GENERIC REACTION-DIFFUSION MODEL FOR TRANSMISSION OF MOSQUITO-BORNE DISEASES: RESULTS OF SIMULATION WITH ACTUAL CASES

Transcription

1 GEERC REACTO-FFUO OEL FOR TRAO OF OQUTO-BORE EAE: REULT OF ULATO WT ACTUAL CAE Cynha u Lan Kon an Jane Laan epamen of Compuaonal ene an ahemas Fauly of Compue ene an nfomaon Tehnoloy Unves alaysa aawak 900 Koa amaahan aawak alaysa Fauly of Enneen Compun an ene wnune Unvesy of Tehnoloy aawak Campus Jalan mpan Ta 950 Kuhn aawak alaysa Emals: ynkonml@homalom an lane@unmasmy KEYWOR malaa ffuson ene moel mosquo-one seases ansmsson ABTRACT osquoes an ause a lo of suffen o humans y ansfen seases alaa s a mosquo-one sease ause y he paase Plasmoum s an aue pul healh ssue n many ounes an an e faal Consen he smlay n he ansmsson of mosquo-one seases a ene spaal-empoal moel fo ansmsson of mulple mosquo-one seases was fomulae The man onen hee s whehe he numeal esuls poue y hs eaonffuson ene moel ae ompaale wh aual ases ee he aual nofe weekly ases fo 6 weeks whh s fom week 9 n 0 o week n 0 fo fou ss n aawak alaysa namely Kap on Belaa an au ae ompae wh smulaons of he ene moel The anom movemen of human an mosquo populaons ae aken no aoun s sovee ha he numeal esuls ae n oo aeemen o he aual malaa ases n he fou ss TROUCTO osquo-one seases suh as enue yellow feve flaass Japanese Enephals Zka feve an malaa ae a few seases whh an e ansme fom human o human houh mosquo es A mosquo wll nes a pahoen when akes a loo meal on an nfeous human e when es a suseple human nes salva an an-oaulans no he human s loo Aon o he Wol ealh Oanzaon hee wee esmae mllon malaa ases epoe wolwe an 8000 eahs n 05 Wol ealh Oanzaon 05 sease moels ae essenal n he amoy of epemoloal eves as hey an e ulze n spe of lmaons n aa The mahemaal moels ae ase on he unesann of he ynams of he hos an pahoen an ae use o pove foeas of he pevalene of an nfeon The faos whh onue o he spea of he nfeon an e enfe an o eemne he es onol measues o eaae hem These moels use mahemaal equaons o nepe he ynams of seases enefoh epemens an e one whou he neessy o ay ou n eal lfe whh mh e unehal By on so quesons suh as wha-f an e answee eemns moels onss of onay ffeenal equaons fo eample moels y Ross 90 Aneson an ay 979 Tumwne e al 007 an Laan e al 009 The ompamenal mahemaal moels llusae whehe he sease wll peval o es ou n a populaon n me Reseahes have een eamnn he mpa of spaal heeoeney an movemens on he spea an pessene of seases Consequenes of onol measues suh as vanaon n loal eon an s ouome an e analyze Thee ae a few appoahes o moeln spaal spea eapopulaon moels Clff 99 n e al 0 ve a populaon o mulple see oups Thee ae wo ways hese moels ae onsue he moly appoah an he ossouple meapopulaon appoah os meapopulaon moels ae he oss-ouple appoah whh onse ansmsson whn an eween oups paally onnuous moels suh as eaonffuson moels assume he populaon s sue onnuously aoss he envonmen an no n see Poeens 0h Euopean Confeene on oelln an mulaon EC Thosen Claus Fank emann hael anz Olve Rose Eos B: / B: C

2 populaons paally onnuous moels Kon an Laan 005 Anţa an Capasso 0 aana an Yan 007 allow mahemaal analyss of he eneal paens of he spea of seases Lae-ase moels oup a paula se as a supopulaon an n ellula auomaa neaons ae assume o ou only eween nehoun s Gson 997 Geoaph nfomaon sysems G ae use o seue olle spaal aa an when neee ean an o ep he spaal fas ene an e ulze fo aa on populaons sease pevalene envonmenal aa an eae a onneon amon hem Eamples of applaon of G ae ae ou y Chapu e al 00 an Kon 000 A eaon-ffuson ene moel fo mosquoone seases was fomulae Kon an Laan 05 ase on he smlay n he manne of ansmsson of hese nfeons All mosquo-one seases ae spea houh veo mosquo; hus hs ommonaly s aken no aoun A eneal moel whh nopoaes oh spaal an empoal faos as well as aes o he many ffeen mosquo-one seases s pofale as mos moels onsue ae fo a spef sease n hs pape he popose new ene moel wll e susse n he ne seon Afe ha he epoe weekly malaa ases n fou ss n aawak ae ompae o smulaons fom he ene moel fo he spea of mosquo-one nfeon n he las seon onlusons an plans fo fuue wok ae susse OEL FORULATO osquo-one an veo-one seases ompamenal moels wee eleae an he smlaes enfe efoe fomulan he ene moel Kon an Laan 0 Ths s eause he oeve s o fomulae a ene moel whh an e apple o ffeen mosquo-one seases The mahn ompamens use fo veo-one seases ae foun o e suseple an nfeous fo oh human an veo populaon Thus he ene mosquo-one seases moel onsss of useple- nfeous ompamens fo oh human hos an veo mosquo Kon an Laan 05 As we wan o nvesae he effe of spaal heeoeney an movemen of human an mosquo populaon on he spea of seases spaal faos ae nopoae n he ene moel The ommon ems use fo spaal spea wee eemne y suyn he spao-empoal sease moels an hey ae foun o e ffuson oeffens an loaon epenen paamees Tems suh as h ae eah ae foe of nfeon an eovey ae wee eulaly nlue n veo-one sease moels The foal pon hee s n he way hese seases ae ansme The anom movemen of human an mosquo populaons ae nlue an hey ae epe as anom walks whee a oup of spesn humans an mosquoes ehave ompaavely o a oup of pales ffusn n Bownan moon a lae spaal sale Canell an Cosne 00 ee he human populaon s ve no wo ompamens namely suseple an nfeous The ensy of suseple an nfeous human populaons ae an whee loaon s onsee s assume ha ynams of oal human populaon oey whee oal human ensy s epesens he anom movemen of oal human populaon aoss he envonmen The ffuson oeffen poays he hane n he ae of hane of human movemen s assume ha ffuson oeffen fo oh suseple an nfeous s onsan The mosquo populaon s also ve no suseple an nfeous an ae he spaal ensy of suseple an nfeous mosquo espevely oeove oal mosquo ensy s vn us he oal human an mosquo ensy a any pon an me ae an espevely An nfeous mosquo ansfes he nfeon f akes loo meal on a suseple human The ae ha suseple human es nfee s whee s he poaly of ansmsson pe e fom an nfeous mosquo o a suseple human s he mean ae of es pe mosquo an s he poaly an nfeous mosquo es a human The n ae s ensy-epenen on he oal human populaon as one y Wan an Zhao 0 n aon he nume of new nfeous ases s wh he laen peo fo human ven as ene he sease s onsee o e ansfee o an nfeous human efoe he laen peo A suseple mosquo es nfee when akes a loo meal on an nfeous human The ae ha suseple mosquo es nfee s whee s ansmsson pe e fom an nfeous human o a suseple mosquo an s he poaly ha a mosquo es an nfeous human The nume of new mosquo

3 nfeous ases s akn no aoun ha ona oue efoe he mosquo nuaon peo The eaon-ffuson ene moel fo ansmsson of mosquo-one nfeon s elow: Paamees use n he moel aove ae as sae n Tale All paamees ae assume o e non-neave Tale : Paamees use n he paal ffeenal equaons moel Paamees ffuson ae fo humans ffuson ae fo mosquoes human eumen ae ansmsson poaly pe e fom human eah ae eovey ae mosquo eumen ae ansmsson poaly pe e fom mosquo eah ae nuaon peo n humans nuaon peo n mosquoes seahn ae of a mosquo me fo a mosquo o onsume loo pe e OEL AALY ne he ene mosquo-one seases moel s fo mulple mosquo-one seases we wan o nvesae whehe hs moel s ale o epoue malaa ases n fou ffeen ss n aawak The aual ases ae aken fom aawak Weekly Ep ews y aawak ae ealh epamen as all malaa ases shoul e nofe whn hous as epoe y he Veo Bone sease Conol eon aawak ealh epamen 0 mulaon esuls fom he ene moel ae ompae wh aual pevalene n fou ss n aawak e Kap on Belaa an au fom week 9 n 0 o week n 0 ha s fo 6 weeks Paamees use ae sae n Tale As hs sysem s mae up of nonlnea paal ffeenal equaons he moel s seze usn he fne ffeene meho Cank olson meho s use as s unononally sale fo ffuson equaons Thomas 995 Fsly le us sa wh equaon y wn a he pon Thus wll e wen as s a enee ffeene appomaon fo a The em s appomae usn he aveae of seon enee ffeenes fo an mla appomaon s ae ou on he ohe populaons ha s fo nfeous human suseple mosquo an nfeous mosquo The equaons afe sezaon an eaanemen ae: 5

4 Tale : Values of paamees use fo Kap on au an Belaa ss 6 7 an 8 Equaons 5-8 fom an alea sysem; hene he sysem s aane n ma fom an solve smulaneously o oan he numeal esuls The nal aa fo suseple an nfeous ompamens fo oh human an mosquo populaons ae polynomal funons To oan he aual ensy of nfeous humans aual ases n on Kap Belaa an au an e oane y vn he pevalene of malaa o he aea of eah s Then he sanes eween hese loaons ae alulae aon o he laue an lonue; hus we e Belaa au onkap Paamees Kap mensons on au Belaa oue 0 km week km week week epamen of ass alaysa aawak 0 5 week Wan an Zhao 0 8 week Chns eelman week epamen of ass alaysa aawak Wllams an Blolan ehlhon week week Aneson an ay 00 week Co

5 Polynomal funons ae foun o ee o epesen he ensy aa fo eah of hese loaons ene he nal aa use ae: an [ 0] [ 0] [075] eumann ounay onon s apple whee an ne we o no have he aa fo mosquo populaon n he ss n aawak he nal aa fo suseple an nfeous mosquo ae esmae o f he aual pevalene To oan es f he oeve s o aan a vey low oo mean squae eo RE RE s he ffeene eween he pee an aual ensy an he smalle s he ee The paamee value fo mosquo suh as eah ae s eemne y fnn he es f numeal esul ompae o pevalene n he fou ss Fo mosquo eah ae f we onse he aveae lfespan of mosquo only n eal suaon he paamee value wll e aoun 0-05 week - [Kon an Laan o e pulshe] As s no possle o measue ely he lfe span of mosquoes n naue he value s vae unl we oan he es f uve The values fo mosquo eah ae n he fou loaons ffe an ae lowe han he pee value fo eal suaon As s hallenn o ee on he value of he spee of he anom movemen of oh human an mosquo populaons he ffuson ae fo human populaon an mosquo populaon ae ee upon ompason of aual an smulaon of he nfeous human ensy Compan Fue whh eps he aual ases n on Kap Belaa an au an he numeal esul poue fom he ene moel n Fue s lea ha he manue an ehavo of he nfeous human ensy s n oo aeemen fo he ffeen loaons n me e we woul lke o ompae he smulae nfeous human ensy o ha of he aual nofe -5 ases n eah of he fou ss The nal onons use ae he same eep fo: [ 0] [ ] [075] Ths s eause he hane n he nal aa fo nfeous mosquo populaon aually neases he auay of he moel n poun smulae ases whh ae smla o aual ases ene he nal onon plays a val ole n en a oo appomaon The smulae ensy s aphe on he same as as he aual ases o ompae hem vsually an he RE s alulae n Fue he ensy of weekly aual malaa ases n on an he pee ases neases fom week 0 o week 5 The sease pevals n he populaon an splays smla ehavo fo oh he aual an smulae ases RE fo hs paula se of aa s 6 0 The numeal esul of he ene moel s ensy of malaa nfeous humans n Kap esemles he aual nofe ases losely as epe n Fue The RE s a low 57 0 alaa ases sue fom week 0 o week 5 an ae alke n oh ases As shown n Fue 5 he aual ensy of nfeous humans s slhly hhe u oh splay smla owh of he sease unl week 5 The RE s alulae o e 68 0 Fnally he aual pevalene of malaa n au an e seen n Fue 5 The numeal esul fom he ene moel shows a seay almos lnea nemen whle he nofe ases eh a shape nease up o week 5 hen onnues o ow u a a slowe ae Boh esuls aee ha he sease pevals n au y week 5 The RE fo hs ompason s Fue : The aual ensy of nfeous humans n me an spae -5

6 Fue : The smulae ensy of nfeous humans n me an spae Fue 5: Weekly aual malaa ases n Belaa fom week 9 n 0 o week n 0 an smulae ases Fue : Weekly aual malaa ases n on fom week 9 n 0 o week n 0 an smulae ases Fue : Weekly aual malaa ases n Kap fom week 9 n 0 o week n 0 an smulae ases Fue 6: Weekly aual malaa ases n au fom week 9 n 0 o week n 0 an smulae ases COCLUO A FUTURE WORK A ene moel fo mulple mosquo-one seases s susse n hs pape Ths ene moel s fomulae o e ulze fo many ffeen ypes of mosquo-one seases ee we woul lke o use hs moel o poue esuls fo malaa mulaons fom hs ene moel ae ompae wh aual malaa ases n fou ss n aawak namely Kap on Belaa an au Thy-s weekly nofe malaa ases ae oane fom aawak ae ealh epamen an ompae wh smulaons The spaoempoal moel s foun o e ale o epoue aual ases n he fou loaons The sease s enem n all fou ss The smulae ases fo on an Kap ae foun o e n oo aeemen wh ha of he aual nofe ases umeal esuls fo Belaa an au shows smla ehavo ha s he sease pevals n he populaon alhouh he manues slhly ffe n hs suy s foun ha he ene moel fo mosquo-one seases s ale o epoue malaa ases whh oespon o he fou ss n aawak Fo fuue wok we woul lke o suy whehe hs ene moel s ale o epoue esuls

7 fo ohe mosquo-one seases suh as enue Faos onenn spaal heeoeney whh onues o he spea of seases wll also e enfe an he opmal onol measue an e eemne ACKOWLEGET Ths wok was suppoe y Unves alaysa aawak an nsy of Euaon houh he Funamenal Reseah Gan heme nume FRG//0/CT07/UA/0/6 o JLaan REFERECE Aneson R an R ay 979 Populaon Boloy of nfeous seases n aue 80:6-67 Aneson R R ay an B Aneson 99 nfeous seases of humans: ynams an onol Vol 8 Ofo: Ofo unvesy pess Anţa an VCapasso 0 alzaon of a eaon ffuson sysem moelln a lass of spaally suue epem sysems va feeak onol n onlnea Analyss: Real Wol Applaons Canell R an C Cosne 00 paal eoloy va eaon-ffuson equaons John Wley & ons Chapu E K; J eek; an R eme 00 paal Analyss of human anuloy ehlhoss nea Lyme Conneu n Emen nfeous seases Chns 005 Ph hess Poam n Apple ahemas Unvesy of Azona Tuson AZ Clff A; P ae; an F oup 99 The Geoaph uue of easles Epems n he noheasen Une aes n Amean Jounal of Epemoloy Co FE 00 soy of human paasoloy n Clnal mooloy evews epamen of ass alaysa aawak Yeaook of ass 0 n ; X Wan; an X n 0 Gloal saly of muloup enue sease ansmsson moel n Jounal of Apple ahemas Gson GJ 997 akov Chan one Calo ehos fo Fn paoempoal ohas oels n Plan Epemoloy n Appl ass 6 5- Kon U 000 Rsk aps:: Tansmsson an Buen of Veo-one seases n Paasoloy oay 68-5 Kon C an J Laan 0 Reaon-ffuson ene moel fo mosquo-one seases n nfomaon Tehnoloy n Asa CTA 0 8h nenaonal Confeene EEE - Kon CL an J Laan 05 mpa of human ffuson an spaal heeoeney on ansmsson ynams of mosquo-one seases n T n Asa CTA 05 9h nenaonal Confeene EEE -6 Kon CL an J Laan 06 mulan he spea of malaa usn a ene ansmsson moel fo mosquoone nfeous seases n n nenaonal Confeene on ahemaal enes an ass C06 To e pulshe Laan J; CL Kon; an F Juan 009 eemns alaa Tansmsson oel wh Aque mmuny n Poeens of he Wol Coness on Enneen an Compue ene 009 Vol WCEC 009 an Fanso aana A an Yan 007 A spaal moel o ese he enue popaaon n Tens n Apple an Compuaonal ahemas ehlhon 00 Enylope efeene of paasoloy: seases eamen heapy Vol pne ene & Busness ea eelman J 98 noulaon an eovey aes n he malaa moel of ez olneau an Thomas n ahemaal Bosenes Ross R The pevenon of malaa John uay Lonon 90 aawak ealh epamen 0 aawak Weekly Ep ews Thomas J W 995 umeal Paal ffeenal Equaons: Fne ffeene ehos Tes n Apple ahemas Beln ew Yok: pne-vela Tumwne J; JYT usha; an L Luoo 007 A mahemaal moel fo he ynams of malaa n a human hos an mosquo veo wh empoay mmuny n Apple ahemas an Compuaon Wan W an X-Q Zhao XQ 0 A nonloal an meelaye eaon-ffuson moel of enue ansmsson n A Jounal on Apple ahemas Wllams A an PB Blolan 00 alaa onol un mass populaon movemens an naual sases aonal Aaemes Pess Wol ealh Oanzaon WO 05 Ahevn he malaa G ae: evesn he nene of malaa AUTOR BOGRAPE CYTA L KO s uenly pusun he Ph n Compuaonal ene n Unves alaysa aawak he s neese n mahemaal moeln populaon ynams an moeln he spea of nfeous seases e pesen wok s on spao-empoal moeln of ansmsson of mosquo-one seases suh as enue an malaa JAE LABA s uenly an Assoae Pofesso a he Fauly of Compue ene an nfomaon Tehnoloy Unves alaysa aawak UA he eeve he Ph n Compuaonal ahemas spealzn n Flu ynams fom he mpeal Collee of ene Tehnoloy an ene Lonon UK n 00 e Bahelo eee n Apple ahemas was fom he same unvesy n 995 he oane he ase n Compuaon n 997 fom he Unvesy of anhese nsue of ene an Tehnoloy UK e eseah nees s n ompuaonal moeln of ynamal sysems