Modeling Infectious Diseases in Humans and Animals

385 Pages·2007·23.9 MB·English

by  Matt J. Keeling

Modeling Infectious Diseases
IN HUMANS AND ANIMALS
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Modeling Infectious Diseases
I N H U M A N S A N D A N I M A L S
Matt J. Keeling and Pejman Rohani
PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD
Copyright(cid:1)c 2008byPrincetonUniversityPress
PublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540
IntheUnitedKingdom:PrincetonUniversityPress,3MarketPlace,Woodstock,OxfordshireOX201SY
AllRightsReserved
LibraryofCongressControlNumber:2006939548
ISBN:978-0-691-11617-4
BritishLibraryCataloging-in-PublicationDataisavailable
ThisbookhasbeencomposedinTimesRoman
Printedonacid-freepaper.∞
press.princeton.edu
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
DedicatedtoAlisonandErin,
foralwaysmakingmelaughandsmile.
Lotsoflove
—MattKeeling
IdedicatethisbooktomywifeRebecca,
andmydaughtersMaeandSophia
Iloveandcherishyouall
—PejRohani
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Contents
Acknowledgments xiii
Chapter1 Introduction 1
1.1 TypesofDisease 1
1.2 CharacterizationofDiseases 3
1.3 ControlofInfectiousDiseases 5
1.4 WhatAreMathematicalModels? 7
1.5 WhatModelsCanDo 8
1.6 WhatModelsCannotDo 10
1.7 WhatIsaGoodModel? 10
1.8 LayoutofThisBook 11
1.9 WhatElseShouldYouKnow? 13
Chapter2 IntroductiontoSimpleEpidemicModels 15
2.1 FormulatingtheDeterministicSIRModel 16
2.1.1 TheSIRModelWithoutDemography 19
2.1.1.1 TheThresholdPhenomenon 19
2.1.1.2 EpidemicBurnout 21
2.1.1.3 WorkedExample:InfluenzainaBoardingSchool 26
2.1.2 TheSIRModelWithDemography 26
2.1.2.1 TheEquilibriumState 28
2.1.2.2 StabilityProperties 29
2.1.2.3 OscillatoryDynamics 30
2.1.2.4 MeanAgeatInfection 31
2.2 Infection-InducedMortalityandSI Models 34
2.2.1 MortalityThroughoutInfection 34
2.2.1.1 Density-DependentTransmission 35
2.2.1.2 FrequencyDependentTransmission 36
2.2.2 MortalityLateinInfection 37
2.2.3 FatalInfections 38
2.3 WithoutImmunity:TheSISModel 39
2.4 WaningImmunity:TheSIRSModel 40
2.5 AddingaLatentPeriod:TheSEIRModel 41
2.6 InfectionswithaCarrierState 44
2.7 Discrete-TimeModels 46
2.8 Parameterization 48
2.8.1 EstimatingR fromReportedCases 50
0
2.8.2 EstimatingR fromSeroprevalenceData 51
0
2.8.3 EstimatingParametersinGeneral 52
2.9 Summary 52
viii CONTENTS
Chapter3 HostHeterogeneities 54
3.1 Risk-Structure:SexuallyTransmittedInfections 55
3.1.1 ModelingRiskStructure 57
3.1.1.1 High-RiskandLow-RiskGroups 57
3.1.1.2 InitialDynamics 59
3.1.1.3 EquilibriumPrevalence 62
3.1.1.4 TargetedControl 63
3.1.1.5 GeneralizingtheModel 64
3.1.1.6 Parameterization 64
3.1.2 TwoApplicationsofRiskStructure 69
3.1.2.1 EarlyDynamicsofHIV 71
3.1.2.2 ChlamydiaInfectionsinKoalas 74
3.1.3 OtherTypesofRiskStructure 76
3.2 Age-Structure:ChildhoodInfections 77
3.2.1 BasicMethodology 78
3.2.1.1 InitialDynamics 80
3.2.1.2 EquilibriumPrevalence 80
3.2.1.3 ControlbyVaccination 81
3.2.1.3 Parameterization 82
3.2.2 ApplicationsofAgeStructure 84
3.2.2.1 DynamicsofMeasles 84
3.2.2.2 SpreadandControlofBSE 89
3.3 DependenceonTimeSinceInfection 93
3.3.1 SEIRandMulti-CompartmentModels 94
3.3.2 ModelswithMemory 98
3.3.3 Application:SARS 100
3.4 FutureDirections 102
3.5 Summary 103
Chapter4 Multi-Pathogen/Multi-HostModels 105
4.1 MultiplePathogens 106
4.1.1 CompleteCross-Immunity 107
4.1.1.1 EvolutionaryImplications 109
4.1.2 NoCross-Immunity 112
4.1.2.1 Application:TheInteractionofMeaslesand
WhoopingCough 112
4.1.2.2 Application:MultipleMalariaStrains 115
4.1.3 EnhancedSusceptibility 116
4.1.4 PartialCross-Immunity 118
4.1.4.1 EvolutionaryImplications 120
4.1.4.2 OscillationsDrivenbyCross-Immunity 122
4.1.5 AGeneralFramework 125
4.2 MultipleHosts 128
4.2.1 SharedHosts 130
4.2.1.1 Application:TransmissionofFoot-and-MouthDisease 131
4.2.1.2 Application:ParapoxvirusandtheDeclineofthe
RedSquirrel 133
CONTENTS ix
4.2.2 VectoredTransmission 135
4.2.2.1 MosquitoVectors 136
4.2.2.2 SessileVectors 141
4.2.3 Zoonoses 143
4.2.3.1 DirectlyTransmittedZoonoses 144
4.2.3.2 Vector-BorneZoonoses:WestNileVirus 148
4.3 FutureDirections 151
4.4 Summary 153
Chapter5 TemporallyForcedModels 155
5.1 HistoricalBackground 155
5.1.1 SeasonalityinOtherSystems 158
5.2 ModelingForcinginChildhoodInfectiousDiseases:Measles 159
5.2.1 DynamicalConsequencesofSeasonality:Harmonicand
SubharmonicResonance 160
5.2.2 MechanismsofMulti-AnnualCycles 163
5.2.3 BifurcationDiagrams 164
5.2.4 MultipleAttractorsandTheirBasins 167
5.2.5 WhichForcingFunction? 171
5.2.6 DynamicalTrasitionsinSeasonallyForcedSystems 178
5.3 SeasonalityinOtherDiseases 181
5.3.1 OtherChildhoodInfections 181
5.3.2 SeasonalityinWildlifePopulations 183
5.3.2.1 SeasonalBirths 183
5.3.2.2 Application:RabbitHemorrhagicDisease 185
5.4 Summary 187
Chapter6 StochasticDynamics 190
6.1 ObservationalNoise 193
6.2 ProcessNoise 193
6.2.1 ConstantNoise 195
6.2.2 ScaledNoise 197
6.2.3 RandomParameters 198
6.2.4 Summary 199
6.2.4.1 ContrastingTypesofNoise 199
6.2.4.2 AdvantagesandDisadvantages 200
6.3 Event-DrivenApproaches 200
6.3.1 BasicMethodology 201
6.3.1.1 TheSIS Model 202
6.3.2 TheGeneralApproach 203
6.3.2.1 SimulationTime 203
6.3.3 StochasticExtinctionsandTheCriticalCommunitySize 205
6.3.3.1 TheImportanceofImports 209
6.3.3.2 MeasuresofPersistence 212
6.3.3.3 VaccinationinaStochasticEnvironment 213
6.3.4 Application:PorcineReproductiveandRespiratorySyndrome 214
6.3.5 Individual-BasedModels 217