Dynamic Modeling of Diseases and Pests Bruce Hannon • Matthias Ruth Dynamic Modeling of Diseases and Pests ABC BruceHannon MatthiasRuth UniversityofIllinois UniversityofMaryland 220DavenportHall,MC150 2101VanMunchingHall Urbana,IL61801 CollegePark,MD20782 ISBN:978-0-387-09559-2 e-ISBN:978-0-387-09560-8 LibraryofCongressControlNumber:2008930143 (cid:1)c 2009SpringerScience+BusinessMedia,LLC Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Usein connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware, orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. 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Printedonacid-freepaper 9 8 7 6 5 4 3 2 1 springer.com Contents PartI Introduction 1 TheWhyandHowofDynamicModeling........................... 3 1.1 Introduction................................................. 3 1.2 Static,ComparativeStatic,andDynamicModels.................. 5 1.3 ModelComplexityandExplanatoryPower....................... 6 1.4 ModelComponents .......................................... 8 1.5 ModelinginSTELLA ........................................ 10 1.6 AnalogyandCreativity ....................................... 21 1.7 STELLA’sNumericSolutionTechniques ........................ 22 1.8 SourcesofModelError ....................................... 26 1.9 TheDetailedModelingProcess ................................ 29 1.10 QuestionsandTasks.......................................... 30 2 BasicEpidemicModels........................................... 31 2.1 BasicModel ................................................ 31 2.2 EpidemicModelwithRandomness ............................. 34 2.3 LossofImmunity............................................ 36 2.4 TwoPopulationEpidemicModel............................... 38 2.5 EpidemicwithVaccination .................................... 43 2.6 QuestionsandTasks.......................................... 47 3 InsectDynamics ................................................. 49 3.1 MatchingExperimentsandModelsofInsectLifeCycles ........... 49 3.2 OptimalInsectSwitching ..................................... 53 3.3 Two-AgeClassParasiteModel................................. 54 3.4 QuestionsandTasks.......................................... 58 v vi Contents PartII Applications 4 MalariaandSickleCellAnemia................................... 63 4.1 Malaria .................................................... 63 4.1.1 BasicMalariaModel.................................. 63 4.1.2 QuestionsandTasks .................................. 70 4.2 SickleCellAnemiaandMalariainBalance ...................... 72 4.2.1 SickleCellAnemia................................... 72 4.2.2 QuestionsandTasks .................................. 76 5 Encephalitis..................................................... 83 5.1 St.LouisEncephalitis ........................................ 83 5.2 QuestionsandTasks.......................................... 90 6 ChagasDisease..................................................101 6.1 ChagasDiseaseSpreadandControlStrategies....................102 6.2 QuestionsandTasks..........................................110 7 LymeDisease....................................................115 7.1 LymeDiseaseModel .........................................115 7.2 QuestionsandTasks..........................................128 8 ChickenPoxandShingles ........................................137 8.1 ModelAssumptionsandStructure ..............................138 8.2 QuestionsandTasks..........................................144 9 Toxoplasmosis...................................................153 9.1 Introduction.................................................153 9.2 ModelConstruction ..........................................154 9.3 Results ....................................................156 9.4 QuestionsandTasks..........................................157 10TheZebraMussel ...............................................161 10.1 Introduction.................................................161 10.2 ModelDevelopment..........................................161 10.3 ModelResults...............................................166 10.4 QuestionsandTasks..........................................168 11BiologicalControlofPestilence....................................171 11.1 HerbivoryandAlgae .........................................171 11.1.1 Herbivore-AlgaePredator-PreyModel ...................171 11.1.2 QuestionsandTasks ..................................174 11.2 BluegillPopulationManagement...............................176 11.2.1 BluegillDynamics....................................176 11.2.2 ImpactsofFishing....................................178 11.2.3 ImpactsofDisease ...................................182 Contents vii 11.2.4 QuestionsandTasks ..................................183 11.3 WollyAdelgid ..............................................191 11.3.1 InfestationofFraserFir ...............................191 11.3.2 AdelgidandFirDynamics .............................191 11.3.3 QuestionsandTasks ..................................197 12Indirect Susceptible-Infected-Resistant Models of Arboviral ∗ EncephalitisTransmission .......................................205 12.1 ModelingWestNileVirusDynamicsEmilyWheelerandTraci Barkley ....................................................205 12.2 Susceptible-Infected-Resistant(SIR)Models inDynamicPopulations ......................................206 12.2.1 ModelStructureandBehavior..........................206 12.2.2 QuestionsandTasks ..................................208 12.3 BaseWNVSIRModelwithaDynamicVectorPopulation..........210 12.3.1 BaseModelStructureandBehavior .....................210 12.3.2 QuestionsandTasks ..................................213 12.4 AvianPopulationEffectsandSeasonalDynamics .................216 12.4.1 ModificationstotheBaseModel........................216 12.4.2 AvianDemographyandDiseasePersistence ..............218 12.4.3 WeatherasanExtrinsicDriverofOutbreakSeverity .......219 12.4.4 QuestionsandTasks ..................................222 13ChaosandPestilence.............................................225 13.1 BasicDiseaseModelwithChaos ...............................226 13.1.1 ModelSet-up........................................226 13.1.2 DetectingandInterpretingChaos .......................227 13.1.3 QuestionsandTasks ..................................230 13.2 ChaoswithNicholson-BaileyEquations .........................231 13.2.1 Host-ParasitoidInteractions............................231 13.2.2 QuestionsandTasks ..................................233 14CatastropheandPestilence .......................................237 14.1 BasicCatastropheModel......................................237 14.2 SpruceBudwormCatastrophe .................................240 14.3 QuestionsandTasks..........................................248 15SpatialPestilenceDynamics.......................................251 15.1 DiseasedandHealthyImmigratingInsects .......................251 15.1.1 QuestionsandTasks ..................................255 15.2 TheSpatialDynamicSpreadofRabiesinFoxes ..................260 15.2.1 Introduction .........................................260 15.2.2 FoxRabiesinIllinois .................................261 15.2.3 PreviousFoxRabiesModels ...........................262 15.2.4 TheRabiesVirus.....................................264 15.2.5 FoxBiology.........................................265 viii Contents 15.2.6 ModelDesign .......................................266 15.2.7 CellularModel.......................................267 15.2.8 ModelAssumptions ..................................269 15.2.9 GeoreferencingtheModelingProcess ...................269 15.2.10 SpatialCharacteristics ................................270 15.2.11 ModelConstraints....................................271 15.2.12 ModelResults .......................................271 15.2.13 RabiesPressure ......................................273 15.2.14 TheEffectsofDiseaseAlone...........................273 15.2.15 HuntingPressure.....................................274 15.2.16 ControllingtheDisease ...............................274 PartIII Conclusions 16Conclusion......................................................283 Index .............................................................285 Chapter 1 The Why and How of Dynamic Modeling 1.1 Introduction Fewtasksarenoblerthanthosethatimprovethelengthandqualityoflifeofhumans andtheirfellowspecies.Andfewtasksaremoredifficulttoaccomplish.Tobesuc- cessful, we must assess the vulnerabilities of individuals to attacks on their health andwell-being,wemustunderstandtheinteractionsofindividualswitheachother andtheirenvironment,andwemustanticipatethelikelyconsequencesofallthese factorsinanever-changingworld—individualvulnerabilitieschange,newdiseases andpestsemerge,oldonesreappear,newmeansaredevelopedtodetectandcom- bat adverse influences on health and well-being, and new standards for health and qualityoflifeareapplied. Therearemanydriversbehindthespreadofdiseasesandpests.Climatechange may create new temperature and precipitation regimes conducive to diseases and pests that would otherwise be irrelevant for particular locations. West Nile fever, malariaandencephalitis,forexample,areincreasinglyofconcerntopublichealth officials.Otherdriversarerelatedtoouruseoftechnologyinaglobalizingworld. For example, ballast water used in ships can carry with it organisms and spread themtoevermorefar-flungplaces.Increasedtravelofpeoplearoundtheglobecan promotedispersalofviruses,bacteria,fungi,andother“agents”thataffectthehealth andwell-beingofspeciesandecosystems. Strategiesforcontrollingthespreadofdiseasesandpests,andespeciallychang- ingtherootcausesforaspreadtooccur,havecreatedamulti-billion-dollarindustry involving the full gamut of societal defenses—from detection and monitoring, to chemical and pharmaceutical products, to medical care, to ecosystem design and restoration. Sound knowledge of the dynamics of diseases and pests and an un- derstanding of the changing roles and relationships among the drivers and the constraintsontheirspreadareneededtomakewisechoicesamongthevariousin- terventionoptions. Thisbookprovidesanintroductiontodynamicmodelingofdiseasesandpests— thevariousformsofinsulttothehealthandwell-beingofspecies,bothhumanand B.HannonandM.Ruth,DynamicModelingofDiseasesandPests, 3 ModelingDynamicSystems, (cid:1)c SpringerScience+BusinessMediaLLC2009 4 1 TheWhyandHowofDynamicModeling animal.Wedrawoninsightsfrombiology,epidemiology,andrelateddisciplinesto identifykeycomponentsof,andinfluenceson,humanandenvironmentalsystems. We use the graphical programming language STELLA to organize these insights intoformalmodelsthatcanberunonacomputer;wethenusethesemodelstoin- vestigate the dynamics of pestilence and explore alternative scenarios for outside interventionintothesystems’dynamics.Inparticular,welookforemergentprop- ertiesofthemodel—thoseresultsthatwedidnotexpect. Weconsiderthiskindofmodelingasasubtlecraft,anartformthatisintended to help us understand the future. And because of the complexity of dynamic sys- tems, the use of formal models and numbers is essential—they help us dispel the complexityofmanyreal-worldprocessesandforceustobespecific.Gooddynamic modelingisanart.Itrequiresmodelingexperiencethatdrawsuponmodelinganalo- giesforthecreationofnewandusefulmodels. Modeling dynamic systems is central to our understanding of real-world phe- nomena. We all create dynamic mental models of the world around us, dissecting our observations into cause and effect. Such mental models enable us, for exam- ple, to cross a busy street or hit a baseball successfully. But we are not mentally equipped to go much further. The complexities of social, economic, or ecological systemsandtheirinteractionsforceustouseaidsifwewanttounderstandmuchof anythingaboutthem. With the advent of personal computers and graphical programming, everyone cancreatemoresophisticatedmodelsofthephenomenaintheworldaroundus.As HeinzPagelsnotedinDreamsofReasonin1988,thecomputermodelingprocessis tothemindwhatthetelescopeandthemicroscopearetotheeye.Wecanmodelthe macroscopicresultsofmicrophenoma,andviceversa.Wecansimulatethevarious possiblefuturesofadynamicprocess.Wecanbegintoexplainandperhapsevento predict. In order to deal with these phenomena, we abstract from details and attempt to concentrateonthelargerpicture—aparticularsetoffeaturesoftherealworldorthe structurethatunderliestheprocessesthatleadtotheobservedoutcomes.Modelsare suchabstractionsofreality.Modelsforceustofacetheresultsofthestructuraland dynamicassumptionsthatwehavemadeinourabstractions. Theprocessofmodelconstructioncanberatherinvolved.However,itispossible to identify a set of general procedures that are followed frequently. These general proceduresareshowninsimplifiedcircularform(Figure1.1). Modelshelpusunderstandthedynamicsofreal-worldprocessesbymimicking with the computer the actual but simplified forces that are assumed to result in a system’sbehavior.Forexample,itmaybeassumedthatthenumberofpeoplecon- tractingadiseaseisdirectlyproportionaltothesizeoftheinfectedandsusceptible populations. In a simple version of this epidemic model, we may abstract away from a variety of factors that impede or stimulate the spread of a disease in addi- tion to factors directly related to the different population sizes and distance. Such anabstractionmayleaveuswithasufficientlygoodpredictoroftheknowninfec- tion rates, or it may not. If it does not, we reexamine the abstractions, reduce the assumptions, and retest the model for its new predictions. Models help us in the 1.2 Static,ComparativeStatic,andDynamicModels 5 Real Events Conclusions and Abstract Version Predictions of Real Events Model Fig.1.1 organizationofourthoughtsanddataandintheevaluationofourknowledgeabout themechanismsthatleadtothesystem’schange. Some people raise philosophic questions as to why one would want to model a system. As pointed out earlier, we all perform mental models of every dynamic system we face. We also learn that in many cases, those mental models are inade- quate.Withaformalmodelathand—amodelthatistransparentenoughforothers tounderstandandcritique,andonethatcanberunoverandoveragaintorevealits behavior under different assumptions—we can specifically address the needs and rewardsofmodeling. Throughoutthisbook,weencounteravarietyofnonlinear,time-laggedfeedback processes,somewithrandomdisturbancesthatgiverisetocomplexsystembehav- ior.Suchprocessescanbefoundinalargerangeofsystems.Thevarietyofmodels in the companion books of this series naturally span only a small range—but the insights on which these models are based can (and should) be used to inform the developmentofmodelsforsystemsthatwedonotcoverhere. Itisourintentiontoshowyouhowtomodel,nothowtousemodels,norhowto setupamodelforsomeoneelse’suse.Thelattertwoarecertainlyworthwhileac- tivities,butwebelievethatthefirststepislearningthemodelingprocess.Inthefol- lowingsection,weintroduceyoutothecomputerlanguagethatisusedthroughout thebook.Thiscomputerlanguagewillbeimmenselyhelpfulasyoudevelopanun- derstandingofdynamicsystemsandusethatunderstandingtosolvenewproblems. 1.2 Static,ComparativeStatic,andDynamicModels Mostmodelsfitinoneofthreegeneralclasses.Thefirsttypeconsistsofmodelsthat representaparticularphenomenonatapointoftime—thesearestaticmodels.For example, a map of the United States may depict the location and size of a city or therateofinfectionwithaparticulardisease,eachinagivenyear.Thesecondtype is the set of comparative static models that compare some phenomena at different