Dynamic Modeling of Diseases and Pests

283 Pages·2009·3.405 MB·English

by  Bruce Hannon, Matthias Ruth (auth.)

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
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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