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AcellularautomatonmodelforthetransmissiondynamicsofschistosomiasisYunLiu,KaiChu,XiaoliXu,HaiweiWuDepartmentofPathogenBiologyNanjingMedicalUniversityNanjing,ChinaChengWanDepartmentofPublicServiceManagementNanjingMedicalUniversityNanjing,ChinaAbstractInthispaper,anewstochasticmodelbasedoncellularautomataisestablishedtosimulatetheoccurrenceanddevelopmentofSchistosomajaponicumS.japonicuminfectioninanendemicpopulation.Weincludedtheprocessofthepathogeninvasionfromexposuretowormdevelopmentandtillwormdeathwhentheinfectionisclearedinthemodel.WefurtherutilizedthemodeltopredicttheprevalenceastheoutcomesoftheselectedchemotherapycarriedoutinJiahuvillage.Comparingmodelpredictedprevalenceandintensitieswiththeobservedparameters,itisanticipatedthatourcellularautomatontransmissionmodelcanserveasatoolforstudyingschistosomiasistransmissiondynamicsinendemicareas.KeywordsS.japonicumcellularautomataSjCAmodeltransmissiondynamicsprevalenceintensityofinfectionI.INTRODUCTIONSchistosomiasisisamajorparasiticdiseasethatrankssecondonlytomalariaintermsofhumansufferinginthetropics.Amongthethreespeciesofschistosomes,onlyS.japonicumisendemicinChinaandmainlydistributedintheareasofintermediateandlowerreachesoftheYangtzeRiver,especiallythePoyangLakeandDongtingLake1,2.Thesimulationofdiseasedynamicsisvitallyimportantasitenablesonetobetterunderstandtheepidemiologyandcontrolmeasuresofschistosomiasis.Inthepastfewdecades,manyresearchers35devotedtothemathematicalmodelforthetransmissiondynamicsofschistosomiasisbyequationbasedmodelingEBM,themainformofwhichwereaseriesofdetermineddifferentialequations.Aftermathematicalmodelswereestablished,theshorttermandlongtermoutcomesofdiseasescanbepredictedinaparticularparameterssetting.Itisnotedthatthosemodelswereperformedincontinuoussystemsimulation.Translationofthepopulationdynamicsandstochasticsintodifferential/differenceequationformwasnottrivial.Besides,thosemodelsusuallytrackedtheaveragewormburdenwithouttakingthevariationsamongindividualsintoaccount.Itisimportanttonotethatomittingthestochasticityorthediscretenatureoftheindividualsoftenleadstoabsurdresults.Mostrecently,computerstochasticsimulatingmethodshavebeenwidelyusedtomimicthetransmissionandimmunedynamicsofdiseases6,7,includingcellularautomataCA.CAisadynamicalsysteminwhichspace,time,andthestatesarediscrete.Unlikeequationbasedmodels,CAmodelsfocusontheindividualandcanthereforehandlebothhomogeneousandheterogeneouspopulations.Thetranslationoftheconceptualmodelintoanumericalsettingisusuallytechnicallysimpleandstraightforward.Hence,CAmodelshavebeendevelopedtosimulatemanybiologicalsystems.Inthispaper,astochasticmodelbasedonCAwenameitasSjCAisestablishedtosimulatethetransmissiondynamicsofschistosomasisjaponicaintheendemicarea.TheSjCAmodelisusedtomimiceachindividualsstateandeffectsoftheselectedchemotherapycarriedoutinJiahuvillage.Andtheoutcomesofshistosomiasisinthisareacanbepredicted.Bycomparingtheobservedprevalenceandintensitieswiththepredicteddataof2006inJiahuvillage,theeffectsofSjCAmodelareshownsatisfactory.II.MATERIALSANDMETHODSA.StudypopulationandsamplecollectionInDecember2005,peoplelivinginJiahuvillagewererecruitedfora2yearcrosssectionalinvestigation8.LocatedonthesoutheasternshoreofPoyangLakeinJiangxiProvince,thisvillagewasaS.japonicumendemicarea.Aquestionnairewassubmittedtocollectthewatercontactofeachresident.Variablesrecordedinthequestionnaireincludedthetypeofactivity,andthefrequencyofwatercontactandsoon.Thescoresofwatercontactrangedfrom0to80.Ateachsurvey,twostoolsampleswerecollectedfromparticipantsatof35daysintervals.KatoKatztechniquewasusedtodetecteggsinthestoolsandresultswererecordedaseggspergramEPG9.Allresidentsfoundtobeeggpositivereceivedasingleoraldoseofpraziquantelof40mg/kgbodyweight.TheselectedchemotherapywascarriedoutinJanuaryof2006,onemonthlaterthanthefirstsurvey.ThestudypopulationinSjCAmodelismadeupofparticipantswithEPGresultsinthe2consecutiveyears.Thereare706subjectsinthestudypopulationaged574years,outofwhich,134eggpositiveindividualsandtheprevalencewas18.98in2005while94eggpositiveindividualsand13.31ofprevalencein2006.ThegeometricmeanofEPGwas0.985±1.548and0.472±1.103,respectively.Figure1showstheresultsofthegeometricmeanofEPGby8agecategoriesof10yearseachinthe2yearsurveys.B.FrameworkofSjCAmodelThedefiningcharacteristicsofCAmodelsarecell,itsneighbourcells,rulesandthespatialenvironmentlattice.Each9781424447138/10/25.00©2010IEEEFigure1.ResultsofthegeometricmeanofEPGby8agecategoriesof10yeaseachin2005greybarsand2006whitebars.Figure2.ModellingflowchartforthesimulationofthranmissiondynamicsoftheinfectionwithS.japonicumcell,definedbyapointinaregularspatiallattice,canhaveanyoneofafinitenumberofstatesthatareupdatedaccordingtoasetoflogicalrules.Thestateofeachcellatasubsequenttimestepisdependentonthecellsownstateand/orthestatesofitsneighboursatthecurrenttimestep.Inourmodel,eachgridrepresentscertaingeographicdistrictinJiahuvillageofJiangxiProvince.TheelementsofeachindividualaredescribedbyPERSON.Wetakeonedayasatimestep.Ateachtimestep,thechangesofwormburdenineachindividualarerelatedtowaterexposure,numberofschistosomesacquiredperwatercontact,wormestablishmentfunctioni.e.fractionofacquiredcercariaesurvivingandthedeathofadultworm.Thepredictionsofprevalenceandintensitiescanbeobtainedaftercertaintimesteps.TheflowchartofsimulationisshowninFigure2.Foreachindividuali,theprincipalvariabletrackedinthemodeliswormburdeniw.TwodifferentparametertypesareusedTableI1fixedparametersthathavethesamevalueinallsimulations,2uncertainparametersforwhichweperformanuncertainanalysis.Besides,inthemodel,thehouselocationisdefinedbythelongitude,latitudeandaltitudeingeographicinformationsystemGIS.C.RulesinSjCAmodel1InitiationaProductionofbasicelementsThenumberofsimulatedindividualsis706,thesizeofstudypopulation.Accordingtotheobserveddata,elementsofeachindividualincludingageia,sexis,longitude,latitudeandaltitudebyGISofeachresidentcanbedetermined.bWormburdeniwEPGofeachindividualiEPGcanbeobtainedfromthe2yearsurveys.Butdataonwormburdenofeachindividualiwarenotavailable.Itisassumedthatthereisaconstantaveragenumberofeggsperwormmatingprobabilitiesarenottakenintoaccountgivenbyie.iwisrelatedtoiEPGby/iiiwEPGe1cAveragewormestablishmentfunctionfItisadensitydependentwormestablishmentfunctionwhichdescribesaprocessinwhichthelikehoodofdevelopingintoanadultwormisassumedtobereducedwhenthecurrentwormburdenishighduetoacrowdingeffect,toconcomitantimmunity,orboth.fcanbegivenas10111kMMfekMγ−−−2ThedistributionofwormsamongstudypopulationinJiahuvillagereflectsanegativebinomialdistributionwiththemeanintensityofinfectionM4.64andtheaggregationparameterk0.0149.Withγ0.0015,f0.7595dWatercontactiρConsideringsomepeoplewiththescoreof0onwatercontact,i.e.iθ0,couldcontactwithcontaminantedwater,wereviseiθwithRandscaledtotherequiredvalueofiρ.eNumberofcercariaeacquiredperpersonperwatercontactεεisassumedtobepropotionaltothedensityofOncomelaniasnails.Accordingtothepastfielddata11,εisanalysisedtorangein0.0037980.0456.2simulationateachtimestepatiεForeachindividuali,thetiεisheredefinedastheexpectednumberofcercariaeacquiredperpersonperwatercontactateachtimestepwithoutacquiredimmunity.tiεisassumedtobearandomnumberwithintherangeofε.bSeasonalfluctuationUnlikeschistosomiasisinPhilippines,severalprocessesofhumanschistosomeinfectioninChinacanbedisturbedbyclimateanddisplayseasonalluctuation14.Furthermore,winteristoocoldandOncomelaniasnailscouldnotshedcercariaelowerthan1℃15。Hence,2ρρspringsummerautumn3intwerε04cEstablishmentfunctionforeachindividualifTheestablishmentfunctionamongindividualsinCAmodelwasassumedtoobeyanegativebinomialdistribution.ThenaTABLEI.DEFAULTPARAMETERSETseriesofrandomnumbersobeyingthisnegativebinomialdistributioncanbegeneratedby,,,,706,1iffnbinrandAAnbinrandAAnbinrandrp∗∈NbinrandANbinrandA5nbinrandAAisarandomnumber,whichbelongstothesetofNbinrandA.Alltheelementsinthesetobeyanegativebinomialdistributionwiththemeanpandaggregationparameterr.Themeanofalltheelementsarestandardedto1.AndthesizeofNbinrandAis706.dTheforceofinfectioniΛThenumbeofnewsuccessfuladdedschistosomesisrelatedtoiiiifερΛ6eiΛNotonlythosefactorsdescribedabove,butalsothetypeandlocationofcontaminantedwatercaninfluencetheprobabilityandseverityofhumanschistosomeinfection.ItisassumedthatthenearertheresidentsliveawayfromthePoyangLake,thehigherprobabilitiesandthemoresevereofschistosomeinfectionsare.ThedistancethateachindividualliveawayfromthePoyangLakeisdefinedasid.iΛisrelatedtoidby,iiiiiiiitdceiltdroundρρ≥ΛΛΛΛ7fThemortalityrateµforwormµispercapitamortalityrateforschistosomes.gThewormburdenofeachindividualatasubsequenttimestepisdependentonthenewaddedwormsandthemortalityrateforwormatthecurrenttimestep,givenby1iiiiwtwtwtµΛ−83TheeffectsofchemotherapyInourmodel,weassumethatonaverage98oftheinfectedresidentstreatedwithpraziquantalarecured,andthata60reductioninwormintensityoccursinhumanswhoareinfected,treated,butnotcured.Thesimulationofeffectsofchemotherapystartatthe31sttimestep.III.RESULTSA.ExperimentaltimesItisshownthatinthesameparameterssetting,theeffectsofsimulationsfor100timesarenotsignificantlydifferentfromthatofsimulationsfor1000times.Hence,weadopt100timessimulationineachparametersetting.B.EffectsofSjCAmodelThesimulationssuggestthebestfitbetweentheobservedandthesimulatedresultswasobtainedusingR20.Thedesignofotherparametershavebeendescribedabove.1PrevalenceAsshowninFigure3,theobservedprevalencein2006is13.31.Allpredictedprevalencesfluctuatearoundthisvalue.AlthoughtherearesignificantdifferencesP0.05betweenthesimulatedandobservedprevalence,theaverageprevalenceof100predictedresults13.59isproximatelyidenticaltotheobservedprevalence.2IntensityofinfectionFigure4showsthepredictedandobservedresultsofthegeometricmeanofEPGby8agecategoriesof10yearseachin2006.Thereareslightdifferencesbetweenthesimulatedandobservedagespecificintensityofinfections.C.ModelingeffectsafterparametersregulationFigure5and6showthepredictedprevalencesof2006inJiahuvillagewithdifferentRanddifferentf.Itisindicatedthatthepredictedprevalencesof2006aredirectlyproportionaltoRandtheestablishmentfunctionf,andthebestfitbetweentheobservedandthesimulatedresultswereobtainedusingtheparameterssettingweadopt,withtheotherparametersunchanged.IV.DISCUSSIONWefirstlyestablishanewapproachbasedoncellularautomatatomodelingthetransmissiondynamicsofschistsosomiasisjaponica.ComparedwiththetraditionalsimulationmethodofEBM,CAmodelingischaracterizedbymimickingtheoccurrenceanddevelopmentofschistosomesineachindividualusingastochasticapproach.AlthoughtherearesignificantdifferencesbetweentheobservationsandpredictionsofprevalenceP0.05andintensities,consideringtherandomnessofeachsimulationbyCAmodel,westillthinkthatCAmodelcansatisfactorilydescribethedevelopmentofS.japonicuminfectioninJiahuvillageofJiangxiProvincebetween20052006.Thispapershowsthattheoneyeareffectsofthismodelaresatisfactory,butitstillneedsfurtherextensionandrefining.ParameterSymbolValueandunitsReferenceFixedTimestept1Minimundurationofsimulation1dayAgeiayearsSexis1or2LongitudeLatitudeAltitudeDistancethateachindividuallivesawayfromthePoyangLakeidEPGperwormie1014ScoresofwatercontactiθRevisedvaluesforwatercontactR20WatercontactiρAveragewormestablishmentfunctionf0.75955,10Wormlifespan1/µ4years15Efficacyofchemotherapy98UncertainforindividualiwormestablishmentfunctionifvariesExpectednumberofcercariaeacquiredperpersonperwatercontactε0.0037980.045611ExpectednumberofcercariaeacquiredperwatercontactateachtimestepitεvariesThetranmissioncyclecanbeclosedbyincludingthedynamicsoftheintermediatehostOncomelaniasnailsandthereserviorhostespeciallythebuffaloeswhichplayanimportantroleinFigure3.Resultsofprevalenceincludingthepredictedprevalenceineachsimulationsquarespotandtheobservedprevalenceblackline.Figure4.ResultsoftheagespecificgeometricmeansofEPGinafunctionof8agecategoriesof10yearseach,includingtheobservationswhitebarsandpredictionsgreybarsbyagecategory.Figure5.Resultsofpredictedprevalencesof2006inJiahuvillagewithdifferentR.Figure6.Resultsofthepredictedprevalencesof2006inJiahuvillagewithdifferentestablishmentfunctionf.thetranmissionandasinfectionsourcesinendemicareas.Furthermore,parametersinthemodelarebasedonfielddataandestimatedequationinexpertopinion,andsomeofthemarenotavailableinfieldinvestigation.InthehopethatCAmodelwilleventuallycontributetotheepidemiologyandtransmissiondynamicsofschistosomiasisjaponica,effortstofurtherdevelopthemodelwillbecontinued.ACKNOWLEDGMENTThisresearchissupportedbytheNationalNaturalScienceFoundationofChina30671836andNaturalScienceFoundationofJiangsuEducationalCommittee08KJD310006.REFERENCES1Ross,A.G.,etal.,FaecaleggaggregationinhumansinfectedwithSchistosomajaponicuminChina.ActaTrop,1998.702p.20510.2YangJZ,Z.Z.,AnalysisontheHouseholdsClusterofPositiveSerumofSchistosomaisis.ChinseJOURNALofChangzhiMedicalCollege,2008.221p.29303Chan,M.S.,etal.,ThedevelopmentofanagestructuredmodelforschistosomiasistransmissiondynamicsandcontrolanditsvalidationforSchistosomamansoni.EpidemiolInfect,1995.1152p.32544.4Chan,M.S.,etal.,Dynamicaspectsofmorbidityandacquiredimmunityinschistosomiasiscontrol.ActaTrop,1996.622p.10517.5Liang,S.,D.Maszle,andR.C.Spear,AquantitativeframeworkforamultigroupmodelofSchistosomiasisjaponicumtransmissiondynamicsandcontrolinSichuan,China.ActaTrop,2002.822p.26377.6Vlas,S.J.,etal.,SCHISTOSIMamicrosimulationmodelfortheepidemiologyandcontrolofschistosomiasis.AmJTropMedHyg,1996.555Supplp.1705.7Chavali,A.K.,etal.,Characterizingemergentpropertiesofimmunologicalsystemswithmulticellularrulebasedcomputationalmodeling.TrendsImmunol,2008.2912p.58999.8Lin,D.D.,etal.,EvaluationofIgGELISAforthediagnosisofSchistosomajaponicuminahighprevalence,lowintensityendemicareaofChina.ActaTrop,2008.1072p.12833.9Zhang,Y.Y.,etal.,EvaluationofKatoKatzexaminationmethodinthreeareaswithlowlevelendemicityofschistosomiasisjaponicainChinaABayesianmodelingapproach.ActaTrop,2009.1121p.1622.10Anderson,R.M.,May,R.M.,Infectiousdiseasesofhumansdynamicsandcontrol.OxfordOxfordUniversityPress,1991.11YuanJ.H.,ZhangS.J.,WuG.L.,Theinfluenceofdiscontinuousandirregularchemotharapyforpopulationstotheepidemiologyofschistosomiasisjaponica.ChineseInformationCompilationfortheStudyofSchistosomiasis,19861990p.5859.12Lin,D.D.,ZhangS.J.,ThegeographicenvironmentandtranmissionofschistosomiasisinPoyangareas.ChinseJOURNALofEpidemiology,2002.234p.9093.13YangGJ,U.J.,SunLP,etal.,EffectoftemperatureonthedevelopmentofSchistosomajaponicumwithinOncomelaniahupensis,andhibernationofO.hupensis.ParasitologyResearch,2007.1004p.695700.14Chan,M.S.,etal.,Dynamicmodelsofschistosomiasismorbidity.AmJTropMedHyg,1996.551p.5262.15Anderson,R.M.,May,R.M.,Helminthinfectionsofhumansmathematicalmodels,populationdynamicsandcontrol.AdvParasitol,1985.24p.1101.
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