas accounting for the

360

heterogeneity of contacts between groups of animal (sometimes due to management

361

practices) may provide more accurate estimates for certain diseases (Marce et al., 2011;

362

Turner et al., 2008), although their usefulness for modeling bTB within-herd transmission in

363

cattle is yet to be assessed.

364 365

5. Future uses of bTB modeling. 15 Page 15 of 29

366

The global situation of bTB has changed considerably in the last century. The disease has been

367

eradicated from certain regions while its prevalence is declining in most developed countries in

368

which ad-hoc programs are in place, thus providing evidence of the usefulness of the currently

369

available diagnostic strategies in certain settings (Cousins and Roberts, 2001; Olmstead and

370

Rhode, 2004; Reviriego Gordejo and Vermeersch, 2006). In addition, several developing

371

countries have initiated control and eradication programs in a variety of epidemiological

372

contexts, thus offering the opportunity to gain new knowledge on the epidemiology of the

373

disease in endemic settings and to consider new diagnostic and control strategies, such as

374

those based on vaccination (Ameni et al., 2010a; Ameni et al., 2010b; Cadmus et al., 2011; de

375

Kantor and Ritacco, 2006; Marassi et al., 2010; Perez et al., 2011). The pathogenesis of bTB and

376

other aspects of its epidemiology are also being unraveled by a combination of experimental

377

and field studies. In this context, and using all the information that is becoming increasingly

378

available, within-herd transmission models may be useful tools to achieve the objectives

379

pursued in each of the steps against the disease: control, eradication and prevention of

380

reoccurrence.

381

 In infected areas within-herd transmission models may help to evaluate current

382

control and eradication programs as well as potential alternative diagnostic and

383

control measures (such as vaccination) as shown before (Barlow et al., 1997; Conlan et

384

al., 2012; Cox et al., 2005; Kean et al., 1999; Perez et al., 2002b). This analysis may

385

provide an estimate of the economic benefits that can be expected from each

386

approach. Modeling may be particularly useful to evaluate control programs when a

387

wildlife reservoir is present given the paucity of data usually available in these species.

388

Use of information in the costs associated with breakdowns (Bennett and Cooke, 2006)

389

may aid in the election of the most cost-effective alternatives.

390

 In low prevalence-areas models can be used to optimize eradications strategies when

391

outbreaks take place: usually in the final stages of the disease when outbreaks are 16 Page 16 of 29

392

detected whole-herd culling is the preferred alternative to minimize the risk of

393

recurrence of the disease in properties with residual infection problems (Cousins and

394

Roberts, 2001). However, this option may be unfeasible if very large numbers of

395

animals are involved. Again, adequate models of within-herd transmission can help to

396

establish risk-based alternatives to herd-depopulation, as test-and-cull programs with

397

optimized testing intervals (Smith et al., 2013b), to guarantee disease freedom with a

398

certain (high) level of confidence.

399

 In countries free from the disease accurate surveillance systems are needed in order to

400

verify that the disease is not introduced again (usually by trade of infected animals)

401

and to maintain freedom status. Due to the impossibility of testing the whole cattle

402

population on a regular basis in officially tuberculosis free (OTF) countries to

403

guarantee freedom of disease, most countries in this situation currently rely on

404

slaughterhouse surveillance (i.e., detection of lesioned animals in the abattoir) but,

405

due to the chronic nature of this disease the effectiveness of this method is limited

406

(Radunz, 2006) (particularly for early detection of outbreaks) and thus impair its trace-

407

back. Thus, other surveillance strategies, based on the combination of different

408

sampling and testing protocols, can be designed and evaluated using modeling

409

techniques (Fischer et al., 2005). Accurate models of within-herd transmission can

410

provide some of the needed inputs (estimates of within-herd prevalence and test

411

performance, likely transmission dynamics in infected herds, etc.) to build realistic and

412

cost-effective output-based surveillance standards for bTB surveillance (Cameron,

413

2012) as those suggested for tuberculosis in deer (More et al., 2009). Multiple-herd

414

models in combination with information on between-herds contact networks can help

415

to evaluate the risk of spread of bTB and the surveillance measures in place at the

416

regional level (Dommergues et al., 2012).

17 Page 17 of 29

417

In conclusion, it is envisioned that control and eradication programs may be revisited in the

418

upcoming years in light of what epidemiological modeling may bring to support scientifically-

419

sound decisions. Such revisions may include the reformulation of critical components of

420

current bTB control programs, such as demonstration of absence of infection and early

421

detection of new cases in a region. Field studies will be needed to parameterize the models

422

accurately and to measure the impact of the predictions, including cost-effectiveness

423

assessments of their implementations.

424 425

Acknowledgements:

426

This study was supported by Agriculture and Food Research Initiative Competitive Grant no.

427

2013-67015-21244 from the USDA National Institute of Food and Agriculture

428 429

References

430

Allen, A.R., Minozzi, G., Glass, E.J., Skuce, R.A., McDowell, S.W., Woolliams, J.A., Bishop, S.C.,

431

2010. Bovine tuberculosis: the genetic basis of host susceptibility. Proc.Biol.Sci. 277,

432

2737-2745.

433

Alvarez, J., Perez, A., Bezos, J., Marques, S., Grau, A., Saez, J.L., Minguez, O., de Juan, L.,

434

Dominguez, L., 2011. Evaluation of the sensitivity and specificity of bovine tuberculosis

435

diagnostic tests in naturally infected cattle herds using a Bayesian approach.

436

Vet.Microbiol.

437

Alvarez, J., Perez, A.M., Bezos, J., Casal, C., Romero, B., Rodriguez-Campos, S., Saez-Llorente,

438

J.L., Diaz, R., Carpintero, J., De Juan, L., Dominguez, L., 2012. Eradication of bovine

439

tuberculosis at a herd-level in Madrid, Spain: study of within-herd transmission

440

dynamics over a 12 year period. BMC.Vet.Res. 8, 100-

441

Ameni, G., Aseffa, A., Engers, H., Young, D., Gordon, S., Hewinson, G., Vordermeier, M., 2007.

442

High prevalence and increased severity of pathology of bovine tuberculosis in

18 Page 18 of 29

443

Holsteins compared to zebu breeds under field cattle husbandry in central Ethiopia.

444

Clin.Vaccine Immunol. 14, 1356-1361.

445

Ameni, G., Aseffa, A., Hewinson, G., Vordermeier, M., 2010a. Comparison of different testing

446

schemes to increase the detection Mycobacterium bovis infection in Ethiopian cattle.

447

Trop.Anim Health Prod. 42, 375-383.

448

Ameni, G., Vordermeier, M., Aseffa, A., Young, D.B., Hewinson, R.G., 2010b. Field evaluation of

449

the efficacy of Mycobacterium bovis bacillus Calmette-Guerin against bovine

450

tuberculosis in neonatal calves in Ethiopia. Clin.Vaccine Immunol. 17, 1533-1538.

451

Anderson, D.P., Ramsey, D.S., Nugent, G., Bosson, M., Livingstone, P., Martin, P.A., Sergeant,

452

E., Gormley, A.M., Warburton, B., 2013. A novel approach to assess the probability of

453

disease eradication from a wild-animal reservoir host. Epidemiol.Infect. 141, 1509-

454

1521.

455 456

Anderson, R.M., May, R.M., 1979. Population biology of infectious diseases: Part I. Nature 280, 361-367.

457

Anon., 1964. Off.J.Eur.L121 p. 1977.

458

Antognoli, M.C., Remmenga, M.D., Bengtson, S.D., Clark, H.J., Orloski, K.A., Gustafson, L.L.,

459

Scott, A.E., 2011. Analysis of the diagnostic accuracy of the gamma interferon assay for

460

detection of bovine tuberculosis in U.S. herds. Prev.Vet.Med. 101, 35-41.

461 462

Barlow, N.D., 2000. Non-linear transmission and simple models for bovine tuberculosis. Journal of Animal Ecology 69, 703-713.

463

Barlow, N.D., Kean, J.M., Hickling, G., Livingstone, P.G., Robson, A.B., 1997. A simulation model

464

for the spread of bovine tuberculosis within New Zealand cattle herds. Prev.Vet.Med.

465

32, 57-75.

466

Begon, M., Bennett, M., Bowers, R.G., French, N.P., Hazel, S.M., Turner, J., 2002. A clarification

467

of transmission terms in host-microparasite models: numbers, densities and areas.

468

Epidemiol.Infect. 129, 147-153. 19 Page 19 of 29

469 470

Bennett, R.M., Cooke, R.J., 2006. Costs to farmers of a tuberculosis breakdown. Vet Rec. 158, 429-432.

471

Cadmus, S.I., Gordon, S.V., Hewinson, R.G., Smith, N.H., 2011. Exploring the use of molecular

472

epidemiology to track bovine tuberculosis in Nigeria: an overview from 2002 to 2004.

473

Vet.Microbiol. 151, 133-138.

474

Cameron, A.R., 2012. The consequences of risk-based surveillance: Developing output-based

475

standards for surveillance to demonstrate freedom from disease. Prev.Vet.Med.

476

Claridge, J., Diggle, P., McCann, C.M., Mulcahy, G., Flynn, R., McNair, J., Strain, S., Welsh, M.,

477

Baylis, M., Williams, D.J., 2012. Fasciola hepatica is associated with the failure to

478

detect bovine tuberculosis in dairy cattle. Nat.Commun. 3, 853-

479

Clegg, T.A., Duignan, A., Whelan, C., Gormley, E., Good, M., Clarke, J., Toft, N., More, S.J., 2011.

480

Using latent class analysis to estimate the test characteristics of the gamma-interferon

481

test, the single intradermal comparative tuberculin test and a multiplex immunoassay

482

under Irish conditions. Vet.Microbiol. 151, 68-76.

483

Conlan, A.J., McKinley, T.J., Karolemeas, K., Pollock, E.B., Goodchild, A.V., Mitchell, A.P., Birch,

484

C.P., Clifton-Hadley, R.S., Wood, J.L., 2012. Estimating the hidden burden of bovine

485

tuberculosis in Great Britain. PLoS.Comput.Biol. 8, e1002730-

486 487 488 489

Costello, E., Doherty, M.L., Monaghan, M.L., Quigley, F.C., O'Reilly, P.F., 1998. A study of cattleto-cattle transmission of Mycobacterium bovis infection. Vet.J. 155, 245-250. Cousins, D.V., Roberts, J.L., 2001. Australia's campaign to eradicate bovine tuberculosis: the battle for freedom and beyond. Tuberculosis (Edinb.) 81, 5-15.

490

Cox, D.R., Donnelly, C.A., Bourne, F.J., Gettinby, G., McInerney, J.P., Morrison, W.I., Woodroffe,

491

R., 2005. Simple model for tuberculosis in cattle and badgers. Proc.Natl.Acad.Sci.U.S.A

492

102, 17588-17593.

493 494

de Jong, M.C.M., 1995. Mathematical modelling in veterinary epidemiology: why model building is important. Prev.Vet.Med. 25, 183-193. 20 Page 20 of 29

495 496 497 498

de Jong, M.C.M., Diekmann, O., Heesterbeek, H., 1995. How does transmission of infection depend on population size. 84-94. de Kantor, I.N., Ritacco, V., 2006. An update on bovine tuberculosis programmes in Latin American and Caribbean countries. Vet.Microbiol. 112, 111-118.

499

de la Rua-Domenech, Goodchild, A.T., Vordermeier, H.M., Hewinson, R.G., Christiansen, K.H.,

500

Clifton-Hadley, R.S., 2006. Ante mortem diagnosis of tuberculosis in cattle: a review of

501

the tuberculin tests, gamma-interferon assay and other ancillary diagnostic

502

techniques. Res.Vet.Sci. 81, 190-210.

503

Dean, G.S., Rhodes, S.G., Coad, M., Whelan, A.O., Cockle, P.J., Clifford, D.J., Hewinson, R.G.,

504

Vordermeier, H.M., 2005. Minimum infective dose of Mycobacterium bovis in cattle.

505

Infect.Immun. 73, 6467-6471.

506

Delahay, R.J., Walker, N., Smith, G.C., Wilkinson, D., Clifton-Hadley, R.S., Cheeseman, C.L.,

507

Tomlinson, A.J., Chambers, M.A., 2013. Long-term temporal trends and estimated

508

transmission rates for Mycobacterium bovis infection in an undisturbed high-density

509

badger (Meles meles) population. Epidemiol.Infect. 141, 1445-1456.

510

Dommergues, L., Rautureau, S., Petit, E., Dufour, B., 2012. Network of contacts between cattle

511

herds in a French area affected by bovine tuberculosis in 2010. Transbound.Emerg.Dis.

512

59, 292-302.

513

Driscoll, E.E., Hoffman, J.I., Green, L.E., Medley, G.F., Amos, W., 2011. A preliminary study of

514

genetic factors that influence susceptibility to bovine tuberculosis in the British cattle

515

herd. PLoS.ONE. 6, e18806-

516 517 518 519

Duncan, A.J., Gunn, G.J., Lewis, F.I., Umstatter, C., Humphry, R.W., 2012. The influence of empirical contact networks on modelling diseases in cattle. Epidemics. 4, 117-123. EFSA panel on Animal Health and Welfare (AHAW), 2012. Scientific opinion on the use of a gamma interferon test for the diagnosis of bovine tuberculosis. EFSA Journal 10, 1-64.

21 Page 21 of 29

520

Finlay, E.K., Berry, D.P., Wickham, B., Gormley, E.P., Bradley, D.G., 2012. A genome wide

521

association scan of bovine tuberculosis susceptibility in Holstein-Friesian dairy cattle.

522

PLoS.ONE. 7, e30545-

523

Fischer, E.A., van Roermund, H.J., Hemerik, L., van Asseldonk, M.A., de Jong, M.C., 2005.

524

Evaluation of surveillance strategies for bovine tuberculosis (Mycobacterium bovis)

525

using an individual based epidemiological model. Prev.Vet.Med. 67, 283-301.

526 527 528 529 530

Garner, M.G., Hamilton, S.A., 2011. Principles of epidemiological modelling. Rev. Sci. Tech. 30, 407-416. Goodchild, A.V., Clifton-Hadley, R.S., 2001. Cattle-to-cattle transmission of Mycobacterium bovis. Tuberculosis.(Edinb.) 81, 23-41. Goodchild, A.V., de la Rua-Domenech, R., Palmer, S., Dale, J., Gordon, S.V., Hewinson, G.R.,

531

Clifton-Hadley,

R.S.,

2003.

Association

between

molecular

type

and

the

532

epidemiological features of Mycobacterium bovis in cattle. Proceedings of the Annual

533

Conference of the Society for Veterinary Epidemiology and Public Health45-59.

534

Gormley, E., Doyle, M.B., Fitzsimons, T., McGill, K., Collins, J.D., 2006. Diagnosis of

535

Mycobacterium bovis infection in cattle by use of the gamma-interferon (Bovigam)

536

assay. Vet.Microbiol. 112, 171-179.

537

Graham, J., Smith, G.C., Delahay, R.J., Bailey, T., McDonald, R.A., Hodgson, D., 2013. Multi-

538

state modelling reveals sex-dependent transmission, progression and severity of

539

tuberculosis in wild badgers. Epidemiol.Infect. 141, 1429-1436.

540

Griffin, J.M., Williams, D.H., Collins, J.D., 2000. A compartmental model for the within-herd

541

spread of M. bovis in irish cattle herds. Proceedings of the 9th International

542

Symposium on Veterinary Epidemiology and Economics

543 544

Hardstaff, J.L., Bulling, M.T., Marion, G., Hutchings, M.R., White, P.C., 2013. Modelling the impact of vaccination on tuberculosis in badgers. Epidemiol.Infect. 141, 1417-1427.

22 Page 22 of 29

545

Johnson, L., Dean, G., Rhodes, S., Hewinson, G., Vordermeier, M., Wangoo, A., 2007. Low-dose

546

Mycobacterium bovis infection in cattle results in pathology indistinguishable from

547

that of high-dose infection. Tuberculosis.(Edinb.) 87, 71-76.

548

Kao, R.R., Roberts, M.G., 1999. A comparison of wildlife control and cattle vaccination as

549

methods for the control of bovine tuberculosis. Epidemiol.Infect. 122, 505-519.

550

Kao, R.R., Roberts, M.G., Ryan, T.J., 1997. A model of bovine tuberculosis control in

551

domesticated cattle herds. Proc.Biol.Sci. 264, 1069-1076.

552

Kean, J.M., Barlow, N.D., Hickling, G.J., 1999. Evaluating potential sources of bovine

553

tuberculosis infection in a New Zealand cattle herd. New Zealand Journal of

554

Agricultural Research 42, 101-106.

555

Keeling, M.J., Rohani, P., 2008. Modeling infectious diseases in humans and animals.

556

Khatri, B.L., Coad, M., Clifford, D.J., Hewinson, R.G., Whelan, A.O., Vordermeier, H.M., 2012. A

557

natural-transmission model of bovine tuberculosis provides novel disease insights.

558

Vet.Rec. 171, 448-

559 560

Kleinlutzum, D., Weaver, G., Schley, D., 2013. Within-group contact of cattle in dairy barns and the implications for disease transmission. Res.Vet Sci. 95, 425-429.

561

Lopez, B., Aguilar, D., Orozco, H., Burger, M., Espitia, C., Ritacco, V., Barrera, L., Kremer, K.,

562

Hernandez-Pando, R., Huygen, K., van, S.D., 2003. A marked difference in pathogenesis

563

and immune response induced by different Mycobacterium tuberculosis genotypes.

564

Clin.Exp.Immunol. 133, 30-37.

565 566

Marassi, C.D., Medeiros, L., Lilenbaum, W., 2010. The use of a Gamma-Interferon assay to confirm a diagnosis of bovine tuberculosis in Brazil. Acta Trop. 113, 199-201.

567

Marce C., Ezanno E., Seegers H., Pfeiffer D.U., Fourichon C., 2011. Within-herd contact

568

structure and transmission of Mycobacterium avium subspecies paratuberculosis in a

569

persistently infected dairy cattle herd. Prev.Vet.Med. 100, 116-125.

23 Page 23 of 29

570 571 572 573

McCallum, H., Barlow, N., Hone, J., 2001. How should pathogen transmission be modelled? Trends Ecol.Evol. 16, 295-300. Monaghan, M.L., Doherty, M.L., Collins, J.D., Kazda, J.F., Quinn, P.J., 1994. The tuberculin test. Vet.Microbiol. 40, 111-124.

574

Monies, R.J., 2000. LP-TB and BVD in a group of housed calves. Paper presented at the Spring

575

Meeting of the British Cattle Veterinary Association Ormskirk, 11-13 April 2000-

576

More, S.J., Cameron, A.R., Greiner, M., Clifton-Hadley, R.S., Rodeia, S.C., Bakker, D., Salman,

577

M.D., Sharp, J.M., De, M.F., Aranaz, A., Boniotti, M.B., Gaffuri, A., Have, P., Verloo, D.,

578

Woodford, M., Wierup, M., 2009. Defining output-based standards to achieve and

579

maintain tuberculosis freedom in farmed deer, with reference to member states of the

580

European Union. Prev.Vet.Med. 90, 254-267.

581

Muller, B., Vounatsou, P., Ngandolo, B.N., guimbaye-Djaibe, C., Schiller, I., Marg-Haufe, B.,

582

Oesch, B., Schelling, E., Zinsstag, J., 2009. Bayesian receiver operating characteristic

583

estimation of multiple tests for diagnosis of bovine tuberculosis in Chadian cattle.

584

PLoS.ONE. 4, e8215-

585 586 587 588 589 590

Neill, S.D., Hanna, J., O'Brien, J.J., McCracken, R.M., 1989. Transmission of tuberculosis from experimentally infected cattle to in-contact calves. Vet.Rec. 124, 269-271. Neill, S.D., O'Brien, J.J., Hanna, J., 1991. A mathematical model for Mycobacterium bovis excretion from tuberculous cattle. Vet.Microbiol. 28, 103-109. Olmstead, A.L., Rhode, P.W., 2004. An impossible undertaking: the eradication of bovine tuberculosis in the United States. Journal of Economic History 64, 1-39.

591

Palanisamy, G.S., DuTeau, N., Eisenach, K.D., Cave, D.M., Theus, S.A., Kreiswirth, B.N.,

592

Basaraba, R.J., Orme, I.M., 2009. Clinical strains of Mycobacterium tuberculosis display

593

a wide range of virulence in guinea pigs. Tuberculosis.(Edinb.) 89, 203-209.

24 Page 24 of 29

594

Perez, A.M., Ward, M.P., Charmandarian, A., Ritacco, V., 2002a. Simulation model of within-

595

herd transmission of bovine tuberculosis in Argentine dairy herds. Prev.Vet.Med. 54,

596

361-372.

597

Perez, A.M., Ward, M.P., Ritacco, V., 2002b. Simulation-model evaluation of bovine

598

tuberculosis-eradication strategies in Argentine dairy herds. Prev.Vet.Med. 54, 351-

599

360.

600 601 602 603 604 605 606 607

Perez, A.M., Ward, M.P., Ritacco, V., 2011. Modelling the feasibility of bovine tuberculosis eradication in Argentina. Rev.Sci.Tech. 30, 635-643. Radunz, B., 2006. Surveillance and risk management during the latter stages of eradication: experiences from Australia. Vet.Microbiol. 112, 283-290. Reviriego Gordejo, F.J., Vermeersch, J.P., 2006. Towards eradication of bovine tuberculosis in the European Union. Vet.Microbiol. 112, 101-109. Schley, D., Whittle, S., Taylor, M., Kiss, I.Z., 2012. Models to capture the potential for disease transmission in domestic sheep flocks. Prev.Vet.Med. 106, 174-184.

608

Smith, R.L., Schukken, Y.H., Lu, Z., Mitchell, R.M., Grohn, Y.T., 2013a. Development of a model

609

to simulate infection dynamics of Mycobacterium bovis in cattle herds in the United

610

States. J.Am.Vet.Med.Assoc. 243, 411-423.

611 612

Smith, R.L., Tauer, L.W., Schukken, Y.H., Lu, Z., Grohn, Y.T., 2013b. Minimization of bovine tuberculosis control costs in US dairy herds. Prev.Vet.Med. 112, 266-275.

613

Sun, L., Song, Y., Riaz, H., Yang, H., Hua, G., Guo, A., Yang, L., 2012. Polymorphisms in toll-like

614

receptor 1 and 9 genes and their association with tuberculosis susceptibility in Chinese

615

Holstein cattle. Vet.Immunol.Immunopathol. 147, 195-201.

616 617

Szmaragd, C., Green, L.E., Medley, G.F., Browne, W.J., 2012. Impact of imperfect test sensitivity on determining risk factors: the case of bovine tuberculosis. PLoS.ONE. 7, e43116-

25 Page 25 of 29

618

Turner, J., Bowers, R.G., Clancy, D., Behnke, M.C., Christley, R.M., 2008. A network model of E.

619

coli O157 transmission within a typical UK dairy herd: the effect of heterogeneity and

620

clustering on the prevalence of infection. J.Theor.Biol. 254, 45-54.

621

USDA, A., 2005. Bovine tuberculosis eradication: Uniform methods and rules. Avalaible at

622

http://www.aphis.usda.gov/animal_health/animal_diseases/tuberculosis/downloads/t

623

b-umr.pdf

624

VLA (Veterinary Laboratories Agency), 2011. Meta-analysis of diagnostic tests and modelling to

625

identify appropriate testing strategies to reduce M. bovis infection in GB herds.

626

Available

627

http://randd.defra.gov.uk/Default.aspx?Menu=Menu&Module=More&Location=None

628

&ProjectID=16114&FromSearch=Y&Publisher=1&SearchText=SE3238&SortString=Proj

629

ectCode&SortOrder=Asc&Paging=10

at

630

Vordermeier, M., Ameni, G., Berg, S., Bishop, R., Robertson, B.D., Aseffa, A., Hewinson, R.G.,

631

Young, D.B., 2012. The influence of cattle breed on susceptibility to bovine

632

tuberculosis in Ethiopia. Comp Immunol.Microbiol.Infect.Dis. 35, 227-232.

633 634

Willeberg, P., Paisley, L.G., Lind, P., 2011. Epidemiological models to support animal disease surveillance activities. Rev. Sci. Tech. 30, 603-614.

635

Willeberg, P., Grubbe, T., Weber, S., Forde-Folle, K., Dube, C., 2011. The World Organisation for

636

Animal Health and epidemiological modelling: background and objectives. Rev. Sci.

637

Tech. 30, 391-405.

638

Wright, D.M., Allen, A.R., Mallon, T.R., McDowell, S.W., Bishop, S.C., Glass, E.J., Bermingham,

639

M.L., Woolliams, J.A., Skuce, R.A., 2013. Detectability of bovine TB using the tuberculin

640

skin test does not vary significantly according to pathogen genotype within Northern

641

Ireland. Infect.Genet.Evol.

642

26 Page 26 of 29

643

Table 1. Assumed or estimated parameters in within-herd transmission models of bovine tuberculosis (ranges are provided in parenthesis when provided). Parameter Transmission coefficient β (per cow and year)

Assumed value Density-dependent transmission (β*)

Estimated value 0.0099 0.00475 0.00134 0.00053 0.000072

1.5 (0.26-4.9) 4.9 (0.99-14.0) 0.52 (0.1-1.6) 3.6 (0.73-8.85) 1.02-1.11 4.13

(Barlow et al., 1997) (Kean et al., 1999) (Kean et al., 1999) (Griffin et al., 2000) (Kao et al., 1997) (Smith et al., 2013a) (Perez et al., 2002a) (Fischer et al., 2005) (Alvarez et al., 2012) (Smith et al., 2013a) (Conlan et al., 2012) (Conlan et al., 2012) (Conlan et al., 2012) (Conlan et al., 2012) (Cox et al., 2005) (Smith et al., 2013a)

0.02

(Smith et al., 2013a)

24 (15-34) 13.3 (4-27)

(Perez et al., 2002a) (Conlan et al., 2012) (Barlow et al., 1997) (Fischer et al., 2005) (Conlan et al., 2012) (Conlan et al., 2012) (Kao et al., 1997) (Smith et al., 2013a)

0.01 Frequency-dependent transmission (β’)

2.23 (-3.4 –7.9) 5.2 2.3 (1.5-3.6) 2.76

Basic reproductive number

λ1 + λ2: Incubation period (from infection to excretion) (months) λ1: Time from infection to detection (detectable by in-vivo diagnostic tests) (days)

22 (14-22) 41 (30-54) 28 (1-119) 44 (14-44)

Reference

1.8 (0-7.7) 275 (24-517) 43.9

Observations a

SORI model SI model

SORI model, herd-size=30 SORI model, herd-size=400 SOR model, herd-size=30 SOR model, herd-size=400 Frequency-dependent transmission, no test-and-cull Frequency dependent transmission, test-and-cull every three months SORI model

SOR model SORI model

27 Page 27 of 29

λ2: Time from detection to infectious (shedding) (months)

6 (3-9) 8.3 (6.3-25) 34.6

Sensitivity of skin test

Specificity of the skin test

644 645 646 647

CFT b CFT CFT CFT CCT c CCT CCT SCT+CCT d CCT severe CCT standard CCT severe CCT standard CFT CFT

35.6 (3-35.6) 100 80 96.8 (63.2-100) 80 90.4 70 (60-80) 99.5 (55.1-100) 65 (55-75) 72 (56-88) 66 (52-80) 48 (34-69) 36 (24-51) 100 100 (98-100)

(Barlow et al., 1997) (Fischer et al., 2005) (Kao et al., 1997) (Smith et al., 2013a) (Perez et al., 2002a) (Barlow et al., 1997) (Kean et al., 1999) (Smith et al., 2013a) (Kao et al., 1997) (Griffin et al., 2000) (Fischer et al., 2005) (Smith et al., 2013a) (Fischer et al., 2005) (Conlan et al., 2012) (Conlan et al., 2012) (Conlan et al., 2012) (Conlan et al., 2012) (Perez et al., 2002a) (Barlow et al., 1997) (Kean et al., 1999) (Griffin et al., 2000) (Kao et al., 1997) (Smith et al., 2013a)

0-30% for animals in O state

SOR model SOR model SORI model SORI model

CCT 99.4 CFT 100 CCT 99.5 (55.1-100) a S=Susceptible, O=Occult, R=Reactive, I=Infectious b CFT=Caudal fold test c CCT=Comparative cervical test d Single cervical test of all animals and confirmation of positives using the comparative cervical test.

28 Page 28 of 29

648

Figure 1. Structure of the compartment models used for simulation of within-herd

649

transmission of bovine tuberculosis, based on the allocation of all animals in two or more

650

mutually exclusive states (Susceptible, Occult, Reactive and Infectious). Solid, dashed and

651

dash-dot-dash lines indicate transition stages existing in SORI, SRI and SI models

652

respectively. λ1 and λ1 represent the estimated lengths of the occult and reactive stages,

653

while β* and β’ are the density-dependent and frequency-dependent transmission

654

coefficients.

655

* Certain models allow detection of animals in the occult stage with a decreased sensitivity

656

of the diagnostic tests.

29 Page 29 of 29