In e na ional Jou nal o
En i onmen al Resea ch
and Public Heal h
A icle
Model o Risk o Exposu e o Lyme Bo eliosis and
Tick-Bo ne Encephali is Vi us-In ec ed Ticks in he
Bo de A ea o he Czech Republic (Sou h Bohemia)
and Ge many (Lowe Ba a ia and Uppe Pala ina e)
Václa Hönig 1,2,3,* , Pa el Š ec 4, Lukáš Ma ek 5, Tomáš M k iˇcka 6, Zub iko áDana 7,8 ,
Ma ia (Vöge l) Wi mann 7, Ondˇ ej Masaˇ 4, Daniela Sz u co á4, Daniel R ˚užek 1,2,3 ,
Ku P is e 7and Libo G ubho e 1,2
1Ins i u e o Pa asi ology, Biology Cen e, Academy o Sciences o Czech Republic, B aniso ska 31,
370 05 Ceske Budejo ice, Czech Republic; [email p o ec ed] (D.R.); libo [email p o ec ed] (L.G.)
2Facul y o Science, Uni e si y o Sou h Bohemia, B aniso ska 31, 370 05 Ceske Budejo ice, Czech Republic
3Ve e ina y Resea ch Ins i u e, Hudco a 296, 621 00 B no, Czech Republic
4Depa men o Geoin o ma ics, VSB—Technical Uni e si y o Os a a, 17. lis opadu 15, 708 00 Os a a,
Czech Republic; [email p o ec ed] (P.S.); [email p o ec ed] (O.M.); daniela.sz u [email p o ec ed] (D.S.)
5GeoHeal h Labo a o y, Geospa ial Resea ch Ins i u e, Uni e si y o Can e bu y, P i a e Bag 4800,
Ch is chu ch 8140, New Zealand; lukas.ma ek@can e bu y.ac.nz
6Facul y o Economics, Uni e si y o Sou h Bohemia, S uden ska 13, 370 05 Ceske Budejo ice, Czech
Republic; [email p o ec ed]
7Ins i u e o Compa a i e T opical Medicine and Pa asi ology, Ludwig-Maximilians-Uni e si ä München,
Leopolds . 5, 80802 Munich, Ge many; [email p o ec ed] (Z.D.); [email p o ec ed] (M.(V.)W.);
[email p o ec ed] (K.P.)
8Ins i u e o Pa asi ology, Slo ak Academy o Sciences, Hlinko a 3, 040 01 Kosice, Slo akia
*Co espondence: honig@pa u.cas.cz
Recei ed: 22 Feb ua y 2019; Accep ed: 26 Ma ch 2019; Published: 2 Ap il 2019


Abs ac :
In Eu ope, Lyme bo eliosis (LB) and ick-bo ne encephali is (TBE) a e he wo ec o -bo ne
diseases wi h he la ges impac on human heal h. Based on da a on he densi y o hos -seeking
Ixodes icinus icks and pa hogen p e alence and using a a ie y o en i onmen al da a, we ha e c ea ed
an aca ological isk model o a egion whe e bo h diseases a e endemic (Czech Republic—Sou h
Bohemia and Ge many—Lowe Ba a ia, Uppe Pala ina e). The da a on ick densi y we e acqui ed
by lagging 50 sampling si es h ee imes in a single season. P e alence o he causa i e agen s o LB
and TBE was de e mined. Da a on en i onmen al a iables (e.g., al i ude, ege a ion co e , NDVI,
land su ace empe a u e) we e ob ained om a ious sou ces and p ocessed using geog aphical
in o ma ion sys ems. Gene alized linea models we e used o es ima e ick densi y, p obabili y o
ick in ec ion, and densi y o in ec ed icks o he whole a ea. A signi ican ly highe incidence o
human TBE cases was eco ded in Sou h Bohemia compa ed o Ba a ian egions, which co ela ed
wi h a lowe ick densi y in Ba a ia. Howe e , he di e ences in pa hogen p e alence a es we e no
signi ican . The model ou pu s we e made a ailable o he public in he o m o isk maps, indica ing
he dis ibu ion o ick-bo ne disease isk in space.
Keywo ds:
ick; Lyme bo eliosis; ick-bo ne encephali is; Ixodes icinus; isk modeling; geog aphical
in o ma ion sys ems
In . J. En i on. Res. Public Heal h 2019,16, 1173; doi:10.3390/ije ph16071173 www.mdpi.com/jou nal/ije ph
In . J. En i on. Res. Public Heal h 2019,16, 1173 2 o 17
1. In oduc ion
Vec o -bo ne diseases ep esen a se ious heal h isk o human and animals in many pa s o he
wo ld. In Eu ope, pa hogens ansmi ed by Ixodes icinus (I. icinus) icks, namely agen s o Lyme
bo eliosis (LB) and ick-bo ne encephali is (TBE), a e he mos widesp ead ec o -bo ne diseases
o human [
1
,
2
]. To be able o ake app op ia e measu es o limi he le el o exposu e o human
popula ions o ec o -bo ne pa hogens, de ailed knowledge o he dis ibu ion o he isk o in ec ion
in space and ime is needed.
Lyme bo eliosis is caused by spi oche es o he Bo elia bu gdo e i sensu la o complex
(Spi ochae ales,Spi ochae aceae) and TBE by he ick-bo ne encephali is i us (Fla i i us,Fla i i idae).
Bo h he diseases a e zoonoses main ained in geog aphically mo e o less speci ied a eas in na u e,
called “na u al oci”. Humans a e acciden al, p edominan ly dead-end hos s, which ge in ec ed when
en e ing he na u al ocus. In hese oci, causa i e agen s o ec o -bo ne diseases a e main ained by
ci cula ion be ween a h opod ec o s and ansmission compe en hos s. The e o e, he epidemiology
o hese in ec ions is in luenced no only by he in insic ea u es o he pa hogen, bu also by he
beha io and ecology o i s ec o s and hos s. Mo eo e , all h ee componen s o ec o -bo ne pa hogen
na u al cycles a e in luenced by nume ous en i onmen al ac o s o abio ic ( empe a u e, ai humidi y,
access o sunligh , al i ude e c.) [
3
–
6
] o bio ic (na u al hos a ailabili y, ansmission compe ence o
he hos , ec o -hos con ac a e, hos immuni y e c.) [
7
–
9
] na u e. Because he en i onmen in luences
all h ee componen s o he na u al ci cula ion, en i onmen al a iables may be used o he p edic ion
o isk o in ec ion o humans en e ing ce ain a eas [10,11].
The exis ing models o ick-bo ne pa hogens c ea ed o ecological o epidemiological pu poses
a e usually based on he es ima ion o hos -seeking ick densi y and/o pa hogen p e alence in he ield,
collec ion o di e en en i onmen al da a, and use o a ious s a is ical app oaches (mul iple linea
eg ession, classi ica ion and eg ession ees, gene alized linea models e c.) in o de o ind a
ma hema ical exp ession o he ela ionship be ween he en i onmen al a iables and cha ac e is ics
o ick and pa hogen dis ibu ion [6,12–17].
The main aim o his s udy was o use a se o ick abundance and pa hogen p e alence da a o
p epa e summa ized, easy o access in o ma ion on he isk o in ec ion by ick-bo ne diseases o
he gene al public. Based on he esul s o an ex ensi e ield sampling and labo a o y analysis o he
ick popula ions [
18
,
19
], we ha e de eloped a model o he p edic ion o he densi y o hos -seeking
I. icinus icks, LB spi oche e and TBEV p e alence, and densi y o LB spi oche e/TBEV-in ec ed icks
using commonly a ailable en i onmen al da a. Using ools o geog aphic in o ma ion sys ems (GIS),
we ha e in eg a ed he esul s o he esea ch, including he isk models, in map ou pu s which ha e
been made a ailable o he public h ough an in e ac i e in e ne -based map po al.
2. Ma e ials and Me hods
2.1. S udy Si es
The da a on he dis ibu ion o I. icinus ick densi y, and TBEV and B. bu gdo e i s.l. p e alence
in icks we e collec ed in he Czech-Ge man bo de land in 2010–2011. Reco ds o e ospec i e LB
and TBE human disease case incidence we e ob ained o he same a ea o he pe iod 2001–2009.
The s udy a ea consis ed o he egion o Sou h Bohemia in he Czech Republic and he egions o
Lowe Ba a ia and Uppe Pala ina e o he Ge man F ee S a e o Ba a ia (Figu e 1). Geog aphically,
clima ically, and biologically, he a ea is conside ably he e ogeneous anging om Danube Valley a
he Ge man-Aus ian bo de o he highes sec ions o Šuma a (Bohemian Fo es ) and Ba a ian Fo es
moun ain ange (280–1450 m a.s.l.). The o al a ea unde su ey comp ised 30,077 km
2
(10,056 km
2
in he Czech Republic and 20,021 km
2
in Ge many). The egions o Sou h Bohemia and Ba a ia a e
ecognized as a eas o endemic occu ence o LB and TBE [20,21].
In . J. En i on. Res. Public Heal h 2019,16, 1173 3 o 17
Figu e 1.
Su eyed a ea o Sou h Bohemia (Czech Republic), Lowe Ba a ia and Uppe Pala ina e
(Ba a ia, Ge many); Lowe Ba a ia—Niede baye n, Uppe Pala ina e (Obe p alz), Baye n—Ba a ia;
localiza ion o ick sampling si es indica ed by a c oss sign.
The aca ological isk o ick-bo ne disease in ec ion is de e mined by he p e alence o he pa hogen
in icks and abundance o he ick popula ion. P e ious s udies ha e shown ha bo h he pa ame e s may
be p edic ed based on hei known ela ionship o ce ain en i onmen al ac o s [
6
,
10
,
22
,
23
]. The e o e,
in he ield, in a ne wo k o 50 s udy si es sp ead h oughou he s udy a ea, we ha e collec ed da a on
he densi y o hos -seeking I. icinus,B. bu gdo e i s.l., and TBEV p e alence. In pa allel, a la ge da ase
o en i onmen al da a was es ablished and subsequen ly used o gene a e p edic ions o hos -seeking
ick densi y and pa hogen p e alence o e e y pixel o he s udy a ea.
2.2. Field S udy
The dis ibu ion o icks and ick-bo ne pa hogens was es ima ed in a ne wo k o 50 s udy si es
(30 in Sou h Bohemia, 20 in Ba a ia—Lowe Ba a ia and Uppe Pala ina e) (Figu e 1), as desc ibed
in [
18
]. The densi y o hos -seeking I. icinus icks was es ima ed by “ lagging” each sampling si e
(600 m
2
pe si e and sampling e en ) h ee imes pe yea (May, June/July, Sep embe /Oc obe ),
esul ing in 150 sepa a e en ies ( o de ails, please see [
18
]). Only nymphal and adul I. icinus icks
we e sampled, as he densi y o la al icks is di icul o es ima e due o hei highly agg ega ed
dis ibu ion, hey a ely in es humans [24], and hey gene ally ha e a low pa hogen p e alence [25].
Collec ed icks we e anspo ed o he labo a o y and es ed o he p esence o DNA o
B. bu gdo e i and TBEV RNA using con en ional PCR o bo elia [
26
,
27
], e e se ansc ip ion
ollowed by con en ional PCR o TBEV (samples om Sou h Bohemia) [
28
], and e e se ansc ip ion
ollowed by eal- ime PCR (samples om Ba a ia) [
29
] ( o mo e de ailed in o ma ion see [
18
] and [
19
]).
The da a o bo h coun ies we e analyzed as a single da ase . Al oge he , da a om 15,150 and 28,862
icks we e a ailable conside ing B. bu gdo e i s.l. and TBEV in ec ion s a us, espec i ely.
2.3. En i onmen al Da a
Apa om he da a on ick and pa hogen dis ibu ion, we ha e used a ious sou ces o collec
epidemiological (numbe s o disease cases), demog aphic (numbe s o inhabi an s), and en i onmen al
da a (al i ude, slope, exposi ion, ege a ion co e , empe a u e e c.). The ypes o da a and hei
espec i e sou ces a e summa ized in Table 1. Sa elli e images acqui ed by he MODIS ins umen
we e used as a sou ce o land su ace empe a u e (LST) and ege a ion co e in o ma ion—no malized
di e ence ege a ion index (NDVI). F om he NASA Land P ocesses Dis ibu ed Ac i e A chi e Cen e ,
In . J. En i on. Res. Public Heal h 2019,16, 1173 4 o 17
he ollowing p oduc s we e downloaded o he whole a ea unde su ey: Su ace Tempe a u e
& Emissi i y 8-Day L3 Global, MOD11A2, and Vege a ion Indices 16-Day L3 Global MOD13Q1.
Indi idual measu emen s we e ex ac ed o he sampling locali ies and speci ied da es.
Table 1. En i onmen al and o he accesso y da a used o model cons uc ion and es ing *.
Type o Da a Da a Desc ip ion Sou ce Czech Rep. Sou ce Ba a ia
Epidemiological numbe LB cases disease cases pe
municipali y
Na ional Ins i u e o
Public Heal h, P ague RKI, Be lin; local public
heal h au ho i ies
numbe TBE cases
Demog aphic numbe o inhabi an s numbe o inhabi an s
pe municipali y Czech S a is ical O ice Fede al S a is ical O ice
Ge many
Physical-geog aphical
al i ude
digi al ele a ion model A cCR500, A cDATA,
P ague
Vek o 500, ATKIS®
Basis DLM, Baye ische
Ve messungs e wal ung
slope
exposi ion
Clima ic
land su ace empe a u e
(LST)
MODIS Land Su ace
Tempe a u e, 1000 m
as e
NASA, LP DAAC NASA, LP DAAC
Vege a ion co e NDVI MODIS NDVI, 250 m
as e NASA, LP DAAC NASA, LP DAAC
o es ype
CORINE landco e 2006,
100 m as e EEA EEA
* LB—Lyme bo eliosis; TBE— ick-bo ne encephali is; NDVI—no malized di e ence ege a ion index; RKI—Robe
Koch Ins i u e; NASA, LP DAAC—Na ional Ae onau ics and Space Adminis a ion, Land P ocesses Dis ibu ed
Ac i e A chi e Cen e ; EEA—Eu opean En i onmen Agency.
Using GIS, he da a we e ex ac ed and op imized o en e he analysis. Wi h ega d o di e ences
in he esolu ion o he sou ce da a, we ha e wo ked wi h an op imized esolu ion o he whole da ase
o a 250 m pixel size. Minimum, maximum, mean seasonal (May–Sep embe ), and mean annual LST
and NDVI alues we e calcula ed o indi idual sampling si es. In he case o physical geog aphical
cha ac e is ics and o es ype, a bu e a ea a ound he collec ion si e was aken in o accoun (pixel
o collec ion si e and eigh su ounding pixels). The cha ac e is ics we e exp essed as he p opo ion
o he a ea o a gi en quali y (e.g., co e ed by deciduous o es s). The densi y o hos -seeking icks
was exp essed as he numbe o icks pe 100 m
2
, and p e alence as po ion o samples posi i e o LB
spi oche es o TBEV o o al samples es ed.
Epidemiological da a we e ob ained (Na ional Ins i u e o Public Heal h, Czech Republic; Robe
Koch Ins i u e and local public heal h au ho i ies, Ge many) as numbe s o human disease cases
egis e ed be ween 2001–2009 in each o he 626 municipali ies in Sou h Bohemia and 536 in he
selec ed egions o Ba a ia. Da a on TBE and LB we e a ailable o Sou h Bohemia, whe e bo h
diseases a e epo ed manda o y. In he case o Lowe Ba a ia and Uppe Pala ina e, only da a on TBE
could be ga he ed. Census o popula ion and housing da a we e used as he sou ce o numbe s o
inhabi an s. Disease incidence was exp essed as he numbe o cases pe 100,000 inhabi an s.
2.4. Model Cons uc ion
Independen models we e c ea ed o he p edic ion o he densi y o hos -seeking icks (nymphal
and adul I. icinus), and p obabili y o in ec ion o a ick by LB spi oche es and TBEV. Subsequen ly,
he ick densi y model was combined wi h ei he he LB spi oche es o TBEV in ec ion p obabili y
model, gi ing a p edic ion o he densi y o in ec ed icks as a measu e o isk o in ec ion o an
un accina ed pe son en e ing a pa icula geog aphical a ea.
Fi s , he co ela ion o all po en ial explana o y a iables was examined by he Spea man
anking es , and c oss-co ela ions among he a iables we e inspec ed. Signi ican ly c oss-co ela ed
explana o y a iables we e g ouped oge he . Subsequen ly, he se o po en ial explana o y a iables
was es ed o co ela ion wi h he dependen a iables. F om each g oup o c oss-co ela ed
explana o y a iables, one ep esen a i e wi h he highes co ela ion coe icien wi h he dependen
a iable was chosen o u he analysis.
Gene alized linea models we e used o hos -seeking ick densi y p edic ion. Wi h ega d o
he cha ac e o he da a, a log-linea model wi h a Poisson dis ibu ion (Poisson eg ession model)
In . J. En i on. Res. Public Heal h 2019,16, 1173 5 o 17
was applied. Indi idual explana o y a iables we e e alua ed based on a Likely-hood ype 3 es .
The quali y o he model was e alua ed using McFadden’s pseudo R2.
In he case o he p edic ion o B. bu gdo e i s.l. and TBEV in ec ion in icks, a logi model was
applied. The ela ionship o a bi a ia e dependen a iable ( ick in ec ed/ ick no in ec ed) wi h
po en ial explana o y a iables o he same da ase as in he case o hos -seeking ick densi y was
examined in he model. Fi s , all he candida e explana o y a iables we e included in he model
and subsequen ly, he a iables ha we e no s a is ically signi ican ly impo an we e excluded, as
is done using a backwa ds s epwise app oach. Indi idual a iables we e excluded based on he
compa ison o Wald s a is ics and (c oss-) co ela ion coe icien alues. BIC and AIC c i e ia we e
con olled, indica ing he pe o mance o he whole model. The pe o mance o he wo esul ing
in ec ion p obabili y models was e alua ed using ROC (Recei e Ope a ing Cha ac e is ic) analysis.
An ROC cu e e alua es he ela ionship be ween he sensi i i y ( ue posi i e ac ion) and speci ici y
( alse posi i e ac ion) o he model [
30
] and i is a sui able measu e o he bina y classi ica ion.
The common way o in e p e a ion o he ROC is quan i ying he ac ion o an a ea unde he ROC
cu e (AUC). Gene ally speaking, he highe he AUC, he be e he abili y o he model o classi y.
A meaning ul model should ha e an AUC highe han 0.5, which indica es ha i is be e han a
andom p edic o [31].
2.5. S a is ical and GIS analyses
S a is ical analyses we e pe o med using STATISTICA e . 9 (S a So CR, P ague, Czech
Republic) and R [
32
]. A non-pa ame ic Mann-Whi ney es was used o a compa ison o disease
incidence a es and hos -seeking ick densi ies, and a chi squa e es o a compa ison o he p e alence
a e (LB) o minimum in ec ion a e (TBEV). Di e ences wi h p< 0.05 we e conside ed s a is ically
signi ican . All GIS analyses we e pe o med and map ou pu s gene a ed using A cGIS 10.X (ESRI,
Redlands, USA). The p ojec ou pu s we e in eg a ed in a web-based map po al using A cGIS o
Se e (ESRI, Redlands, USA).
3. Resul s
3.1. Disease Incidence
In he pe iod o 2001–2009, al oge he , 1453 TBE cases we e egis e ed in Sou h Bohemia compa ed
o 417 cases epo ed in Lowe Ba a ia and Uppe Pala ina e. When exp essed as incidence, 231 TBE
cases pe /100,000 inhabi an s we e epo ed om he Sou h Bohemian egion compa ed o 18 cases om
Ba a ia. The di e ences we e ound o be s a is ically signi ican (Mann-Whi ney UTes , p< 0.0001).
3.2. Densi y o Hos -Seeking I. Ricinus Ticks and Pa hogen P e alence
All he analyses we e based on agg ega ed da a om Sou h Bohemia and Ba a ia, esul ing in
50 s udy si es, 150 indi idual sampling e en s, 15,150 I. icinus icks analyzed o he p esence o
B. bu gdo e i s.l., and 28,862 icks es ed o TBEV. The mean densi y o hos -seeking icks eached
30.1 nymphs/100 m
2
( ange 1.3–110.2), and 2.0 adul icks/100 m
2
(0–10.7). The mean densi y o all
hos -seeking icks and nymphal icks in Sou h Bohemian sampling si es eached signi ican ly highe
alues (37.4 icks/100 m
2
and 34.9 nymphs/100 m
2
) han he abundance o hos -seeking icks in
Ba a ian si es (24.5 icks/100 m
2
and 22.8 nymphs/100 m
2
) (Mann-Whi ney U es , p< 0.001). In he
case o adul icks, he di e ence was no s a is ically signi ican (2.3 adul icks/100 m
2
in Sou h
Bohemia and 1.7 adul s/100 m2in Ba a ia).
The o al p e alence o LB spi oche es eached 12.3% (1865 posi i e samples/15,150 es ed),
and he minimum in ec ion a e (MIR) (samples es ed in pools) o TBEV eached 0.30% (87/28,862).
Sligh ly highe p e alence a es o B. bu gdo e i we e obse ed in samples om Ba a ia, whe eas
highe MIRs o TBEV we e ound in Sou h Bohemian samples. The only s a is ically signi ican
di e ences (
χ2
es ; p< 0.01) we e ound be ween he Bo elia p e alence in adul icks, which was

In . J. En i on. Res. Public Heal h 2019,16, 1173 6 o 17
signi ican ly highe in samples om Ba a ian locali ies (Tables 2and 3). Ticks posi i e o DNA o
B. bu gdo e i s.l. we e ound a each o he 50 s udy si es. A leas one TBEV posi i e ick was sampled
a 21 o 30 (70%) locali ies in Sou h Bohemia and a 7 o 20 (35%) s udy si es loca ed in Ba a ia.
Table 2. P e alence o Bo elia bu gdo e i s.l. in ield-collec ed Ixodes icinus icks.
Tick S age Nymphs Adul s To al
Posi i e/Tes ed P e alence Posi i e/Tes ed P e alence Posi i e/Tes ed P e alence
S. Bohemia 1239/9809 12.63% 117/1373 8.52% * 1356/11,182 12.13%
Ba a ia 458/3599 12.73% 51/369 13.82% * 509/3968 12.83%
To al 1697/13,408 12.66% 168/1742 9.64% 1865/15,150 12.31%
S a is ically signi ican di e ences (p< 0.05) a e indica ed by *.
Table 3. Minimum in ec ion a e o TBEV in ield-collec ed Ixodes icinus icks.
Tick De elopmen al
S age Nymphs Adul s To al
Posi i e/Tes ed MIR Posi i e/Tes ed MIR Posi i e/Tes ed MIR
S. Bohemia 54/18,829 0.29% 10/1228 0.81% 64/20,057 0.32%
Ba a ia 20/8203 0.24% 3/602 0.50% 23/8805 0.26%
To al 74/27,032 0.27% 13/1830 0.71% 87/28,862 0.30%
MIR—minimum in ec ion a e. S a is ically signi ican di e ences (p< 0.05) a e indica ed by *.
3.3. Hos -Seeking Tick Densi y Model
Based on he Spea man anking es , a se o po en ial explana o y a iables was iden i ied
(Table 4) o be included in he ini ial model. Al i ude as a well-known ac o in luencing ick densi y was
included in he model, despi e i s poo co ela ion wi h he dependen a iable in he es . Fu he mo e,
signi ican di e ences we e ound among he di e en sampling e en s sp ing—summe —au umn
(ANOVA; p< 0.01) and hus he sampling e en was added o he model as a ca ego ical p edic o .
Table 4.
Co ela ion o po en ial explana o y a iables wi h he densi y o hos -seeking Ixodes
icinus icks *.
Va iable Spea man R p-Le el
LST da e o collec ion 0.136 0.096
LST seasonal mean 0.323 0.001
LST seasonal minimum −0.174 0.033
LST seasonal maximum 0.231 0.004
Al i ude 0.089 0.277
Deciduous o es p opo ion −0.073 0.373
Coni e ous o es p opo ion 0.016 0.843
Mixed o es p opo ion 0.207 0.011
O he eg. co e p opo ion −0.174 0.034
P opo ion slope o e 5% −0.028 0.732
P opo ion no hwa ds 0.053 0.523
P opo ion sou hwa ds −0.267 0.001
A e age al i ude −0.008 0.924
NDVI Da e o collec ion −0.055 0.501
NDVI May −0.047 0.569
NDVI June −0.090 0.276
NDVI July −0.226 0.005
In . J. En i on. Res. Public Heal h 2019,16, 1173 7 o 17
Table 4. Con .
Va iable Spea man R p-Le el
P opo ion sou hwa ds −0.267 0.001
A e age al i ude −0.008 0.924
NDVI Da e o collec ion −0.055 0.501
NDVI May −0.047 0.569
NDVI June −0.090 0.276
NDVI July −0.226 0.005
NDVI Augus −0.257 0.002
NDVI Sep embe −0.235 0.004
NDVI seasonal mean −0.244 0.003
NDVI July-Sep embe mean −0.286 0.001
NDVI seasonal maximum −0.126 0.124
NDVI seasonal minimum −0.310 0.001
* LST—land su ace empe a u e, NDVI—no malized di e ence ege a ion index eco ded in he indica ed mon h
o he yea o ick sampling. Seasonal minimum, maximum, and mean alues we e calcula ed o he pe iod
May–Sep embe . P opo ions o a ea o a pa icula cha ac e and a e age al i ude we e calcula ed om a pixel o
sampling si e and eigh su ounding pixels, pixel size—250 m. Va iables included in he ini ial model a e indica ed
in bold.
A log-linea model wi h a Poisson dis ibu ion was used o hos -seeking ick densi y p edic ion.
Acco ding o he esidual analysis, an ou lie was iden i ied and excluded om u he analysis.
All included a iables we e ound o be signi ican in he model (Likely-hood ype 3 es , p< 0.001).
The pa ame e s we e es ima ed, esul ing in he ollowing equa ion (Table 5):
ln (hos -seeking ick densi y) = 5.973866 + season + 0.019914 LST Seasonal Mean
−
0.000770 Al i ude
−
0.492528 Po ion Sou hwa ds −1.046671 NDVI Augus
Table 5. Pa ame e es ima es—hos -seeking ick densi y model *.
Pa ame e Coe icien S anda d E o Wald S a is ics Lowe Con .
Limi (95%)
Uppe Con .
Limi (95%) p
In e cep 5.9739 0.1178 50.7313 5.7429 6.2045 <0.001
LST Seasonal Mean 0.0199 0.0039 5.0860 0.0122 0.0276 <0.001
Al i ude −0.0008 0.0001 −9.5683 −0.0009 −0.0006 <0.001
P opo ion Sou hwa ds −0.4925 0.0208 −23.6768 −0.5333 −0.4518 <0.001
NDVI Augus −1.0467 0.0601 −17.4058 −1.1641 −0.9284 <0.001
Pe iod—Sp ing 0.3935 0.0144 27.2851 0.3652 0.4218 <0.001
Pe iod—Summe 0.0968 0.0154 6.2837 0.0666 0.1269 <0.001
* LST—land su ace empe a u e, NDVI Augus —no malized di e ence ege a ion index eco ded in Augus .
Seasonal mean LST alues we e calcula ed o he ime pe iod o May–Sep embe . P opo ions o a ea o a pa icula
cha ac e (a ea o sou h– acing slopes) we e calcula ed om he o al a ea o he pixel o sampling si e and eigh
su ounding pixels, pixel size—250 m.
Fo he only ca ego ical a iable, “season”, he ollowing pa ame e s we e es ima ed:
sp ing = 0.393470
, summe = 0.096751, au umn = 0. Thus, h ee independen models we e c ea ed o
he di e en pa s o he ick season.
The McFadden’s pseudo R
2
o he p esen ed model eached he alue o 0.203, indica ing a model
wi h e y good i . The compa ison o obse ed and p edic ed ick coun s on indi idual loca ions
oge he wi h i s con idence in e al is depic ed in Figu e 2.
In . J. En i on. Res. Public Heal h 2019,16, 1173 8 o 17
Figu e 2.
Compa ison o obse ed (de e mined in ield) and p edic ed (es ima ed by he model o
hos -seeking ick densi y) I. icinus ick coun s on indi idual sampling si es. G ey lines show he
obse ed alues, ed c osses indica e he alue p edic ed by he model, and ed lines ep esen he
con idence in e al.
3.4. B. bu gdo e i and TBEV P obabili y o In ec ion Model
The p obabili y o in ec ion o a ick by B. bu gdo e i s.l. o TBEV was p edic ed using a logi
model. The pa ame e es ima es and goodness o i da a o he p obabili y o in ec ion o he ick by
B. bu gdo e i and TBEV a e p esen ed in Tables 6and 7, espec i ely. Season o collec ion, he only
ca ego ical explana o y a iable, was no ound o be signi ican o ei he Bo elia o o he TBEV
isk model.
The p obabili y o in ec ion o a ick by spi oche es o Lyme bo eliosis was exp essed by he
ollowing equa ion (Φs anding o he no mal dis ibu ion unc ion):
P obabili y o B. bu gdo e i in ec ion =
Φ
(0.546025
−
1.064178 NDVI May
−
0.153217 Po ion
No hwa ds + 0.000483 Al i ude −0.051443 LST Seasonal Mean)
Table 6. Pa ame e es ima es o he model o p obabili y o B. bu gdo e i in ec ion o icks *.
Pa ame e Coe icien S anda d E o Wald S a is ics Lowe Con .
Limi 95%
Uppe Con .
Limi 95% p
In e cep 0.5460 0.2657 2.0553 0.0243 1.0674 0.040
NDVI May −1.0642 0.167 −6.3716 −1.3926 −0.7328 <0.001
P opo ion no hwa ds −0.1532 0.0422 −3.6290 −0.2360 −0.0713 <0.001
Al i ude 0.0005 0.0002 3.0032 0.0002 0.0008 0.003
LST seasonal mean −0.0514 0.0084 −6.159 −0.0679 −0.0351 <0.001
* LST—land su ace empe a u e, NDVI May—no malized di e ence ege a ion index eco ded in May. Seasonal
mean LST alue was calcula ed o May-Sep embe . P opo ions o a ea o a pa icula cha ac e (a ea o no h- acing
slopes) we e calcula ed om he o al a ea o he pixel o sampling si e and eigh su ounding pixels a ea, pixel
size—250 m.
The p obabili y o in ec ion o a ick by TBEV was exp essed by he ollowing equa ion (
Φ
s anding
o he no mal dis ibu ion unc ion):
P obabili y o TBEV in ec ion =
Φ
(
−
2.275259–0.038585 LST seasonal minimum + 0.218823 Mixed
o es po ion −2.526153 NDVI May + 2.323306 NDVI seasonal maximum).
In . J. En i on. Res. Public Heal h 2019,16, 1173 9 o 17
Table 7. Pa ame e es ima es o he model o p obabili y o TBEV in ec ion in icks *.
Pa ame e Coe icien S anda d E o Wald S a is ics Lowe Con .
Limi 95%
Uppe Con .
Limi 95% p
In e cep −2.2753 0.4913 −4.6309 −3.2658 −1.3322 <0.001
LST seasonal minimum −0.0386 0.0151 −2.5633 −0.0682 −0.0091 0.010
P opo ion mixed o es 0.2188 0.0858 2.5497 0.0497 0.3884 0.011
NDVI May −2.5262 0.5601 −4.5103 −3.6222 −1.4000 <0.001
NDVI seasonal
maximum 2.3233 0.6853 3.3903 0.9201 3.6734 0.001
* LST—land su ace empe a u e, NDVI May—no malized di e ence ege a ion index eco ded in May. LST
seasonal minimum and maximum alues we e calcula ed o May-Sep embe . P opo ions o a ea o a pa icula
cha ac e (a ea co e ed by mixed o es s) we e calcula ed om he o al a ea o he pixel o sampling si e and eigh
su ounding pixels, pixel size—250 m.
Valida ion o he classi ica ion abili y o he p e ious wo models was e alua ed using ROC
analysis. ROC cu es a e depic ed in Figu e 3, oge he wi h hei AUC. AUC o he model o
B. bu gdo e i was 0.58, while he model o TBEV in ec ion eached he le el o 0.64.
Figu e 3.
Recei e ope a ing cha ac e is ics (ROC) o classi ica ion abili y o B. bu gdo e i in ec ion
p obabili y model (a) and TBEV in ec ion p obabili y model (b); AUC—a ea unde ROC cu e.
By joining he model o hos -seeking ick densi y p edic ion wi h ei he he model o p obabili y
o B. bu gdo e i o TBEV in ec ion, a isk model p edic ing he densi y o in ec ed icks was c ea ed.
The ma hema ical models we e in eg a ed in o he GIS sys em and isk maps we e gene a ed (Figu e 4).
Compa ison o he classi ica ion (p edic ion o gene al densi y o icks wi hou he in luence o
season) o he Sou h Bohemian and Ba a ian egions is p esen ed in Table 8. Fu he mo e, all he
epidemiological da a and isk models we e made a ailable o he gene al public ia an online map
po al (h p://gisak. sb.cz/klis a a/index_en.h ml).
In . J. En i on. Res. Public Heal h 2019,16, 1173 16 o 17
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