scieee Open visual document viewer

Towards integrated surveillance of zoonoses: spatiotemporal joint modeling of rodent population data and human tularemia cases in Finland

Rotejanaprasert, C.,Lawson, A.,Rossow, H.,Sane, J.,Huitu, O.,Henttonen, H.,Del Rio Vilas, V.J.

Full text

RESEARCH ARTICLE Open Access Towa ds in eg a ed su eillance o zoonoses: spa io empo al join modeling o oden popula ion da a and human ula emia cases in Finland C. Ro ejanap ase 1* , A. Lawson 2 , H. Rossow 3 , J. Sane 4 , O. Hui u 5 , H. Hen onen 5 and V. J. Del Rio Vilas 6 Abs ac Backg ound: The e a e an inc easing numbe o geo-coded in o ma ion s eams a ailable which could imp o e public heal h su eillance accu acy and e iciency when p ope ly in eg a ed. Speci ically, o zoono ic diseases, knowledge o spa ial and empo al pa e ns o animal hos dis ibu ion can be used o aise awa eness o human isk and enhance ea ly p edic ion accu acy o human incidence. Me hods: To his end, we de elop a spa io empo al join modeling amewo k o in eg a e human case da a and animal hos da a o o e a modeling al e na i e o combining mul iple su eillance da a s eams in a no el way. A case s udy is p o ided o spa io empo al modeling o human ula emia incidence and oden popula ion da a om Finnish heal h ca e dis ic s du ing yea s 1995–2012. Resul s: Spa ial and empo al in o ma ion o oden abundance was shown o be use ul in p edic ing human cases and in imp o ing ula emia isk es ima es in 40 and 75% o heal h ca e dis ic s, espec i ely. The human ela i e isk es ima es’s anda d de ia ion wi h oden ’s in o ma ion inco po a ed a e smalle han hose om he model ha has only human incidence. Conclusions: These esul s suppo he in eg a ion o oden popula ion a iables o educe he unce ain y o ula emia isk es ima es. Howe e , mo e in o ma ion on se e al co a ia es such as en i onmen al, beha io al, and socio-economic ac o s can be in es iga ed u he o deepe unde s and he zoono ic ela ionship. Keywo ds: Su eillance in eg a ion, Join diseases modeling, Zoonoses, Tula emia, Finland Backg ound Disease isk mapping is impo an o he unde s anding o he spa ial epidemiology o in ec ious diseases. In mos cases and e en o mul i-hos diseases such as zoonoses, isk es i- ma ion has been conduc ed in a uni a ia e ashion based on humancaseda aalone.Modelingo mul i a ia eheal h da a, in o med by mul iple s eams o geo-coded in o ma- ion, allows obse a ion o concu en pa e ns among da a s eams and condi ioning on one ano he . As a esul , mul i- a ia e me hods can deli e g ea e s a is ical powe and lead o mo e p ecise isk es ima ion and enhanced e en de ec ion. Speci ically, o zoono ic diseases, knowledge o spa ial and empo al pa e ns o he animal hos could in- o m incidence in humans. In eg a ion o da a and analyses, whe he o popula ion o heal h ela ed a iables, has been sugges ed o imp o e zoo- noses su eillance accu acy and e iciency [1,2]. In eg a ion appea s mo e easible o endemic zoonoses, and o hose wi h domes ica ed animals as sou ce, gi en he likely g ea e a ailabili y o animal heal h da a. Fo zoonoses wi h a non-domes ica ed animal sou ce (e.g. syl a ic yellow e e , u- la emia), a ailabili y o animal heal h da a is likely o be a lim- i ing ac o owa ds in eg a ion and al e na i e animal da a sou ces mus be sough . Tula emia is an in ec ious disease caused by an in acellu- la bac e ium, F ancisella ula ensis.Thediseaseisendemic * Co espondence: [email p o ec ed] 1 Depa men o T opical Hygiene, Facul y o T opical Medicine, Mahidol Uni e si y, Ra cha hewi, Bangkok 10400, Thailand Full lis o au ho in o ma ion is a ailable a he end o he a icle © The Au ho (s). 2018 Open Access This a icle is dis ibu ed unde he e ms o he C ea i e Commons A ibu ion 4.0 In e na ional License (h p://c ea i ecommons.o g/licenses/by/4.0/), which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided you gi e app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e Commons license, and indica e i changes we e made. The C ea i e Commons Public Domain Dedica ion wai e (h p://c ea i ecommons.o g/publicdomain/ze o/1.0/) applies o he da a made a ailable in his a icle, unless o he wise s a ed. Ro ejanap ase e al. BMC Medical Resea ch Me hodology (2018) 18:72 h ps://doi.o g/10.1186/s12874-018-0532-8 in No h Ame ica and pa s o Eu ope, wi h ecu en ou - b eaks in Sweden and Finland [3,4]. F ancisella ula ensis has a wide ange o hos s wi h ansmission mos commonly ia a h opod ec o s [5]. Roden s could play a ole in he zoono ic ansmission o he disease a e indings o a ela- ionship be ween ole popula ion cycles and human ula - emia incidence in Finland [6] and Sweden [7]. Speci ically in Finland, oden popula ion dynamics displayed a spa io em- po al ela ionship wi h human ula emia cases, such ha human case numbe s peaked one yea a e peak oden densi ies [6]. Simila indings, om s udies o ula emia ou - b eaks, indica e ha high oden densi ies migh ela e o occu ences in humans [8–11]. This wo k explo es he applica ion o spa io empo al join models o concu en animal and human geo- e e enced da a sou ces in an e o o explain possible pa e ns be- ween he dis ibu ion and/o he abundance o he animal hos and human disease.. The p oposed me hodology is e alua ed on i s pe o mance in p edic ing human disease isk and imp o ing isk es ima ion in a case s udy o ula - emia human incidence and oden popula ion da a in Finland. No only ou me hod con ains me hodological no - el y wi h po en ial applica ions in spa ial epidemiology, i also helps o e eal a disease pa e n in he case s udy which was no conside ed in p e ious s udies. Me hods Da a sou ces A comple e desc ip ion o he oden popula ion and human ula emia incidence da a is a ailable om ea lie epo s [6]. B ie ly, da a on oden popula ion le els, p edominan ly bank oles (Myodes gla eolus) and ield oles (Mic o us ag es is), we e collec ed ac oss Finland by he Na u al Resou ces Ins i- u e Finland and ca ego ized in o h ee popula ion le els: de- cline, inc ease, and peak [12]. Human ula emia cases we e epo ed as labo a o y-con i med o he Na ional In ec ious Disease Regis e , kep by he Na ional Ins i u e o Heal h and Wel a e o Finland. Bo h human cases and oden da a we e agg ega ed in o 20 Finnish heal hca e dis ic s o e he pe iod 1995–2012 [6]. An indica o o quan i y he in luence o o- den popula ion le els on human incidence is de eloped o each heal h dis ic . Plo s o human cases and bina y oden s a us o he 20 Finnish heal h dis ic s in he pe iod 1995– 2012 show a one-yea lagged inc ease in he numbe o hu- man ula emia cases a e oden popula ion peaks o ce ain dis ic s and yea s (Fig. 1). A simila pa e n was ound be- ween human cases and he ca ego ical oden popula ion s a- us (Fig. 2). These suppo he choice o spa io empo al models which will be de eloped in he nex sec ion. S a is ical me hodology Wep oposeaBayesian amewo k ojoin lyanalyze oden popula ion s a us and human case incidence. We assume ha he human cases a e associa ed wi h oden s’s a us h ough a la en s uc u e. Le human cases (coun s), h i ,a heal h dis ic iand ime ollow a Poisson dis ibu ion wi h mean = e i θ i whe e e i is he expec ed numbe o human cases in he i h heal h dis ic (p esumably cons an ac oss he yea s) and θ i is he ela i e isk a he i h heal h dis ic and yea The e a e a numbe o ways o calcula e he ex- pec ed a e. In his pape , he expec ed a es, e i , a e calcu- la ed as he a e age case coun a a ea io e he ime pe iod as ei¼P hi Twhe e Tis he leng h o s udy pe iod Fig. 1 Human cases (solid line) and 2-le el oden s a us (do ) o he 20 Finnish heal h dis ic s o e yea s 1995–2012 Ro ejanap ase e al. BMC Medical Resea ch Me hodology (2018) 18:72 Page 2 o 8 (T= 8 yea s).Human popula ion da a was ob ained om he Finnish Popula ion Regis e Cen e [13]. Howe e , he popula ion a ia ion be ween egions was ound o be lim- i ed and combined wi h he low o e all a e o he disease, i was decided ha a ime a e aged a e would be app o- p ia e in his case. A simple app oach o join ly model human incidence and oden popula ion da a is o conside a 2-le el o- den popula ion indica o as in [6]. As a bina y a iable, we deno e i = 0 i he numbe o oden s declined and i = 1 i he numbe o oden s is a peak o inc eased. The 2-class oden s a us is hen assumed o ollow a Be noulli dis ibu ion wi h pa ame e p i being he p ob- abili y o oden o he i h heal h dis ic and yea .To speci y he pa ame e s in he join likelihoods, θ i o humans and p i o oden s, linea p edic o s a e decom- posed addi i ely in o spa ial, and space- ime in e ac ion andom e ec s as ollows α ,α h a e he o e all mean le els o oden and hu- man espec i ely, and assumed o ha e ze o-mean Gaussian p io dis ibu ions. The la en a iables uh i;u i; h i; ia e included o model non- empo al backg ound a ia ion wi h spa ial and non-spa ial p io dis ibu ions. The spa ial s uc u e o uh i;u i ollow an in insic condi- ional au o eg essi e (ICAR) [14] model and he non-spa ial dis ibu ion o h i; iis assumed o be ze o-mean Gaussian p io dis ibu ion. A Gaussian dis- ibu ion wi h ze o mean is assumed o λh ;λ a =1 and an au o eg essi e p io dis ibu ion is assumed o λh ;λ a > 1 which allows o a ype o nonpa ame ic empo al e ec . δh i ;δ i ep esen he empo al end o each heal h dis ic a yea . We also assume ha he space- ime andom e ec s o human and oden a e p o- po ional wi h one-yea lag. This is suppo ed by he inding sugges ed in [6] ha 1-yea empo al lag e ec humani ¼hi Poisson eiθi ðÞ log θi ðÞ¼αhþuh iþ h iþλh þδh i δh i ¼βiδ i −1 βi¼βp i i −1þβn i1− i −1 ðÞ oden i ¼ i Be noulli pi ðÞ logi pi ðÞ¼α þu iþ iþus kþ s kþλ þδ i αhN0;τ−1 αh  ;α N0;τ−1 α  δh i N0;τ−1 δh  ;δ i N0;τ−1 δ  λh Nλh −1;τ−1 λh  ;λ Nλ −1;τ−1 λ  λh 1N0;τ−1 λh  ;λ 1N0;τ−1 λ  uh iICAR τ−1 uh  ; h iN0;τ−1 h  u iICAR τ−1 u  ; iN0;τ−1  us kICAR τ−1 us  ; s kN0;τ−1 s  βp iN0;τ−1 βp  ;βn iN0;τ−1 βn  τ−1=2 Uni o m 0;10ðÞ Fig. 2 Human cases (solid line) and 3-le el oden s a us (do ed line) o he 20 Finnish heal h dis ic s o e yea s 1995–2012 Ro ejanap ase e al. BMC Medical Resea ch Me hodology (2018) 18:72 Page 3 o 8 can be bene icial o p edic human ula emia ou b eaks. To model unobse ed ecological e ec s associa ed wi h ole cycles a he i e bo eal zones in Finland (Sou he n Finland, Sou hwes e n and Inland Finland, Eas e n Finland, No he n Finland, and Lapland) [13], wo add- i ional pa ame e s us k; s ka e included as he spa ial and non-spa ial con ex ual a iables o egional s a e le el k. δ i ;βp i;βn ia e assumed o ollow a ze o-mean Gaussian p io dis ibu ion and he uni o m dis ibu ion on (0,10) is used o model all s anda d de ia ion pa ame e s [15]. Al hough he e is some e idence ha a 2-le el oden s a us could ha e a lagged p edic i e abili y on human ula emia [6], we also wan o ex end ou conside a ion o include he o iginal h ee oden le els in he join modeling and assume a ca ego ical likelihood o oden popula ion s a us. A speci ica ion o mul iple ca ego ies o oden s a us can be de ined as humani ¼hi Poisson eiθi ðÞ log θi ðÞ¼αhþuh iþ h iþλh þδh i δh i ¼βi; i −1δ i −1;i −1 oden i ¼ i Ca ego ical p1;i ;p2;i ;p3;i  pj;i ¼ exp μj;i  P3 j¼1exp μj;i  μj;i ¼α þu iþ iþus kþ s kþλ þδ j;i whe e j= 1 indica es he declining oden popula ion le el, j= 2 is he inc easing le el, and j= 3 is he oden ’s popula ion a peak, and δ j;i Nð0;τ−1 δ Þ. The o he p io dis ibu ions o he andom e ec s e ms a e assumed he same as he 2-le el model. We u he assume ha he space- ime andom e ec s o human and oden a e p opo ional wi h one-yea lag. Tha is δh i αδ i −1;i −1, i.e. δh i ¼βi; i −1δ i −1;i −1whe e βi; i −1 is he p opo ional pa ame e . This speci ica ion is de- eloped o examine he lagged e ec o oden s a us, δ i −1;i −1, a le el j= i -1 in heal h dis ic ia ime -1on he numbe o human cases h ough he space- ime in e ac ion e m,δh i . Model e alua ion To e alua e he models, we use wo goodness o i mea- su es: he De iance In o ma ion C i e ion (DIC) [16,17] whe e he e ec i e numbe o pa ame e s is es ima ed in e ms o de iance’s a iance, and he Wa anabe-Akaike in o ma ion c i e ion (WAIC) [18–20]. Bo h measu es a e compu ed unde he likelihood o human da a o compa e he models’ i wi h and wi hou he con ex ual a iables. We also compa e he pos e io s anda d de ia- ions o θ i om he wo models (bina y and ca ego ical) wi h he oden da a, wi h hose om a model based only human da a, o examine he bene i s o inco po a ing animal da a in su eillance. Resul s a e ob- ained om 10,000 pos e io samples using WinBUGS so wa e a e a bu n-in pe iod o 10,000 d aws. To as- sess he mixing o pos e io sample s, we adop Gelman’sR bs a is ics p oposed in [18,21] o mul iple chain con e gence and con e ged chains should ha e he alue o R bapp oxima ely 1. Resul s The his og ams o R bes ima es o θ i om pos e io sam- ple unde he models a e displayed in Fig. 3. The R bes i- ma es unde all he models a e app oxima ely o less han 1.005 which indica es he chains con e ge o a pos- e io dis ibu ion. Table 1displays he DIC and he measu es o model pe o mance. We compa ed he models (bina y s. poly omous) on hei DIC and WAIC alues unde he human likelihood. The bina y model wi hou he con ex ual e ec shows he smalles DIC and WAIC alues and hence i can be conside ed as ha - ing he bes i o he da a. To p o ide e idence o he bene i s om inco po a ing oden in o ma ion in o he model, he pos e io es ima es o s anda d de ia ion (SD) o θ i om bo h bina y and poly omous models a e compa ed and p esen ed in Table 2 o each a ea o e he ime pe iod. The SD es ima es o θ i wi h oden ’s in- o ma ion inco po a ed a e smalle han hose om he model ha has only human incidence. This esul sup- po s he in eg a ion o oden popula ion a iables o educe he unce ain y o ula emia isk es ima es. To help assess he p edic i e pe o mance o oden abundance da a on he occu ence o human cases, we de elop a me ic on he 0 o 1 scale, namely he deg ee o posi i e indica o (DP) o each heal h dis ic as DPi¼expðβp iÞ expðβp iÞþ1:The DP indica o is de i ed om he bina y model wi hou he con ex ual ac o s as his was he model wi h he lowes DIC and WAIC. High alues o DP (close o 1) would indica e heal h dis ic s wi h a high numbe o human ula emia cases in he cu en yea , gi en inc easing o a peak oden popu- la ions in he pas yea . DP can be in e p e ed in a simila ashion o he sensi i i y o a diagnos ic es . High alues o DP would sugges good p edic i e alue o he oden da a on he occu ence o human ula - emia cases. Yea -speci ic modeling was no conside ed due o insu icien da a. Thus posi i e dependence alues ep esen an a e aged e ec o oden popula- ions on human incidence ac oss all he yea s (Table 3). The e a e 8 (40%) heal h dis ic s, mos ly on he wes and sou h o he coun y, wi h mean DP alues la ge han 0.8 and he lowe 95% c edible in e al abo e 0.5 (Fig. 4). Ro ejanap ase e al. BMC Medical Resea ch Me hodology (2018) 18:72 Page 4 o 8 Discussion O he modi ica ions a e possible. Fo example, in join modeling human and oden da a we could conside hu- man cases being dependen on oden popula ion h ough p i as a ca ego ical co a ia e. Fo spa ial uni , smalle o adminis a i e a eas di e en om heal h dis- ic s may ha e led o mo e disc imina o y indings (o no gi en inc eased noise om smalle uni s). Simila ly, mo e in o ma i e da a on oden popula ion le els, e.g. oden densi ies as in o he s udies [11] migh ha e e- sul ed in mo e desc ip i e models. Roden popula ions luc ua e wi h a highly a ying ampli ude, which means ha abundances may a y subs an ially om one peak o he nex , e en wi hin he same egions [12]. I ula - emia ansmission o humans is a phase and densi y dependen p ocess, as i mos likely is [6], a ia ion in ole abundance du ing successi e peaks may educe he p edic i e alue o models employed he e. Subsequen s udies mus explo e he inco po a ion o da a on he p ecise loca ion o he oden apping si es h ough he use o some o m o in e pola ion [22]. In addi ion o hos popula ion changes, en i onmen al ac o s also seem o impac on he occu ence o ula emia ou - b eaks [23,24]. Inco po a ion o e idence on mosqui o dis ibu ion (no pu posely cap u ed a his momen in Finland), ain all and wa e bodies in o ou models would be s aigh o wa d. Conclusions Space- ime p oximi y and con ac pa e ns be ween humans and animals play a cen al ole in in ec ion isk. In his esea ch, we a emp ed o assess he su eillance ele ance o egula ly collec ed oden popula ion da a o i) imp o e ula emia isk es ima es and ii) in o m Table 1 DIC (pD) and WAIC (pWAIC) co esponding o he human likelihood o he model compa ison Roden s a us Con ex ual e ec DIC pD WAIC pWAIC Bina y Wi h 4269.945 1115.127 3463.587 557.5636 Wi hou 4262.807 1110.623 3458.687 555.3114 Poly omous Wi h 4276.408 1123.747 3465.682 561.8733 Wi hou 4324.426 1170.232 3482.997 585.1162 Fig. 3 His og ams o ^ Rs a is ics o θ i om pos e io sample unde models Ro ejanap ase e al. BMC Medical Resea ch Me hodology (2018) 18:72 Page 5 o 8 ea ly p edic ion o human ula emia cases in Finland. To ha e ec , we de eloped bina y and poly omous a chi- ec u es o join ly model human incidence and oden s a us wi h one-yea lag. Ou esul s e u ned a he e o- geneous pic u e bu o many heal h dis ic s oden popula ion s a us was ele an o he occu ence o hu- man ula emia cases. We ha e shown ha he inco po - a ion o oden popula ion da a led o an imp o emen in he accu acy o human isk es ima es in 15 (75%) heal h dis ic s, compa ed o models only conside ing human ula emia cases. Fu he mo e, ou pu posely buil indica o (DP) showed ha in 8 (40%) o he heal h dis ic s, inc easing and a -peak oden popula ions we e obus p edic o s o human ula emia cases in he ollowing yea . Howe e , o ew dis ic s (e.g. Länsi-- Pohja and Kainuu) whe e he model based only on hu- man da a leads o mo e p ecise es ima es o incidence, hese a eas also ha e he low alues o posi i e indica o (DP) wi h he co esponding c edible in e als c ossing 0.5. This sugges s ha he dis ibu ion o zoono ic pa h- ogens in animal and human popula ions spa ially a ies as we assumed acco ding o local bio ic and abio ic de- e minan s. To conduc u he in es iga ion, we need mo e in o ma ion on se e al co a ia es such as en i on- men al, beha io al, and socio-economic ac o s. How- e e , he pla o m p oposed in his esea ch can acili a e in iden i ica ion o geog aphical a eas ha a e po en ially sui able o ansmission. Ou objec i e was o de elop di e en models o combine mul iple da a sou ces al eady a ailable, on animals and humans, o be e in o m he occu ence o zoonoses. The p esen wo k shows he u iliza ion o animal popula ion da a (in he absence o animal heal h- ela ed da a on oden s) o in o m human isk. Al hough di e en model pa ame e iza ions and, in pa icula , e idence on o he pu a i e p edic o s, as epo ed elsewhe e [25], could con ibu e u he Table 2 S anda d de ia ion o θ i calcula ed om pos e io sample s o each a ea o e he ime pe iod o he models Heal h dis ic Bina y Ca ego ical Only Human Wi h con ex ual e ec Wi hou con ex ual e ec Wi h con ex ual e ec Wi hou con ex ual e ec Sou hwes Finland 1.0216 1.0193 1.1402 1.1569 1.3604 Sa akun a 3.6330 3.6124 3.5493 3.5371 3.6365 Kan a-Häme 0.7336 0.7354 0.7632 0.7689 1.0398 Pi kanmaa 3.2779 3.2862 3.2114 3.2071 3.4309 Päijä -Häme 0.9032 0.9011 0.9682 1.0048 1.0475 Kymenlaakso 2.4761 2.4859 2.5092 2.4819 2.7240 Sou h Ka elia 0.5381 0.5268 0.5841 0.6060 0.6480 Sou he n Sa onia 0.7490 0.7518 0.7448 0.7722 0.8808 Eas e n Sa onia 0.7536 0.7551 0.7024 0.6833 0.7279 No h Ka elia 0.5753 0.5695 0.5475 0.5732 0.5982 No he n Sa onia 1.5263 1.5273 1.4859 1.5119 1.6492 Cen al Finland 5.5499 5.5361 5.5562 5.6234 6.0488 Sou h Bo hnia 4.7209 4.7507 4.7506 4.7505 4.7708 Vaasa 2.1997 2.2187 2.2057 2.1912 2.1572 Cen al Bo hnia 3.2251 3.2411 3.2267 3.1927 3.1619 No h Bo hnia 7.7036 7.6829 7.6786 7.6660 7.5354 Kainuu 0.1984 0.1957 0.2255 0.2468 0.2596 Länsi-Pohja 0.7437 0.7415 0.7377 0.7399 0.6897 Lapland 0.4929 0.4905 0.4979 0.5332 0.6323 Helsinki and Uusimaa 3.3256 3.3243 3.3982 3.4146 3.8419 A e age o e all a eas 2.2174 2.2176 2.2242 2.2331 2.3421 Table 3 The mean alues and 95% c edible in e als (C I) o DP unde he bina y oden model wi hou he con ex ual e ec o 20 heal h dis ic s Heal h dis ic Lowe 95% C I Mean Uppe 95% C I Sou hwes Finland 0.0129 0.4974 0.9881 Sa akun a 0.8447 0.9686 1.0000 Kan a-Häme 0.0019 0.5099 0.9985 Pi kanmaa 0.7794 0.9428 0.9996 Päijä -Häme 0.0037 0.4921 0.9951 Kymenlaakso 0.0000 0.5057 1.0000 Sou h Ka elia 0.0004 0.5031 0.9996 Sou he n Sa onia 0.0001 0.5010 1.0000 Eas e n Sa onia 0.9407 0.9929 1.0000 No h Ka elia 0.0000 0.5005 1.0000 No he n Sa onia 0.0006 0.3543 0.9965 Cen al Finland 0.9485 0.9931 1.0000 Sou h Bo hnia 0.9276 0.9901 1.0000 Vaasa 0.9621 0.9953 1.0000 Cen al Bo hnia 0.9755 0.9973 1.0000 No h Bo hnia 0.8998 0.9832 1.0000 Kainuu 0.0004 0.5060 0.9992 Länsi-Pohja 0.0000 0.5789 1.0000 Lapland 0.0013 0.5064 0.9993 Helsinki and Uusimaa 0.0347 0.4788 0.9568 Ro ejanap ase e al. BMC Medical Resea ch Me hodology (2018) 18:72 Page 6 o 8 e idence o be e in o m human isk, ou p oposed me hodology demons a es i s abili y o quan i y he associa ion be ween he oden s a us and human incidence. This is po en ially use ul in p edic ion o human ou b eak when pu in he heal h-policy pe spec i e. Abb e ia ions C I: C edible in e al; DIC: De iance In o ma ion C i e ion; DP: Deg ee o posi i e indica o ; ICAR: In insic condi ional au o eg essi e model; SD: S anda d de ia ion; WAIC: Wa anabe-Akaike in o ma ion c i e ion Acknowledgemen s We would like o hank he e iewe s o commen s ha g ea ly imp o ed he manusc ip . Funding This esea ch is pa ially suppo ed by he Facul y o T opical Medicine, Mahidol Uni e si y. The unding body had no ole in he design o analysis o he s udy, in e p e a ion o esul s, o w i ing o he manusc ip . A ailabili y o da a and ma e ials The da a om he Na ional Ins i u e o Heal h and Wel a e o Finland is a ailable on public domain and upon eques . The da a om he Na u al Resou ces Ins i u e is a ailable o om he ep esen ing au ho s upon eques . Au ho s’con ibu ions Au ho s CR, AL and VJDRV designed he s udy wi h c i ical e iew om HR. CR pe o med he s a is ical analyses in consul a ion wi h AL, VJDRV, HR, JS, OH and HH. CR d a ed he pape wi h inpu om AL and VJDRV. HR, JS, OH and HH we e esponsible o c i ical e ision and imp o emen s o he manusc ip . All au ho s ead and app o ed he inal manusc ip . E hics app o al and consen o pa icipa e Su eillance da a om he Na ional In ec ious Disease Regis e is agg ega e, de-iden i ed da a o public use and he seconda y analyses a e no subjec ed o e hical app o al p ocess, acco ding o he Finnish In ec ious Disease Ac (Sec ion 42). Consen o publica ion No Applicable. Compe ing in e es s The au ho s decla e ha hey ha e no compe ing in e es s. Publishe ’sNo e Sp inge Na u e emains neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a ilia ions. Au ho de ails 1 Depa men o T opical Hygiene, Facul y o T opical Medicine, Mahidol Uni e si y, Ra cha hewi, Bangkok 10400, Thailand. 2 Depa men o Public Heal h Sciences, Medical Uni e si y o Sou h Ca olina, Cha les on, SC 29425, USA. 3 Depa men o Ve e ina y Biosciences, Facul y o Ve e ina y Medicine, Uni e si y o Helsinki, Helsinki, Finland. 4 Na ional Ins i u e o Heal h and Wel a e, Helsinki, Finland. 5 Na u al Resou ces Ins i u e Finland, Helsinki, Finland. 6 School o Ve e ina y Medicine, Uni e si y o Su ey, Guild o d, UK. Recei ed: 28 July 2017 Accep ed: 27 June 2018 Re e ences 1. V bo a L, e al. U ili y o algo i hms o he analysis o in eg a ed Salmonel la su eillance da a. Epidemiol In ec . 2016;144(10):2165–75. 2. Wend A, K eienb ock L, Campe A. Join use o dispa a e da a o he su eillance o Zoonoses: a easibili y s udy o a one heal h app oach in Ge many. Zoonoses Public Heal h. 2016;63(7):503–14. 3. Rossow H, e al. Risk ac o s o pneumonic and ulce oglandula ula aemia in Finland: a popula ion-based case-con ol s udy. Epidemiol In ec . 2014; 142(10):2207–16. 4. Eliasson H, e al. The 2000 ula emia ou b eak: a case-con ol s udy o isk ac o s in disease-endemic and eme gen a eas, Sweden. Eme g In ec Dis. 2002;8(9):956–60. 5. Dennis DT, e al. Tula emia as a biological weapon: medical and public heal h managemen . Jama. 2001;285(21):2763–73. 6. Rossow H, e al. Incidence and se op e alence o ula aemia in Finland, 1995 o 2013: egional epidemics wi h cyclic pa e n. Eu o Su eill. 2015;20(33). h ps://doi.o g/10.2807/1560-7917.ES2015.20.33.21209 7. Tä n ik A, Sands öm G, Sjös ed A. Epidemiological analysis o ula emia in Sweden 1931–1993. FEMS Immunol Med Mic obiol. 1996;13(3):201–4. 8. Rein jes R, e al. Tula emia ou b eak in es iga ion in Koso o: case con ol and en i onmen al s udies. Eme g In ec Dis. 2002;8(1):69–73. 9. Allue M, e al. Tula aemia ou b eak in Cas illa y León, Spain, 2007: an upda e. Eu o Su eill. 2008;13(32) 10. G unow, R., e al., Su eillance o ula aemia in Koso o*, 2001 o 2010.2012. 11. Luque-La ena JJ, e al. Tula emia ou b eaks and common ole (Mic o us a alis) i up i e popula ion dynamics in no hwes e n Spain, 1997–2014. Vec o Bo ne Zoono ic Dis. 2015;15(9):568–70. 12. Ko pela K, e al. Nonlinea e ec s o clima e on bo eal oden dynamics: mild win e s do no nega e high-ampli ude cycles. Glob Chang Biol. 2013; 19(3):697–710. 13. Sane J, e al. Regional di e ences in long- e m cycles and seasonali y o Puumala i us in ec ions, Finland, 1995–2014. Epidemiol In ec . 2016;144(13): 2883–2888. 14. Besag J. Spa ial in e ac ion and he s a is ical analysis o la ice sys ems. J R S a Soc Se B Me hodol. 1974:192–236. Fig. 4 Map o mean o DP unde he bina y oden model wi hou he con ex ual e ec o each heal h dis ic Ro ejanap ase e al. BMC Medical Resea ch Me hodology (2018) 18:72 Page 7 o 8 15. Gelman A. P io dis ibu ions o a iance pa ame e s in hie a chical models (commen on a icle by B owne and D ape ). Bayesian Anal. 2006;1(3):515–34. 16. Spiegelhal e DJ, e al. Bayesian measu es o model complexi y and i . J R S a Soc Se ies B S a Me hodol. 2002;64(4):583–639. 17. Celeux G, e al. De iance in o ma ion c i e ia o missing da a models. Bayesian Anal. 2006;1(4):651–73. 18. Gelman A, e al. Bayesian da a analysis, ol. 2. USA: Chapman & Hall/CRC Boca Ra on, FL; 2014. 19. Gelman A, Hwang J, Veh a i A. Unde s anding p edic i e in o ma ion c i e ia o Bayesian models. S a Compu . 2014;24(6):997–1016. 20. Wa anabe S. A widely applicable Bayesian in o ma ion c i e ion. J Mach Lea n Res. 2013;14(Ma ):867–97. 21. B ooks SP, Gelman A. Gene al me hods o moni o ing con e gence o i e a i e simula ions. J Compu G aph S a . 1998;7(4):434–55. 22. Diggle PJ, Menezes R, Su Tl. Geos a is ical in e ence unde p e e en ial sampling. J R S a Soc: Se C: Appl S a . 2010;59(2):191–232. 23. Fai h S, e al. G ow h condi ions and en i onmen al ac o s impac ae osoliza ion bu no i ulence o F ancisella ula ensis in ec ion in mice. F on Cell In ec Mic obiol. 2012;2:126. 24. Leblebicioglu H, e al. Ou b eak o ula emia: a case–con ol s udy and en i onmen al in es iga ion in Tu key. In J In ec Dis. 2008;12(3):265–9. 25. A iza-Miguel J, e al. Molecula in es iga ion o ula emia ou b eaks, Spain, 1997–2008. Eme g In ec Dis. 2014;20(5):754. Ro ejanap ase e al. BMC Medical Resea ch Me hodology (2018) 18:72 Page 8 o 8