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.
4
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:
7
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:
10
11 with culikm the number of vectors feeding on an infected viraemic imported host equals at BRkm x Vir x Ckm
12
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.
31
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:
36
37
38 1. Probability for a host to be infected during period z in the month m in area j
39
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.
42
43 a. No quarantine and CF test are required
44 Entire period of being at risk of infection is the high risk period (HRP).
45
46 Probability that the imported host is infected before clin
47 If HRP < e
48
49
50 If HRP > e
51 If HRP < 30 + e
2 52
53
54 If HRP > 30 + e
55
56
57 Probability that the imported host is infected after clin
58
59
60 b. Quarantine and CF tests required
61
62 Probability that the imported host is infected before q
63 If q – e < 30
64
65
66
67 If q – e > 30
68
69
70 Probability that the imported host is infected between q and cf1
71 If e – cf1 < 0
72 If q > 30 + e
73
3 74 If q < 30 + e
75
76 if e – cf1 > 0
77 if q > 30 + e
78
79
80 if q < 30 + e
81
82
83 Probability that the imported host is infected between cf1 and cf2
84 If e < cf2
85
86
87 If e > cf2
88 if cf1 > 30 + e
89
90
91 if cf1 < 30 + e
92
93
94 Probability that the imported host is infected after cf2
95 If e < cf2
96
97 If e > cf2
98
99
4 100
101 2. Probability for a host to be vireamic or incubating when imported to area B given being infected
102
103 Calculation is based on a constant viraemic and latent period, which is equal for each equine of species i.
104
105 a. No quarantine and CF test are required
106 When infected before clin
107 If In + Vir < tAB + clin
108 = 0
109
110 If In + Vir > HRP + tAB + clin
111 = 1
112
113 If In + Vir < HRP + tAB + clin
114
115
116 When infected after clin
117 If In > tAB + clin
118 = 1
119
120 If In < tAB + clin
121 If In + Vir > tAB + clin
122 = 1
123
124 If In + Vir < tAB + clin
125
5 126 b. Quarantine and CF tests required
127 When infected before q
128 If In + Vir > Inftime + q + tAB
129 = 1
130
131 If In + Vir < q + tAB
132 = 0
133
134 If In + Vir < Inftime + q + tAB
135
136
137 When infected between q and cf1
138 If In + Vir > q + tAB
139 = 1
140
141 If In + Vir < cf1 + tAB
142 = 0
143
144 If q + tAB > In + Vir > cf1 + tAB
145
146
147 When infected between cf1 and cf2
148 If In + Vir > cf1 + tAB
149 = 1
150
151 If In + Vir < cf2 + tAB
6 152 = 0
153
154 If cf1 + tAB > In + Vir > cf2 + tAB
155
156
157 When infected after cf2
158 If In + Vir > cf2 + tAB
159 = 1
160
161 If In + Vir < tAB
162 = 0
163
164 If cf2 + tAB > In + Vir > tAB
165
166
167 3. Probability for an infected host to be detected during importation procedure
168
169 a. No quarantine and CF test are required
170 Probability to be detected during importation procedure = Probability to be detected by clinical inspection
171 When infected before clin
172 If In > HRP – clin
173 = 0
174
175 If In < HRP – clin
176 If In + Vir < HRP – clin
177
7 178 If In + Vir > HRP – clin
179
180 When infected after clin
181 = 0
182
183 b. Quarantine and CF tests required
184
185 i. Probability for an infected host to be detected by cf1
186 When infected before q
187 if q – cf1 < Sero
188 = Se
189
190 If Inftime + q – cf1 < Sero
191 = 1 – Sp
192
193 If Inftime + q – cf1 > Sero
194
195
196 When infected between q and cf1
197 If q – cf1 < Sero
198 = 1 – Sp
199
200 if q – cf1 > Sero
201
202
203
8 204 ii. Probability for an infected host to be detected by cf2
205 Assumption: cf1 and cf2 are independent
206 When infected before q
207 if q – cf2 > Sero
208 = Se
209
210 If Inftime + q – cf2 < Sero
211 = 1 – Sp
212
213 If Inftime + q – cf2 > Sero
214
215
216 When infected between q and cf1
217 if q – cf2 < Sero
218 = 1 – Sp
219
220 If q – cf2 > Sero
221 If cf1 – cf2 > Sero
222 = Se
223
224 If cf1 – cf2 < Sero
225
226
227 When infected between cf1 and cf2
228 if cf1 – cf2 < Sero
229 = 1 – Sp
9 230
231 If cf1 – cf2 > Sero
232
233
234
235 iii. P(clin) = Probability for an infected host to be detected by clinical inspection
236 When infected before q
237 If In + Vir < q – clin or In > Inf_time + q – clin
238 = 0
239
240 If In + Vir > Inf_time + q – clin
241 If In < q – clin
242 = Seclin
243
244 If In > q – clin
245
246 If Inf_time + q – clin > In + Vir > q – clin
247 If In < q – clin
248
249 If In > q – clin
250
251 When infected between q and cf1
252 If In + Vir < cf1 – clin or In > q – clin
253 = 0
254
255 If In + Vir > q – clin
10 256 If In < cf1 – clin
257 = Seclin
258
259 If In > cf1 – clin
260
261 If q – clin > In + Vir > cf1 – clin
262 If In < cf1 – clin
263
264 If In > cf1 – clin
265
266 When infected between cf1 and cF2
267 If In + Vir < cf2 – clin or In > cf1 – clin
268 = 0
269
270 If In + Vir > cf1 – clin
271 If In < cf2 – clin
272 = Seclin
273
274 If In > cf2 – clin
275
276 If cf1 – clin > In + Vir > cf2 – clin
277 If In < cf2 – clin
278
279 If In > cf2 – clin
280
281
11 282 When infected after cf2
283 If In > cf2 – clin
284 = 0
285
286 If In < cf2 – clin
287 If In + Vir > cf2 – clin
288
289
290 If In + Vir < cf2 – clin
291
292
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.
295
296 a. No quarantine and CF test
297 When infected before clin
298 If In > HRP + tAB - clin
299 = 0
300
301 If In < HRP + TAB - clin
302 If In + Vir < HRP – clin
303
304
305 If In + Vir > HRP – clin
306
307
12 308 When infected after clin
309 If In > tAB + clin
310 = 0
311
312 If In < tAB + clin
313 If In + Vir < clin + tAB
314
315
316 If In + Vir > clin + tAB
317
318
319 b. Quarantine and CF tests required
320 When infected before q
321 If In + Vir < q + tAB or In > Inf_time + q + tAB
322 = 0
323
324 If In + Vir > Inf_time + q + tAB
325 If In > q + tAB
326
327
328 If In < q + tAB
329 = Seclin
330
331 If Inf_time + q + tAB > In + Vir > q + tAB
332 If In > q + tAB
333
13 334
335 If In < q + tAB
336
337
338 When infected between q and cf1
339 If In + Vir < cf1 + tAB or In > q + tAB
340 = 0
341
342 If In + Vir > q + tAB
343 If In > cf1 + tAB
344
345
346 If In < cf1 + tAB
347 = Seclin
348
349 If q + tAB > In + Vir > cf1 + tAB
350 If In > cf1 + tAB
351
352
353 If In < cf1 + tAB
354
355
356 When infected between cf1 and cf2
357 If In + Vir < cf2 + tAB or In > cf1 + tAB
358 = 0
359
14 360 If In + Vir > cf1 + tAB
361 If In > cf2 + tAB
362
363
364 If In < cf2 + tAB
365 = Seclin
366
367 If cf1 + tAB > In + Vir > cf2 + tAB
368 If In > cf2 + tAB
369
370
371 If In < cf2 + tAB
372
373
374 When infected after cf2
375 If In > cf2 + tAB
376 = 0
377
378 If In < cf2 + tAB
379 If In + Vir > cf2 + tAB
380
381
382 If In + Vir > cf2 + tAB
383
384
385 5. Probability that the vector survives to the EIP and can have a blood meal during the month m
15 386
387
388
389
390
391
392
393
16