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外文资料--A cellular automaton model for the transmission dynamics of schistosomiasis.PDF

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外文资料--A cellular automaton model for the transmission dynamics of schistosomiasis.PDF

ACELLULARAUTOMATONMODELFORTHETRANSMISSIONDYNAMICSOFSCHISTOSOMIASISYUNLIU,KAICHU,XIAOLIXU,HAIWEIWUDEPARTMENTOFPATHOGENBIOLOGYNANJINGMEDICALUNIVERSITYNANJING,CHINACHENGWANDEPARTMENTOFPUBLICSERVICEMANAGEMENTNANJINGMEDICALUNIVERSITYNANJING,CHINAABSTRACTINTHISPAPER,ANEWSTOCHASTICMODELBASEDONCELLULARAUTOMATAISESTABLISHEDTOSIMULATETHEOCCURRENCEANDDEVELOPMENTOFSCHISTOSOMAJAPONICUMSJAPONICUMINFECTIONINANENDEMICPOPULATIONWEINCLUDEDTHEPROCESSOFTHEPATHOGENINVASIONFROMEXPOSURETOWORMDEVELOPMENTANDTILLWORMDEATHWHENTHEINFECTIONISCLEAREDINTHEMODELWEFURTHERUTILIZEDTHEMODELTOPREDICTTHEPREVALENCEASTHEOUTCOMESOFTHESELECTEDCHEMOTHERAPYCARRIEDOUTINJIAHUVILLAGECOMPARINGMODELPREDICTEDPREVALENCEANDINTENSITIESWITHTHEOBSERVEDPARAMETERS,ITISANTICIPATEDTHATOURCELLULARAUTOMATONTRANSMISSIONMODELCANSERVEASATOOLFORSTUDYINGSCHISTOSOMIASISTRANSMISSIONDYNAMICSINENDEMICAREASKEYWORDSSJAPONICUM;CELLULARAUTOMATA;SJCAMODEL;TRANSMISSIONDYNAMICS;PREVALENCE;INTENSITYOFINFECTIONIINTRODUCTIONSCHISTOSOMIASISISAMAJORPARASITICDISEASETHATRANKSSECONDONLYTOMALARIAINTERMSOFHUMANSUFFERINGINTHETROPICSAMONGTHETHREESPECIESOFSCHISTOSOMES,ONLYSJAPONICUMISENDEMICINCHINAANDMAINLYDISTRIBUTEDINTHEAREASOFINTERMEDIATEANDLOWERREACHESOFTHEYANGTZERIVER,ESPECIALLYTHEPOYANGLAKEANDDONGTINGLAKE1,2THESIMULATIONOFDISEASEDYNAMICSISVITALLYIMPORTANTASITENABLESONETOBETTERUNDERSTANDTHEEPIDEMIOLOGYANDCONTROLMEASURESOFSCHISTOSOMIASISINTHEPASTFEWDECADES,MANYRESEARCHERS35DEVOTEDTOTHEMATHEMATICALMODELFORTHETRANSMISSIONDYNAMICSOFSCHISTOSOMIASISBYEQUATIONBASEDMODELINGEBM,THEMAINFORMOFWHICHWEREASERIESOFDETERMINEDDIFFERENTIALEQUATIONSAFTERMATHEMATICALMODELSWEREESTABLISHED,THESHORTTERMANDLONGTERMOUTCOMESOFDISEASESCANBEPREDICTEDINAPARTICULARPARAMETERSSETTINGITISNOTEDTHATTHOSEMODELSWEREPERFORMEDINCONTINUOUSSYSTEMSIMULATIONTRANSLATIONOFTHEPOPULATIONDYNAMICSANDSTOCHASTICSINTODIFFERENTIAL/DIFFERENCEEQUATIONFORMWASNOTTRIVIALBESIDES,THOSEMODELSUSUALLYTRACKEDTHEAVERAGEWORMBURDENWITHOUTTAKINGTHEVARIATIONSAMONGINDIVIDUALSINTOACCOUNTITISIMPORTANTTONOTETHATOMITTINGTHESTOCHASTICITYORTHEDISCRETENATUREOFTHEINDIVIDUALSOFTENLEADSTOABSURDRESULTSMOSTRECENTLY,COMPUTERSTOCHASTICSIMULATINGMETHODSHAVEBEENWIDELYUSEDTOMIMICTHETRANSMISSIONANDIMMUNEDYNAMICSOFDISEASES6,7,INCLUDINGCELLULARAUTOMATACACAISADYNAMICALSYSTEMINWHICHSPACE,TIME,ANDTHESTATESAREDISCRETEUNLIKEEQUATIONBASEDMODELS,CAMODELSFOCUSONTHEINDIVIDUALANDCANTHEREFOREHANDLEBOTHHOMOGENEOUSANDHETEROGENEOUSPOPULATIONSTHETRANSLATIONOFTHECONCEPTUALMODELINTOANUMERICALSETTINGISUSUALLYTECHNICALLYSIMPLEANDSTRAIGHTFORWARDHENCE,CAMODELSHAVEBEENDEVELOPEDTOSIMULATEMANYBIOLOGICALSYSTEMSINTHISPAPER,ASTOCHASTICMODELBASEDONCAWENAMEITASSJCAISESTABLISHEDTOSIMULATETHETRANSMISSIONDYNAMICSOFSCHISTOSOMASISJAPONICAINTHEENDEMICAREATHESJCAMODELISUSEDTOMIMICEACHINDIVIDUAL’SSTATEANDEFFECTSOFTHESELECTEDCHEMOTHERAPYCARRIEDOUTINJIAHUVILLAGEANDTHEOUTCOMESOFSHISTOSOMIASISINTHISAREACANBEPREDICTEDBYCOMPARINGTHEOBSERVEDPREVALENCEANDINTENSITIESWITHTHEPREDICTEDDATAOF2006INJIAHUVILLAGE,THEEFFECTSOFSJCAMODELARESHOWNSATISFACTORYIIMATERIALSANDMETHODSASTUDYPOPULATIONANDSAMPLECOLLECTIONINDECEMBER2005,PEOPLELIVINGINJIAHUVILLAGEWERERECRUITEDFORA2YEARCROSSSECTIONALINVESTIGATION8LOCATEDONTHESOUTHEASTERNSHOREOFPOYANGLAKEINJIANGXIPROVINCE,THISVILLAGEWASASJAPONICUMENDEMICAREAAQUESTIONNAIREWASSUBMITTEDTOCOLLECTTHEWATERCONTACTOFEACHRESIDENTVARIABLESRECORDEDINTHEQUESTIONNAIREINCLUDEDTHETYPEOFACTIVITY,ANDTHEFREQUENCYOFWATERCONTACTANDSOONTHESCORESOFWATERCONTACTRANGEDFROM0TO80ATEACHSURVEY,TWOSTOOLSAMPLESWERECOLLECTEDFROMPARTICIPANTSATOF35DAYSINTERVALSKATOKATZTECHNIQUEWASUSEDTODETECTEGGSINTHESTOOLSANDRESULTSWERERECORDEDASEGGSPERGRAMEPG9ALLRESIDENTSFOUNDTOBEEGGPOSITIVERECEIVEDASINGLEORALDOSEOFPRAZIQUANTELOF40MG/KGBODYWEIGHTTHESELECTEDCHEMOTHERAPYWASCARRIEDOUTINJANUARYOF2006,ONEMONTHLATERTHANTHEFIRSTSURVEYTHESTUDYPOPULATIONINSJCAMODELISMADEUPOFPARTICIPANTSWITHEPGRESULTSINTHE2CONSECUTIVEYEARSTHEREARE706SUBJECTSINTHESTUDYPOPULATIONAGED574YEARS,OUTOFWHICH,134EGGPOSITIVEINDIVIDUALSANDTHEPREVALENCEWAS1898IN2005WHILE94EGGPOSITIVEINDIVIDUALSAND1331OFPREVALENCEIN2006THEGEOMETRICMEANOFEPGWAS09851548AND04721103,RESPECTIVELYFIGURE1SHOWSTHERESULTSOFTHEGEOMETRICMEANOFEPGBY8AGECATEGORIESOF10YEARSEACHINTHE2YEARSURVEYSBFRAMEWORKOFSJCAMODELTHEDEFININGCHARACTERISTICSOFCAMODELSARECELL,ITSNEIGHBOURCELLS,RULESANDTHESPATIALENVIRONMENTLATTICEEACH9781424447138/10/25002010IEEEFIGURE1RESULTSOFTHEGEOMETRICMEANOFEPGBY8AGECATEGORIESOF10YEASEACHIN2005GREYBARSAND2006WHITEBARSFIGURE2MODELLINGFLOWCHARTFORTHESIMULATIONOFTHRANMISSIONDYNAMICSOFTHEINFECTIONWITHSJAPONICUMCELL,DEFINEDBYAPOINTINAREGULARSPATIALLATTICE,CANHAVEANYONEOFAFINITENUMBEROFSTATESTHATAREUPDATEDACCORDINGTOASETOFLOGICALRULESTHESTATEOFEACHCELLATASUBSEQUENTTIMESTEPISDEPENDENTONTHECELL’SOWNSTATEAND/ORTHESTATESOFITSNEIGHBOURSATTHECURRENTTIMESTEPINOURMODEL,EACHGRIDREPRESENTSCERTAINGEOGRAPHICDISTRICTINJIAHUVILLAGEOFJIANGXIPROVINCETHEELEMENTSOFEACHINDIVIDUALAREDESCRIBEDBYPERSONWETAKEONEDAYASATIMESTEPATEACHTIMESTEP,THECHANGESOFWORMBURDENINEACHINDIVIDUALARERELATEDTOWATEREXPOSURE,NUMBEROFSCHISTOSOMESACQUIREDPERWATERCONTACT,WORMESTABLISHMENTFUNCTIONIEFRACTIONOFACQUIREDCERCARIAESURVIVINGANDTHEDEATHOFADULTWORMTHEPREDICTIONSOFPREVALENCEANDINTENSITIESCANBEOBTAINEDAFTERCERTAINTIMESTEPSTHEFLOWCHARTOFSIMULATIONISSHOWNINFIGURE2FOREACHINDIVIDUALI,THEPRINCIPALVARIABLETRACKEDINTHEMODELISWORMBURDENIWTWODIFFERENTPARAMETERTYPESAREUSEDTABLEI1FIXEDPARAMETERSTHATHAVETHESAMEVALUEINALLSIMULATIONS,2UNCERTAINPARAMETERSFORWHICHWEPERFORMANUNCERTAINANALYSISBESIDES,INTHEMODEL,THEHOUSELOCATIONISDEFINEDBYTHELONGITUDE,LATITUDEANDALTITUDEINGEOGRAPHICINFORMATIONSYSTEMGISCRULESINSJCAMODEL1INITIATIONAPRODUCTIONOFBASICELEMENTSTHENUMBEROFSIMULATEDINDIVIDUALSIS706,THESIZEOFSTUDYPOPULATIONACCORDINGTOTHEOBSERVEDDATA,ELEMENTSOFEACHINDIVIDUALINCLUDINGAGEIA,SEXIS,LONGITUDE,LATITUDEANDALTITUDEBYGISOFEACHRESIDENTCANBEDETERMINEDBWORMBURDENIWEPGOFEACHINDIVIDUALIEPGCANBEOBTAINEDFROMTHE2YEARSURVEYSBUTDATAONWORMBURDENOFEACHINDIVIDUALIWARENOTAVAILABLEITISASSUMEDTHATTHEREISACONSTANTAVERAGENUMBEROFEGGSPERWORMMATINGPROBABILITIESARENOTTAKENINTOACCOUNTGIVENBYIEIWISRELATEDTOIEPGBY/IIIWEPGE1CAVERAGEWORMESTABLISHMENTFUNCTIONFITISADENSITYDEPENDENTWORMESTABLISHMENTFUNCTIONWHICHDESCRIBESAPROCESSINWHICHTHELIKEHOODOFDEVELOPINGINTOANADULTWORMISASSUMEDTOBEREDUCEDWHENTHECURRENTWORMBURDENISHIGHDUETOA‘CROWDINGEFFECT’,TOCONCOMITANTIMMUNITY,ORBOTHFCANBEGIVENAS10111KMMFEKMΓ−−−2THEDISTRIBUTIONOFWORMSAMONGSTUDYPOPULATIONINJIAHUVILLAGEREFLECTSANEGATIVEBINOMIALDISTRIBUTIONWITHTHEMEANINTENSITYOFINFECTIONM464ANDTHEAGGREGATIONPARAMETERK00149WITHΓ00015,F07595DWATERCONTACTIΡCONSIDERINGSOMEPEOPLEWITHTHESCOREOF0ONWATERCONTACT,IEIΘ0,COULDCONTACTWITHCONTAMINANTEDWATER,WEREVISEIΘWITHRANDSCALEDTOTHEREQUIREDVALUEOFIΡENUMBEROFCERCARIAEACQUIREDPERPERSONPERWATERCONTACTΕΕISASSUMEDTOBEPROPOTIONALTOTHEDENSITYOFONCOMELANIASNAILSACCORDINGTOTHEPASTFIELDDATA11,ΕISANALYSISEDTORANGEIN0003798004562SIMULATIONATEACHTIMESTEPATIΕFOREACHINDIVIDUALI,THETIΕISHEREDEFINEDASTHEEXPECTEDNUMBEROFCERCARIAEACQUIREDPERPERSONPERWATERCONTACTATEACHTIMESTEPWITHOUTACQUIREDIMMUNITYTIΕISASSUMEDTOBEARANDOMNUMBERWITHINTHERANGEOFΕBSEASONALFLUCTUATIONUNLIKESCHISTOSOMIASISINPHILIPPINES,SEVERALPROCESSESOFHUMANSCHISTOSOMEINFECTIONINCHINACANBEDISTURBEDBYCLIMATEANDDISPLAYSEASONALLUCTUATION14FURTHERMORE,WINTERISTOOCOLDANDONCOMELANIASNAILSCOULDNOTSHEDCERCARIAELOWERTHAN1℃15。HENCE,2ΡΡSPRINGSUMMERAUTUMN3INTWERΕ04CESTABLISHMENTFUNCTIONFOREACHINDIVIDUALIFTHEESTABLISHMENTFUNCTIONAMONGINDIVIDUALSINCAMODELWASASSUMEDTOOBEYANEGATIVEBINOMIALDISTRIBUTIONTHENATABLEIDEFAULTPARAMETERSETSERIESOFRANDOMNUMBERSOBEYINGTHISNEGATIVEBINOMIALDISTRIBUTIONCANBEGENERATEDBY,,,,706,1IFFNBINRANDAANBINRANDAANBINRANDRP∗∈NBINRANDANBINRANDA5NBINRANDAAISARANDOMNUMBER,WHICHBELONGSTOTHESETOFNBINRANDAALLTHEELEMENTSINTHESETOBEYANEGATIVEBINOMIALDISTRIBUTIONWITHTHEMEANPANDAGGREGATIONPARAMETERRTHEMEANOFALLTHEELEMENTSARESTANDARDEDTO1ANDTHESIZEOFNBINRANDAIS706DTHEFORCEOFINFECTIONIΛTHENUMBEOFNEWSUCCESSFULADDEDSCHISTOSOMESISRELATEDTOIIIIFΕΡΛ6EIΛNOTONLYTHOSEFACTORSDESCRIBEDABOVE,BUTALSOTHETYPEANDLOCATIONOFCONTAMINANTEDWATERCANINFLUENCETHEPROBABILITYANDSEVERITYOFHUMANSCHISTOSOMEINFECTIONITISASSUMEDTHATTHENEARERTHERESIDENTSLIVEAWAYFROMTHEPOYANGLAKE,THEHIGHERPROBABILITIESANDTHEMORESEVEREOFSCHISTOSOMEINFECTIONSARETHEDISTANCETHATEACHINDIVIDUALLIVEAWAYFROMTHEPOYANGLAKEISDEFINEDASIDIΛISRELATEDTOIDBY,IIIIIIIITDCEILTDROUNDΡΡ≥ΛΛΛΛ7FTHEMORTALITYRATEFORWORMISPERCAPITAMORTALITYRATEFORSCHISTOSOMESGTHEWORMBURDENOFEACHINDIVIDUALATASUBSEQUENTTIMESTEPISDEPENDENTONTHENEWADDEDWORMSANDTHEMORTALITYRATEFORWORMATTHECURRENTTIMESTEP,GIVENBY1IIIIWTWTWTΛ−83THEEFFECTSOFCHEMOTHERAPYINOURMODEL,WEASSUMETHATONAVERAGE98OFTHEINFECTEDRESIDENTSTREATEDWITHPRAZIQUANTALARECURED,ANDTHATA60REDUCTIONINWORMINTENSITYOCCURSINHUMANSWHOAREINFECTED,TREATED,BUTNOTCUREDTHESIMULATIONOFEFFECTSOFCHEMOTHERAPYSTARTATTHE31STTIMESTEPIIIRESULTSAEXPERIMENTALTIMESITISSHOWNTHATINTHESAMEPARAMETERSSETTING,THEEFFECTSOFSIMULATIONSFOR100TIMESARENOTSIGNIFICANTLYDIFFERENTFROMTHATOFSIMULATIONSFOR1000TIMESHENCE,WEADOPT100TIMESSIMULATIONINEACHPARAMETERSETTINGBEFFECTSOFSJCAMODELTHESIMULATIONSSUGGESTTHEBESTFITBETWEENTHEOBSERVEDANDTHESIMULATEDRESULTSWASOBTAINEDUSINGR20THEDESIGNOFOTHERPARAMETERSHAVEBEENDESCRIBEDABOVE1PREVALENCEASSHOWNINFIGURE3,THEOBSERVEDPREVALENCEIN2006IS1331ALLPREDICTEDPREVALENCESFLUCTUATEAROUNDTHISVALUEALTHOUGHTHEREARESIGNIFICANTDIFFERENCESP005BETWEENTHESIMULATEDANDOBSERVEDPREVALENCE,THEAVERAGEPREVALENCEOF100PREDICTEDRESULTS1359ISPROXIMATELYIDENTICALTOTHEOBSERVEDPREVALENCE2INTENSITYOFINFECTIONFIGURE4SHOWSTHEPREDICTEDANDOBSERVEDRESULTSOFTHEGEOMETRICMEANOFEPGBY8AGECATEGORIESOF10YEARSEACHIN2006THEREARESLIGHTDIFFERENCESBETWEENTHESIMULATEDANDOBSERVEDAGESPECIFICINTENSITYOFINFECTIONSCMODELINGEFFECTSAFTERPARAMETERSREGULATIONFIGURE5AND6SHOWTHEPREDICTEDPREVALENCESOF2006INJIAHUVILLAGEWITHDIFFERENTRANDDIFFERENTFITISINDICATEDTHATTHEPREDICTEDPREVALENCESOF2006AREDIRECTLYPROPORTIONALTORANDTHEESTABLISHMENTFUNCTIONF,ANDTHEBESTFITBETWEENTHEOBSERVEDANDTHESIMULATEDRESULTSWEREOBTAINEDUSINGTHEPARAMETERSSETTINGWEADOPT,WITHTHEOTHERPARAMETERSUNCHANGEDIVDISCUSSI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