Additional File 1: Mo Del Calculation for PW-Host

1 Additional file 1: Model calculation for PW-host2 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 2.45 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: 78 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 Ckm1213 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.3132 The probability of release by species i from region j to area k during a specific month m ( is thus calculated33 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:363738 1. Probability for a host to be infected during period z in the month m in area j 3940 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-2.4243 a. No quarantine and CF test are required44 Entire period of being at risk of infection is the high risk period (HRP). 4546  Probability that the imported host is infected before clin 47 If HRP < e484950 If HRP > e51 If HRP < 30 + e2 525354 If HRP > 30 + e555657  Probability that the imported host is infected after clin 585960 b. Quarantine and CF tests required6162  Probability that the imported host is infected before q 63 If q – e < 3064656667 If q – e > 30686970  Probability that the imported host is infected between q and cf1 71 If e – cf1 < 072 If q > 30 + e733 74 If q < 30 + e7576 if e – cf1 > 077 if q > 30 + e787980 if q < 30 + e818283  Probability that the imported host is infected between cf1 and cf2 84 If e < cf2858687 If e > cf288 if cf1 > 30 + e899091 if cf1 < 30 + e929394  Probability that the imported host is infected after cf2 95 If e < cf2 9697 If e > cf298994 100101 2. Probability for a host to be vireamic or incubating when imported to area B given being infected102103 Calculation is based on a constant viraemic and latent period, which is equal for each equine of species i. 104105 a. No quarantine and CF test are required106  When infected before clin 107 If In + Vir < tAB + clin108 = 0109110 If In + Vir > HRP + tAB + clin111 = 1112113 If In + Vir < HRP + tAB + clin114115116  When infected after clin 117 If In > tAB + clin118 = 1119120 If In < tAB + clin121 If In + Vir > tAB + clin122 = 1123124 If In + Vir < tAB + clin1255 126 b. Quarantine and CF tests required127  When infected before q 128 If In + Vir > Inftime + q + tAB129 = 1130131 If In + Vir < q + tAB132 = 0133134 If In + Vir < Inftime + q + tAB135136137  When infected between q and cf1 138 If In + Vir > q + tAB139 = 1140141 If In + Vir < cf1 + tAB142 = 0143144 If q + tAB > In + Vir > cf1 + tAB 145146147  When infected between cf1 and cf2 148 If In + Vir > cf1 + tAB149 = 1150151 If In + Vir < cf2 + tAB6 152 = 0153154 If cf1 + tAB > In + Vir > cf2 + tAB 155156157  When infected after cf2 158 If In + Vir > cf2 + tAB159 = 1160161 If In + Vir < tAB162 = 0163164 If cf2 + tAB > In + Vir > tAB 165166167 3. Probability for an infected host to be detected during importation procedure 168169 a. No quarantine and CF test are required170 Probability to be detected during importation procedure = Probability to be detected by clinical inspection171  When infected before clin 172 If In > HRP – clin 173 = 0174175 If In < HRP – clin176 If In + Vir < HRP – clin1777 178 If In + Vir > HRP – clin179180  When infected after clin 181 = 0182183 b. Quarantine and CF tests required184185 i. Probability for an infected host to be detected by cf1 186  When infected before q 187 if q – cf1 < Sero188 = Se189190 If Inftime + q – cf1 < Sero191 = 1 – Sp192193 If Inftime + q – cf1 > Sero194195196  When infected between q and cf1 197 If q – cf1 < Sero198 = 1 – Sp199200 if q – cf1 > Sero2012022038 204 ii. Probability for an infected host to be detected by cf2205 Assumption: cf1 and cf2 are independent206  When infected before q 207 if q – cf2 > Sero208 = Se209210 If Inftime + q – cf2 < Sero211 = 1 – Sp212213 If Inftime + q – cf2 > Sero214215216  When infected between q and cf1 217 if q – cf2 < Sero218 = 1 – Sp219220 If q – cf2 > Sero221 If cf1 – cf2 > Sero222 = Se223224 If cf1 – cf2 < Sero225226227  When infected between cf1 and cf2 228 if cf1 – cf2 < Sero229 = 1 – Sp9 230231 If cf1 – cf2 > Sero232233234235 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 – clin238 = 0239240 If In + Vir > Inf_time + q – clin241 If In < q – clin242 = Seclin243244 If In > q – clin245246 If Inf_time + q – clin > In + Vir > q – clin247 If In < q – clin248249 If In > q – clin250251  When infected between q and cf1 252 If In + Vir < cf1 – clin or In > q – clin253 = 0254255 If In + Vir > q – clin10 256 If In < cf1 – clin257 = Seclin258259 If In > cf1 – clin260261 If q – clin > In + Vir > cf1 – clin262 If In < cf1 – clin263264 If In > cf1 – clin265266  When infected between cf1 and cF2 267 If In + Vir < cf2 – clin or In > cf1 – clin268 = 0269270 If In + Vir > cf1 – clin271 If In < cf2 – clin272 = Seclin273274 If In > cf2 – clin275276 If cf1 – clin > In + Vir > cf2 – clin277 If In < cf2 – clin278279 If In > cf2 – clin28028111 282  When infected after cf2 283 If In > cf2 – clin284 = 0285286 If In < cf2 – clin287 If In + Vir > cf2 – clin288289290 If In + Vir < cf2 – clin291292293 4. Probability for an infected host to be detected during transport from A to B given having passed294 the examinations and testing prior to embarkation.295296 a. No quarantine and CF test297  When infected before clin 298 If In > HRP + tAB - clin299 = 0300301 If In < HRP + TAB - clin302 If In + Vir < HRP – clin303304305 If In + Vir > HRP – clin30630712 308  When infected after clin309 If In > tAB + clin310 = 0311312 If In < tAB + clin313 If In + Vir < clin + tAB314315316 If In + Vir > clin + tAB317318319 b. Quarantine and CF tests required320  When infected before q 321 If In + Vir < q + tAB or In > Inf_time + q + tAB322 = 0323324 If In + Vir > Inf_time + q + tAB325 If In > q + tAB326327328 If In < q + tAB329 = Seclin330331 If Inf_time + q + tAB > In + Vir > q + tAB332 If In > q + tAB33313 334335 If In < q + tAB336337338  When infected between q and cf1 339 If In + Vir < cf1 + tAB or In > q + tAB340 = 0341342 If In + Vir > q + tAB343 If In > cf1 + tAB344345346 If In < cf1 + tAB347 = Seclin348349 If q + tAB > In + Vir > cf1 + tAB350 If In > cf1 + tAB351352353 If In < cf1 + tAB354355356  When infected between cf1 and cf2 357 If In + Vir < cf2 + tAB or In > cf1 + tAB358 = 035914 360 If In + Vir > cf1 + tAB361 If In > cf2 + tAB362363364 If In < cf2 + tAB365 = Seclin366367 If cf1 + tAB > In + Vir > cf2 + tAB368 If In > cf2 + tAB369370371 If In < cf2 + tAB372373374  When infected after cf2 375 If In > cf2 + tAB376 = 0377378 If In < cf2 + tAB379 If In + Vir > cf2 + tAB380381382 If In + Vir > cf2 + tAB383384 385 5. Probability that the vector survives to the EIP and can have a blood meal during the month m 15 38638738838939039139239316

Additional File 1: Mo Del Calculation for PW-Host

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