Additional file 3: Model calculation for PW-vector
1
2
All the parameters used are detailed in the Additional file 2.
3
4
The probability to introduce a single vector from j to k during the month m which is able to induce an
5
entire transmission cycle in which at least one local host is infected by a local vector is defined as:
6
𝑃(𝑖𝑛𝑡𝑟𝑜𝐵𝑗𝑘𝑚 ) = 𝑃(𝑟𝑒𝑙𝐵𝑗𝑘𝑚 ) × 𝑃(𝑒𝑠𝑡𝐵𝑗𝑘𝑚 )
7
Where P(relBjkm ) = P (transculijm ) × P (survtrans jkm ) × P(inf⁡_culijm ⁡) × ntransjkm
8
And P(estBjkm ) = P (surv𝑎𝑟𝑟𝑖𝑣𝑎𝑙jkm ) × bequik × IVH × [1 − [1 − IVH × P(survkm ) × bequik ×
9
IHV ]
culikm
]
10
With culikm the number of vector feeding on an infected viraemic imported host calculated as:
11
culikm = BRkm x Vir x Ckm
12
13
1. 𝐏(𝐢𝐧𝐟⁡_𝐜𝐮𝐥𝐢𝐣𝐦 ) =⁡Probability for a vector to be infected the month m in area j
14
15
P(inf⁡_culijm ) = POjm × rjm
16
17
2. 𝐏 (𝐭𝐫𝐚𝐧𝐬𝐜𝐮𝐥𝐢𝐣𝐦 ) =⁡Probability for a vector to be transported after infection from area j
18
Only a vector which is infected and transported poses a risk, therefore we only consider those
19
vectors that are infected and transported during their life time. We assume that an infected vector
20
will be infected at a uniformly distributed time during its life, Dinf. Additionally, we assume that a
21
vector is transported at a uniformly distributed moment during its life time, which is exponentially
22
distributed with mean 1/MRjm. The probability that the moment of transportation occurs after the
23
infection event is equal to the part of the total lifetime of the vector that it is infected. Thus
24
P (transculijm ) is estimated, as made by Napp et al. [1], as:
1
25
P (transculijm ) =
(1/MR jm − Dinf )
= 1 − Dinf ⁡MR jm
1/MR jm
26
27
NB: Temperature in departure area j was assumed to be constant over months and thus MRjm is here
28
also constant over months.
29
30
3. 𝐏 (𝐬𝐮𝐫𝐯𝐭𝐫𝐚𝐧𝐬𝐣𝐤𝐦 ) =⁡Probability for a vector to stay alive from j until the arrival in area k during
the month m
31
32
The conditions during travel (e.g. temperature) are assumed to not affect the viability of culicoides
33
except when pest control is applied (worst case scenario). There is no data available on survival rate
34
of culicoides in an unfavorable context as assumed to occur during transport. Moreover the
35
conditions during transports have a high variability and information are impossible to collect.
36
The probability to stay alive until the arrival is the probability to survive until transport and during
37
the time of transport.
38
P (survtransjkm ) = e−MRjm ×(Dtrans +tjk) × (1 − Prot vect )
39
40
4. 𝐏 (𝐬𝐮𝐫𝐯𝐚𝐫𝐫𝐢𝐯𝐚𝐥𝐣𝐤𝐦 ) =⁡The vector survives to the transport from j, the EIP and can have at least a
blood meal after the end of EIP and when arrives in the area k the month m
41
42
43
If TB < 0 culicoides are assumed to not survive
44
=0
45
46
If (Nm.GCjm) > (Dtransp + tjk)
47
= eMRkm ×(Dtrans +tjk)−Nm ×GCjm
48
49
If (Nm.GCjm) < (Dtransp + tjk)
2
50
If tjk > GCjm
51
we assume that the last GCm is spent half during transport and half in the arrival area k.
52
= e−MRkm ×
GCjm
2
53
54
If tjk < GCjm
55
we assume that the last GCm is spent half in the departure area j and half in the arrival area k.
56
= e−MRkm ×
GCjm −𝑡𝑗𝑘
2
57
58
NB : if Tk < T_min (9.5°C), where T_min is the minimal temperature for formulae for MR and GC (if Tk
59
is lower, the formulae are not valid), we will use the T_min in our calculus (worst case scenario).
60
61
62
5. 𝐏(𝐬𝐮𝐫𝐯𝐤𝐦 ) =⁡Probability that the local vector survives to the EIP and can have a blood meal
during the month m in the area k
63
64
P(survkm ) = ⁡ 𝑒 −(𝑁𝑘𝑚×𝐺𝐶𝑘𝑚 ×𝑀𝑅𝑘𝑚)
65
66
67
BIBLIOGRAPHIE⁡
68
69
70
1. Napp S, García-Bocanegra I, Pagès N, Allepuz A, Alba A, Casal J: Assessment of the risk of a
bluetongue outbreak in Europe caused by Culicoides midges introduced through intracontinental
transport and trade networks. Med Vet Entomol 2012, 27:19–28.
71
3