Additional File 1: Mo Del Calculation for PW-Host

1 Additional file 1: Model calculation for PW-host

2 Every calculus below is made for an equine from species i imported from an area j to the free area k the

3 month m. All the parameters used are detailed in the Additional file 2.

5 The probability of introduction for PW-host is the probability to import at least one infected host able to

6 transmit the infection to at least one local host and is defined as:

8 Where , the probability of release, depends of the importation procedure implemented and the periods

9 where a host is infected and, the probability of establishment, is defined as:

11 with culikm the number of vectors feeding on an infected viraemic imported host equals at BRkm x Vir x Ckm

13 For each category of exporting region, there is different import procedure implemented and thus

14 different periods z where a host can be infected. For a given region j, there is a total of w different time

15 periods z where the equine can be infected depending on the import procedure implemented for the

16 region j. The different periods z for each region j are presented below:

17 - High risk countries: host can be infected 1) Before quarantine, 2) During quarantine but before

18 the first serological test CF1, 3) During quarantine but between the both serological tests CF1 and

19 CF2, 4) During quarantine but after CF2 and before clinical exam, or 5) After clinical exam.

20 - Low risk countries:

21 o Non EU country member: host can be infected 1) Before quarantine, 2) During

22 quarantine but before CF1, 3) During quarantine but between CF1 and CF2, 4) During

23 quarantine but after CF2 and before clinical exam, or 5) After clinical exam.

24 o EU country member: host can be infected 1) Before clinical exam, or 2) After clinical

25 exam.

1 26 - Very low risk countries:

27 o Non EU country member: host can be infected 1) Before clinical exam, or 2) After clinical

28 exam.

29 o EU country member: host can be infected 1) Before clinical exam, or 2) After clinical

30 exam.

32 The probability of release by species i from region j to area k during a specific month m ( is thus calculated

33 as:

34 Where is the probability of release when the animal i is infected during the time period z.

35 P(relAijkmz) is calculated for each period z as:

38 1. Probability for a host to be infected during period z in the month m in area j

40 The probability of infection during a certain period z (before or during the import procedure) depends on

41 the fraction of this period z spend in each of the months m, m-1 and m-2.

43 a. No quarantine and CF test are required

44 Entire period of being at risk of infection is the high risk period (HRP).

46  Probability that the imported host is infected before clin

47 If HRP < e

50 If HRP > e

51 If HRP < 30 + e

54 If HRP > 30 + e

57  Probability that the imported host is infected after clin

60 b. Quarantine and CF tests required

62  Probability that the imported host is infected before q

63 If q – e < 30

67 If q – e > 30

70  Probability that the imported host is infected between q and cf1

71 If e – cf1 < 0

72 If q > 30 + e

3 74 If q < 30 + e

76 if e – cf1 > 0

77 if q > 30 + e

80 if q < 30 + e

83  Probability that the imported host is infected between cf1 and cf2

84 If e < cf2

87 If e > cf2

88 if cf1 > 30 + e

91 if cf1 < 30 + e

94  Probability that the imported host is infected after cf2

95 If e < cf2

97 If e > cf2

101 2. Probability for a host to be vireamic or incubating when imported to area B given being infected

103 Calculation is based on a constant viraemic and latent period, which is equal for each equine of species i.

106  When infected before clin

107 If In + Vir < tAB + clin

108 = 0

110 If In + Vir > HRP + tAB + clin

111 = 1

113 If In + Vir < HRP + tAB + clin

116  When infected after clin

117 If In > tAB + clin

118 = 1

120 If In < tAB + clin

121 If In + Vir > tAB + clin

122 = 1

124 If In + Vir < tAB + clin

5 126 b. Quarantine and CF tests required

127  When infected before q

128 If In + Vir > Inftime + q + tAB

129 = 1

131 If In + Vir < q + tAB

132 = 0

134 If In + Vir < Inftime + q + tAB

137  When infected between q and cf1

138 If In + Vir > q + tAB

139 = 1

141 If In + Vir < cf1 + tAB

142 = 0

144 If q + tAB > In + Vir > cf1 + tAB

147  When infected between cf1 and cf2

148 If In + Vir > cf1 + tAB

149 = 1

151 If In + Vir < cf2 + tAB

6 152 = 0

154 If cf1 + tAB > In + Vir > cf2 + tAB

157  When infected after cf2

159 = 1

161 If In + Vir < tAB

162 = 0

164 If cf2 + tAB > In + Vir > tAB

167 3. Probability for an infected host to be detected during importation procedure

170 Probability to be detected during importation procedure = Probability to be detected by clinical inspection

172 If In > HRP – clin

173 = 0

175 If In < HRP – clin

176 If In + Vir < HRP – clin

7 178 If In + Vir > HRP – clin

180  When infected after clin

181 = 0

185 i. Probability for an infected host to be detected by cf1

187 if q – cf1 < Sero

188 = Se

190 If Inftime + q – cf1 < Sero

191 = 1 – Sp

193 If Inftime + q – cf1 > Sero

197 If q – cf1 < Sero

198 = 1 – Sp

200 if q – cf1 > Sero

8 204 ii. Probability for an infected host to be detected by cf2

205 Assumption: cf1 and cf2 are independent

207 if q – cf2 > Sero

208 = Se

210 If Inftime + q – cf2 < Sero

211 = 1 – Sp

213 If Inftime + q – cf2 > Sero

217 if q – cf2 < Sero

218 = 1 – Sp

220 If q – cf2 > Sero

221 If cf1 – cf2 > Sero

222 = Se

224 If cf1 – cf2 < Sero

228 if cf1 – cf2 < Sero

229 = 1 – Sp

231 If cf1 – cf2 > Sero

235 iii. P(clin) = Probability for an infected host to be detected by clinical inspection

237 If In + Vir < q – clin or In > Inf_time + q – clin

238 = 0

240 If In + Vir > Inf_time + q – clin

241 If In < q – clin

242 = Seclin

244 If In > q – clin

246 If Inf_time + q – clin > In + Vir > q – clin

247 If In < q – clin

249 If In > q – clin

252 If In + Vir < cf1 – clin or In > q – clin

253 = 0

255 If In + Vir > q – clin

10 256 If In < cf1 – clin

257 = Seclin

259 If In > cf1 – clin

261 If q – clin > In + Vir > cf1 – clin

262 If In < cf1 – clin

266  When infected between cf1 and cF2

267 If In + Vir < cf2 – clin or In > cf1 – clin

268 = 0

270 If In + Vir > cf1 – clin

272 = Seclin

276 If cf1 – clin > In + Vir > cf2 – clin

11 282  When infected after cf2

284 = 0

287 If In + Vir > cf2 – clin

290 If In + Vir < cf2 – clin

293 4. Probability for an infected host to be detected during transport from A to B given having passed

294 the examinations and testing prior to embarkation.

296 a. No quarantine and CF test

298 If In > HRP + tAB - clin

299 = 0

301 If In < HRP + TAB - clin

302 If In + Vir < HRP – clin

305 If In + Vir > HRP – clin

12 308  When infected after clin

309 If In > tAB + clin

310 = 0

312 If In < tAB + clin

313 If In + Vir < clin + tAB

316 If In + Vir > clin + tAB

321 If In + Vir < q + tAB or In > Inf_time + q + tAB

322 = 0

324 If In + Vir > Inf_time + q + tAB

325 If In > q + tAB

328 If In < q + tAB

329 = Seclin

331 If Inf_time + q + tAB > In + Vir > q + tAB

332 If In > q + tAB

13 334

335 If In < q + tAB

339 If In + Vir < cf1 + tAB or In > q + tAB

340 = 0

342 If In + Vir > q + tAB

343 If In > cf1 + tAB

346 If In < cf1 + tAB

347 = Seclin

349 If q + tAB > In + Vir > cf1 + tAB

357 If In + Vir < cf2 + tAB or In > cf1 + tAB

358 = 0

14 360 If In + Vir > cf1 + tAB

365 = Seclin

367 If cf1 + tAB > In + Vir > cf2 + tAB

374  When infected after cf2

376 = 0

385 5. Probability that the vector survives to the EIP and can have a blood meal during the month m

15 386