Epidemics: Models and Data using R

318 Pages·2018·18.5 MB·English

by  Ottar N. Bjørnstad

UseR!
Ottar N. Bjørnstad
Epidemics
Models and Data using R
Use R!
SeriesEditors
RobertGentleman KurtHornik GiovanniParmigiani
Moreinformationaboutthisseriesathttp://www.springer.com/series/6991
Ottar N. Bjørnstad
Epidemics
Models and Data using R
123
OttarN.Bjørnstad
CenterforInfectiousDiseaseDynamics
PensylvaniaStateUniversity
UniversityPark,PA,USA
ISSN2197-5736 ISSN2197-5744 (electronic)
UseR!
ISBN978-3-319-97486-6 ISBN978-3-319-97487-3 (eBook)
https://doi.org/10.1007/978-3-319-97487-3
LibraryofCongressControlNumber:2018953687
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ForKatriona,Esme,andMichael
Preface
DespiteanundergraduatedegreeinZoologyandanMSconthebehaviorofvoles,
I have long been fascinated by theoretical biology and the relationship between
models and data, and the feedback between statistical analysis and conceptual de-
velopmentsintheareaofinfectiousdiseasedynamics,inparticular,andecological
dynamicsingeneral.Myperpetualfrustrationhasbeentoreadallthewonderfully
cleverbooksandjournalarticlesexudingallsortsofniftymathsandstats,butnot
quite being able to do any of it myself when it came to infectious diseases that
I care about. This frustration led me to attempt to make myself some worked ex-
amples of all this cleverness. Over the years the stack of how-tos has grown, and
thefollowingchaptersareanattemptatorganizingthesesotheymaybeusefulfor
others. I have tried to organize the chapters and sections in a reasonably logical
way:Chaps.1–10areamixandmatchofmodels,data,andstatisticspertainingto
localdiseasedynamics;Chaps.11–13pertaintospatialandspatiotemporaldynam-
ics;Chap.14highlightssimilaritiesbetweenthedynamicsofinfectiousdiseaseand
parasitoid-host dynamics; finally, Chaps.15 and 16 overview additional statistical
methodology I have found useful in studies of infectious disease dynamics. Some
sections are marked as “advanced” for one of two reasons: (1) either the maths or
statsisabitmoreinvolvedor(2)thetopicinfocusisabitmoreesoteric.Although
notmarkedassuch,mostofChap.10isadvancedinthisrespect.Whilelessrun-of-
the-mill, I have thought it important to include these sections, because they cover
topicsthatmaybelesseasytofindcodeforonline.
I have had invaluable help from students, colleagues, and collaborators in my
quest.Thepreconferenceworkshopsof“EcologyandEvolutionofInfectiousDis-
eases”thatIco-taughtbetween2005and2008enhancedmymotivationtoannotate
manyworkedexamples;barebonesofseveralofthefollowingsectionswerewrit-
tenduringfrantic24-hstintspriortotheseworkshops.Muchoftheothermaterial
arose from interactions with students and postdocs at Pennsylvania State Univer-
sity’s Center for Infectious Disease Dynamics (CIDD). Parts of the epidemics on
networksandtheR removalestimatorisfromMattFerrari’sPhDresearch,andthe
0
age-structuredSIRsimulatorandtheSIRWSmodelarefromJennieLavine’sPhD
vii
viii Preface
work.Workingwithdistributed-delaymodelshasbeenacollaborationwithBillNel-
sonandmystudentsLindsayBeck-JohnsonandMeganGreischar.AngieLuisandI
cookeduptheRcodetodotransferfunctionsaspartofherPhDresearch.Muchof
thecodeonthecatalyticmodelisfromcollaborationswithLauraPomeroyandthen
CIDDpostdoctoralfellowsGrainneLongandJessMetcalf.Thein-hostTSIRwas
also a collaboration with Jess. The Gillespie code arose from collaborations with
postdoctoral fellow Shouli Li and my honor student Reilly Mummah. Reilly also
taught me how to write my first Shiny app. Away from Penn State, Aaron King
and Ben Bolker have at various times been unbelievably patient in teaching me
bitsofmaths Ididnotunderstand. Roger Nisbetpainstakingly guided methrough
my first transfer functions during my postdoctoral fellowship at NCEAS. During
the same period, Jordi Bascompte introduced me to coupled map lattice models.
Finally,BryanGrenfellshowedmewaveletsandintroducedmetothefieldofinfec-
tiousdiseasedynamicssome20yearsago.
ThedatausedhasbeenkindlysharedbyJanisAntonovics,JeremyBurdon,Re-
becca Grais, Sylvije Huygen, Jenn Keslow, Sandy Leibhold, Grainne Long, and
MaryPoss.ThefirstdraftofthetextwascompletedwhileIwasonsabbaticalatthe
University of Western Australia and University of Oslo/the Norwegian Veterinary
Instituteduring2017.Myworkleadinguptothistexthasvariouslybeenfundedby
theNationalScienceFoundation,theNationalInstitutesofHealth,theUSDepart-
mentofAgriculture,andtheBillandMelindaGatesFoundation.
UniversityPark,PA,USA OttarN.Bjørnstad
May2018
Contents
1 Introduction................................................. 1
1.1 Preamble .............................................. 1
1.2 In-HostPersistence ...................................... 2
1.3 PatternsofEndemicity ................................... 4
1.4 R ..................................................... 6
1.5 OtherResources ........................................ 8
2 SIR......................................................... 9
2.1 TheSIRModel ......................................... 9
2.2 NumericalIntegrationoftheSIRModel .................... 11
2.3 FinalEpidemicSize ..................................... 14
2.4 OpenEpidemic ......................................... 18
2.5 PhaseAnalyses ......................................... 18
2.6 StabilityandPeriodicity.................................. 21
2.7 Advanced:MoreRealisticInfectiousPeriods ................ 23
2.8 ShinyApp.............................................. 27
3 R .......................................................... 31
0
3.1 PrimacyofR .......................................... 31
0
3.2 Preamble:RatesandProbabilities.......................... 32
3.3 EstimatingR fromaSimpleEpidemic ..................... 33
0
3.4 MaximumLikelihood:TheChain-BinomialModel ........... 35
3.5 StochasticSimulation .................................... 40
3.6 FurtherExamples ....................................... 41
3.6.1 InfluenzaA/H1N11977............................ 41
3.6.2 EbolaSierraLeone2014–2015...................... 43
3.6.3 EbolaDRC1995 ................................. 46
3.7 R fromS(E)IRFlows ................................... 47
0
3.8 OtherRulesofThumb ................................... 49
3.8.1 MeanAgeofInfection............................. 49
ix
x Contents
3.8.2 FinalEpidemicSize............................... 49
3.8.3 ContactTracing .................................. 49
3.9 Advanced:TheNext-GenerationMatrix .................... 51
3.9.1 SEIR ........................................... 51
3.9.2 SEIHFR......................................... 53
4 FoIandAge-DependentIncidence ............................. 57
4.1 BurdenofDisease....................................... 57
4.2 ForceofInfection ....................................... 58
4.3 ProbabilityofInfectionatAge:TheCatalyticModel.......... 59
4.4 MoreFlexibleφ-Functions ............................... 62
4.5 ALog-SplineModel..................................... 66
4.6 Rubella................................................ 69
4.7 WAIFW ............................................... 74
4.8 Advanced:RASModel................................... 76
5 Seasonality .................................................. 81
5.1 EnvironmentalDrivers ................................... 81
5.2 TheSeasonallyForcedSEIRModel........................ 84
5.3 Seasonalityinβ......................................... 85
5.4 BifurcationAnalysis..................................... 89
5.5 StroboscopicSection..................................... 90
5.6 SusceptibleRecruitment.................................. 92
5.7 ShinyApp.............................................. 94
6 Time-SeriesAnalysis ......................................... 95
6.1 TaxonomyofMethods ................................... 95
6.2 TimeDomain:ACFandARMA ........................... 95
6.2.1 ARMA.......................................... 97
6.3 FrequencyDomain ...................................... 99
6.4 Wavelets............................................... 100
6.5 MeaslesinLondon ...................................... 102
6.6 ProjectTycho........................................... 107
6.7 LombPeriodogram:WhoopingCough...................... 107
6.8 TriennialCycles:PhiladelphiaMeasles ..................... 108
6.9 WaveletReconstructionandWaveletFilter:Diphtheria ........ 111
6.10 Advanced:FFTandReconstruction ........................ 114
7 TSIR ....................................................... 117
7.1 StochasticVariability .................................... 117
7.2 EstimatingParametersinDynamicModels .................. 120
7.3 EstimationUsingtheTSIR ............................... 121
7.3.1 Inference(Hypothetical) ........................... 121
7.4 Inference(forReal)...................................... 122
7.4.1 SusceptibleReconstruction ......................... 122
7.4.2 Estimation....................................... 124