Supplementary Information
Tick life cycle model. The model was designed to capture the complexity of ticks life cycle
in its simplest possible terms: (i) interstadial development rates, including oviposition,
incubation and nymphal to adult molting; (ii) daily probability of tick questing; (iii) daily
probability of tick attachment to a host (host finding rates); and (iv) daily tick mortality rates,
specific to each stage and state (questing, feeding and engorged). The model moves by 10days increments. Ticks on each stage experience a daily probability of moving to the next
stage, using temperature (T) and pressure of water vapour (WV) to obtain development and
mortality rates for each stage at every grid cell in the studied area. Both larvae and adults
must find a host and feed before entering the next stage of the life cycle. Host finding rates
are commonly modelled as a force equation proportional to the densities of both ticks and
hosts (Ogden et al., 2005). Therefore, it is necessary to know the densities of available hosts
and their contribution to feeding different tick stages to have a rough estimation of host
finding rates. A simplification was assumed in the model because the lack of homogeneous
data on hosts across the target geographical region. Tick questing activity rates were assumed
to fluctuate with temperature. Then, the mortality of each active stage (larvae or adults) varied
accordingly to the time of the year. It was thus assumed that ticks were active over a threshold
T of 12 ºC (Enigk and Grittner, 1953) and that host-finding rates were related to temperature.
Because the lack of knowledge about host densities in the studied area, which influence tick
attachment rates, host-finding rates for both larvae and adults were adjusted to simulate the
cohort of active ticks to find a host in a maximum of 30 days if daily T > 12 ºC.
Description of the next-generation matrix. Herein, a brief description of the nextgeneration matrix (NGM) elements is described (Hartemink et al., 2008). First, we
distinguished the types-at-infection. Essentially they mean the state of an individual
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immediately after the moment it becomes infected. It is only these types that are required for
the calculation of R0. For tick-borne pathogens these types are:
1
tick infected as eggs (via transovarial transmission)
2
tick infected as larvae (while taking its first blood meal)
3
tick infected as nymphs (while taking its second blood meal)
4
tick infected as adult females (while taking its third blood meal)
5
systemically infective vertebrate host
Each of the matrix elements kij represent the expected number of new cases of type-atinfection i caused by one infected individual of type-at-infection j during its entire infectious
period. It should be kept in mind that ticks take only one blood meal per life stage, so in order
to be infective, a tick must have been infected in an earlier life stage. In our model, nymphs
feed on the same host as the larvae are feeding because H. marginatum is a two-hosts tick, i.e.
larvae molt on host after the blood meal is completed and then nymphs feed again on the
same host. We decided to keep this category even if the ticks feed again on the same host
because this matrix element introduces an interesting way to explore the importance of nonsystemic virus transmission route.
A female tick infected during her blood meal (type-at-infection; ref. 4), cannot pass on the
infection, except to eggs (k14). Therefore k24, k34, k44 and k54 are zero. Elements k15 and k55 are
also zero as infected vertebrate hosts cannot infect tick eggs, nor can they infect other
vertebrate hosts. The remaining non-zero elements are described below, grouped according to
the virus transmission route that they represent. The definitions of the parameters can be
found in Tables S1 and S2.
The NGM consists of a 5 x 5 matrix that contains 25 well-defined parameters:
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(1)
The elements k11, k12, k13 and k14 refer to transovarial transmission (Hartemink et al., 2008).
The elements k21, k22, k23 as well as k31, k32, k33 and k41, k42, k43 involve non-systemic
transmission between ticks. The non-zero elements in the fifth column (k25, k35 and k45) and
the fifth row (k51, k52 and k53) represent transmission from a systemically infected host to ticks
and transmission from ticks to hosts, respectively. The elasticity matrix E is again a 5 x 5
matrix:
(2)
where the elasticity of each of the matrix elements is calculated as follows:
.
(3)
Systemic transmission. The elements k51, k52 and k53 refer to the number of hosts
systemically infected by a tick that was infected as egg, larvae or nymph, respectively. These
elements involve parameters for transmission efficiency that were named as qL, qN and qA.
(Matser et al., 2009). In our approach, we included one single element (Q) because the partial
rates for larvae, nymphs and adults were considered the same. The survival probabilities of
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each tick stage (sL, sN and sA) account for the probability that a tick survives and develops to a
certain stage. These values were provided by the model (Estrada-Peña et al., 2011). Every 10days interval, the tick model provides an estimation of the survival of each tick stage,
including the mortality rates of the developmental periods and those derived from questing
ticks. The number of larvae, nymphs and adult ticks infected by a systemically-infected host
are denoted by k25, k35 and k45, respectively. The parameters involved are the transmission
efficiencies (pL, pN and pA), the average number of ticks of each stage on a host (N LH, N NH or
N AH), the duration of attachment (D L, D N or D A) and the duration of the infective period (i).
Again, the series of transmission efficiency values was included as a single parameter (P)
because it was assumed that the transmission rates from hosts to the different tick stages are
the same. In the analysis, we commonly referred to P+Q because we changed both parameters
in the same way.
The duration of tick attachment is a fixed value, different for larvae, nymphs and adults
(Table S1). Values for N
LH,
N
NH
or N
AH
were derived from the model. To know tick loads
on each host it is necessary to know the number of active ticks and the host density. An
important feature of tick life cycle is its dependence on tick-host associations, namely the
density-dependent mortality or the mortality of the tick produced by the immune response of
the host, which is dependent upon the density of ticks. It was not possible to model this part
of the tick life cycle as densities of hosts can only be estimated. Models have accounted with
this in different ways (Dobson et al., 2011). We included a fixed host density of 4 animals/ha,
which is a realistic approach based on field studies (Acevedo et al., 2007; Bruinderink et al.,
2003). Since the model of the tick life cycle produces an estimation of the seasonal activity as
well as the percentage of active ticks at every 10-days interval, we converted this value into a
percentage of infested hosts, assuming a negative binomial distribution (Poulin, 1993) and a
maximum number of ticks per host as detailed in Table S1. The percentage of infested hosts
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and the estimation of ticks per host is a value driven by the seasonal dynamics of the tick, and
therefore influenced by the temperature.
Non-systemic transmission. Non-systemic transmission is possible for immature ticks. A
tick infected as an egg via transovarial transmission may infect other ticks, either larvae (k 21)
or nymphs (k31) during its firs or second blood meal, respectively. Similarly, transmission
from a tick infected as larvae (k22, k32 and k42) is possible to nymphs and adults, whereas a
tick infected as a nymph (k23, k33 and k43) can only pass the infection to an adult during its
third and last blood meal. All terms were weighted by the chance that a tick survives each life
stage (sL, sN and sA) and the probability that a blood meal is taken on a host competent for
non-systemic transmission (Hartemink et al., 2008). Although H. marginatum has a two-host
life cycle, both nymphs and larvae feeding simultaneously on the same host, we modelled this
process as separated feeds, because nymphs may non-systemically infect co-feeding larvae
arriving later to the same host.
Transovarial transmission. Transovarial transmission occurs when infected females that had
either hatched from an infected egg themselves (k11) or become infected as feeding larvae
(k12), nymphs (k13) or adults (k14) go on to produce infected eggs. The expected number of
infected eggs per infected individual depends on the probability that the originally infected
tick survives to become a female adult tick, the number of eggs per female (E) and the
probability of transmission (R) (Hartemink et al., 2008).
Additional information on the variation of model parameters. Great interest exists to
know the epidemic potential of CCHFV in the western Palearctic and how the local
configuration of the epidemiological parameters of the model may affect the geographical
range of the pathogen, as linked to the seasonal processes of the main tick vector, H.
marginatum (Gale et al., 2010).
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We simulated a continuum of changes in the parameters governing the model and looked for
causal relationships. Because the system is expected to be locally tuned, and because the tick
has different activity patterns among sites in the studied area, it is expected that changes in the
model parameters will not affect the R0 output with the same strength and in the same
direction at every site. We used Latin Hypercube sampling for this evaluation, conducted in R
2.7.2 (using the "lhs" package; R Development Core Team, 2011).
We also tested the effects of temperature on tick development and survival rates and thus the
indirect impact of the tick seasonal processes on the epidemiological parameters of R0.
Climate is recognized as an important driver of tick population processes and it is of interest
to check for its impact on tick seasonal processes and indirectly on the R0 values. Instead of
using different climate scenarios, we used the maximum and minimum "normal" values
provided by the local climate estimator New LocClim (Grieser et al., 2006), to have a climate
upper and lower limits to work with. Thus, we ran the model with the average climate values
and then again with the upper and lower temperature limits for each of the 3,890 points
selected in the studied area. Biotic parameters of the model were left at their normal values
(Table S2) for runs with different temperature values. After each run, the sensitivity of the
system and combined elasticity were computed to assess changes in R0 and how changes in T
accounted for the contribution of each viral transmission route.
Pathogen-specific parameters (Table S2) included transmission efficiencies from host to tick,
from tick to host and from tick to tick. There is no information available for the efficiencies of
transmission of CCHFV between ticks and between ticks and hosts, as well as only partial
estimates of efficiency in transovarial transmission. Therefore, we used in the model estimates
reported in the literature (Gonzalez et al., 1992; Logan et al., 1989; Shepherd et al., 1989;
Wilson et al., 1991; Zeller et al., 1994).References
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http://www.R-project.org/.
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truncatum ticks. Res Virol 143, 23-28.
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Table S1. Tick-related parameters.
Parameter
Value
E
Mean # of eggs per adult
1500
Sl
Survival probabilities from egg to feeding larva
Model derived
Sn
Survival probabilities from larva to feeding nymph
0.02 - 0.11
Sa
Survival probabilities from nymph to feeding adult
Model derived
Cll
Mean # of larvae co-feeding with a larva
Model derived
Cnl
Mean # of nymphs co-feeding with a larva
Model derived
Cal
Mean # of adults co-feeding with a larva
0
Cln
Mean # of larvae co-feeding with a nymph
Model derived
Cnn
Mean # of nymphs co-feeding with a nymph
Model derived
Can
Mean # of adults co-feeding with a nymph
0
Cla
Mean # of larvae co-feeding with an adult
0
Cna
Mean # of nymphs co-feeding with an adult
0
Caa
Mean # of adults co-feeding with an adult
Model derived
10
Cs
Mean fraction of ticks on a host feeding close enough for non-systemic transmission
0
Nlh
Mean # of larvae on competent host
Model derived
Nnh
Mean # of nymphs on competent host
Model derived
Nah
Mean # of adults on competent host
Model derived
Dl
Days of attachment of larva
6
Dn
Days of attachment of nymph
15
Da
Days of attachment of adult
12
Hcn
Fraction of blood meals on hosts competent for systemic transmission
0.2 (varied between 0.1 and 0.9 for sensitivity analysis)
Hcs
Fraction of blood meals on hosts competent for non-systemic transmission
0.2 (varied between 0.1 and 0.9 for sensitivity analysis)
Non model-derived values were obtained from reference 5.
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Table S2. Pathogen-related parameters.
Mea
n
valu
es
Range of values in Latin Hypercube sampling (sensitivity analysis)
I
Systemic infection duration
2 13
1-20 4
θ
Efficiency from tick to tick
0.04
13
0.01 - 0.2 4
Pl,n,a
Efficiency from competent host to tick
0.3
14,15
0.02 - 0.67 4
Ql,n,a
Efficiency from tick to competent host
0.4
15, 16,
17
0.13 - 0.71 4
R
Efficiency from adult to egg
0.17
13, 16,
17
0.1-0.9 4, 16, 17
Reference numbers are shown as superindexes.
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