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Modeling COVID-19 latent prevalence to assess a public health intervention at a state and regional scale

PhilipJ.Turk1,PhD,MS;Shih-HsiungChou,PhD;MarcA.Kowalkowski,PhD;PoojaP.Palmer,MS;JenniferS.Priem,PhD;MelanieD.Spencer,PhD,MBA;YhennekoJ.Taylor,PhD;AndrewD.McWilliams,MD,MPH

CorrespondingAuthor:PhilipTurk,PhD,MSCenterforOutcomesResearchandEvaluation(CORE)AtriumHealth1540GardenTerrace,Suite408Charlotte,NC28203

AbstractBackground:EmergenceofCOVID-19caughttheworldoff-guardandunprepared,initiatinga global pandemic. In the absence of evidence, individual communities had to take timelyactiontoreducetherateofdiseasespreadandavoidoverburdeningtheirhealthcaresystems.Althoughafewpredictivemodelshavebeenpublishedtoguidethesedecisions,mosthavenottakenintoaccountspatialdifferencesandhaveincludedassumptionsthatdonotmatchthelocal realities. Access to reliable information that is adapted to local context is critical forpolicymakerstomakeinformeddecisionsduringarapidlyevolvingpandemic.Objective:Thegoalof thisstudywas todevelopanadaptedsusceptible-infected-removed(SIR)model topredict the trajectoryof theCOVID-19pandemic inNorthCarolinaand theCharlottemetropolitanregionandtoincorporatetheeffectofapublichealthinterventiontoreducediseasespread,whileaccountingforuniqueregionalfeaturesandimperfectdetection.Methods: Three SIR models were fit to prevalence data from the state and the greaterCharlotteregionandthenrigorouslycompared.Oneofthesemodels(SIR-Int)accountedforastay-at-homeinterventionandimperfectdetectionofCOVID-19cases.Results:Presently, theCOVID-19outbreak is rapidlydecelerating inNCand theCharlotteregion.Infectioncurvesareflatteningatboththestateandregionallevel.Relativelyspeaking,thegreaterCharlotteregionhasrespondedmorefavorablytothestay-at-homeinterventionthanNCasawhole.WhileaninitialbasicSIRmodelservedthepurposeofinformingdecisionmakingintheearlydaysofthepandemic, itsforecastincreasinglydidnotfitthedataovertime.However,asthepandemicandlocalconditionsevolved,theSIR-Intmodelprovidedagoodfittothedata.Conclusions: Using local data and continuous attention tomodel adaptation, our findingshaveenabledpolicymakers,publichealthofficialsandhealthsystemstodocapacityplanningandevaluatetheimpactofapublichealthintervention.OurSIR-Intmodelforestimatedlatentprevalencewasreasonablyflexible,highlyaccurate,anddemonstratedtheefficacyofastay-at-homeorderatboth thestateandregional level.Ourresultshighlight the importanceofincorporatinglocalcontextintopandemicforecastmodeling,aswellastheneedtoremainvigilantandinformedbythedataasweenterintoacriticalperiodoftheoutbreak.Keywords: COVID-19, public health surveillance, novel coronavirus 2019, pandemic,forecasting,SIRmodel,detectionprobability

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Introduction

InDecember2019,anovelcoronavirusemergedinWuhan,Hubeiprovince,China[1].Thepathogencausesarespiratoryillness,nowknownasthecoronavirusdisease2019(COVID-19)[2,3].FromitsoriginalepicenterinWuhan,thevirusspreadrapidlywithin30daystootherpartsofmainlandChinaandalsoexportedtoothercountries[4,5,6,7,8].AsofApril10,2020,210countriesandterritorieshavereported1,673,423confirmedcasesofCOVID-19and101,526deaths[9].Duetothespreadacrossmultiplecountriesandthelargenumberofpeople impacted,onMarch11 theWorldHealthOrganizationrecognized thenovel severeacuterespiratorysyndromecoronavirus2(SARS-CoV-2) asapandemic thatposesamajorglobalpublichealththreat[10,11].

While theeffectsof theCOVID-19pandemicareexperiencedglobally,manykeyhealth

policydecisionsdesigned toreduce transmissionsaredeterminedatnationalandregionallevels. These critical policy decisions must be implemented quickly and evaluatedcontinuously so they can be adapted to the local context, recognizing the clear effect thatgeography,communitycontext,densityandsocialdeterminantsofhealthhaveonCOVID-19outcomes.InNorthCarolina(NC),thefirstCOVID-19casewasreportedonMarch2,2020,andcases increased to 3,963 total confirmed cases as of April 10 [12]. To slow the rapidlyincreasing transmission rate,withina fewweeksafter the1st casewasdetected,NCstateofficials promoted social distancing strategies (i.e., deliberately increasing physical space),banned largesocialgatherings, andclosedpublic schoolsanduniversities. Subsequently, astay-at-homeorder,whichonlyallowsforessentialtraveloutsidethehome,wasissuedinthesouthwesternpartof the statebyMecklenburgCountyeffectiveat8amMarch26, lastingthrough April 16 (since extended to April 29), while a statewide stay-at-home orderwasissuedeffectiveat5pmMarch30,lastingtoApril29.

BecausetheCOVID-19landscapeevolvesrapidlyduetotheconfluenceoflocallyrelevantfactors, timelydatatodrivedecisionmakingaroundcontainment, treatment,andresourceplanningiscritical.Forecastingmodelsareusedtogenerateearlywarningstoidentifyhowapandemicmightevolve.DuringtheearlystagesoftheCOVID-19pandemic,forecastingwasfrequentlyappliedtopredictnationalandinternationalinfectiontransmissiontrends[13,14].Localcommunitiesandhealthsystemsturnedtothesenationalandinternationalmodelsfortheir own planning; however, the generalizability of suchmodels to the local situation islimitedandignoresimportantcommunity-levelpopulationcharacteristicsandtransmissiondynamics[3,15,16,17].Anobjectiveofthisstudywastounderstandhowspatialdifferencesimpactmodelresultsandtheirinterpretation.

Inresponsetotheneedforactionabledatainsightsinourcommunityandhealthsystem,

investigatorsfromtheAtriumHealthCenterforOutcomesResearchandEvaluation(CORE)developedaseriesofCOVID-19forecastingmodels,whichwereusedtoguideAtriumHealth’sinitialproactiveresponsetoensuresufficientcapacitytotreattheexpectedsurgeinpatientcare demands. In this study, we present an initial Susceptible-Infected-Removed (SIR)epidemic model and its evolution to the Susceptible-Infected-Removed-Social Distancing-Detection Rate (SIR-Int) model. Here we describe and compare thesemodels, the spatial

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differencesinapandemic,thesignificanceofobservedcasesversusactualprevalenceinthesetting of rapidly evolving testing strategies, the current epidemiological trends and thepotentialeffectsofnon-pharmaceuticalinterventionsappliedlocally(e.g.,socialdistancing).Wealsoofferrecommendationsforhowcommunityandhealthsystemleadersmayinterpretourmodels tobetterprepare and act todecrease thenegative consequencesof COVID-19spreadwithintheirowncommunities.

Methods

The observed cumulative case and death counts were obtained daily at noon startingMarch2,2020fromtheNorthCarolinaDepartmentofHealthandHumanServiceswebsiteforall 100 counties [12]. Data collection for this manuscript ended on April 7. In order toaccuratelyestimatetheactual latentprevalenceat timet, thecumulativecasecountswereadjusted for imperfect detection by dividing them by 0.14. While estimates of detectionprobabilityforcoronavirus,alsoknownastheascertainmentrate,varyintheliterature,oursis in linewiththosereported[18,19,20,21,22].Next,cumulativedeathsweresubtractedfromadjustedcumulativecases.Wealsoadjustedcumulativecasesforrecoveriesbyremovingcasesafter20days,theestimatedmediandurationofviralsheddingfromillnessonset[23].Dailyincrementalincidencewasobtainedbysubtractingtheestimatedlatentprevalenceattimet−1fromthatattimet.Crucially,inourresearch,wemodelestimatedlatentprevalenceasconstructedhere,notobservedprevalence.Forthesakeofbrevitymovingforward,weusetheterms‘latentprevalence’and‘prevalence’interchangeably.

TheUSCentersforDiseaseControlandPrevention’sCitiesReadinessInitiative(CRI)isa

federally funded program designed to enhance preparedness in the nation’s largestpopulationcentersinordertoeffectivelyrespondtolargepublichealthemergencies.WithinNC, 11 counties are grouped into a CRI region that includes Anson, Cabarrus, Catawba,Cleveland,Gaston,Iredell,Lincoln,Mecklenburg,Rowan,Stanly,andUnion.Collectively,wehenceforthrefertothesecountiesas‘theCRI’(Figure1).BecausetheCRIcloselymirrorsthelargeareaservedbyAtriumHealth’sgreaterCharlottemarket,weusedthispopulationbaseforour localmodelingefforts.TheCRI includesover2.5million residents (24%of theNCpopulation)andrangesfromruralsettingslikeAnsonCountytoMecklenburgCounty,whichcontainsNC’s largest city, Charlotte. Tounderstandhowspatial differences impactmodelresultsandtheirinterpretation,wecomparedtheCRItoNCthroughouttheearlyphasesofthispandemic.

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Figure1:MapofNorthCarolinashowingtheCRIregion.

WeintroducetheSIRdeterministiccompartmentalmodeloriginallydescribedbyKermackandMcKendrick[24]anddepictitinFigure2.

Figure2:SIRmodeldiagramshowingcompartmentsandflow.

Sisthenumberofindividualsthataresusceptibletoinfectioninthepopulation,Iisthenumberofindividualsthatareinfected,andRisthenumberofindividualsthatareremovedfrom the population via recovery and subsequent immunity or death from infection. ThismutuallyexclusiveandexhaustivepartitionissuchthatS+I+R=N,whereNistheclosedpopulationsize.Wefurtherassumealluninfectedindividualsaresusceptibletoinfection.Thetransitionflowisdescribedbythearrowsinthefigurelabeledwithtworates.Theparameterβ is the infection rateand canbe furtherdecomposedas theproductof theprobabilityoftransmissionpercontactandtherateofcontactperpersonperunittime.γistheremovalrate.

Moreformally,theSIRmodelisasystemofthreeordinarydifferentialequations(ODEs)involvingtwounknownparameters:

𝑑𝑆𝑑𝑡 = −

𝛽𝐼𝑆𝑁

𝑑𝐼𝑑𝑡 =

𝛽𝐼𝑆𝑁 − 𝛾𝐼

𝑑𝑅𝑑𝑡 = 𝛾𝐼

NotethatallofS,I,andRandtheirderivativesarefunctionsoftimet(e.g.,S=S(t)),althoughwedonotdenotethisnotationallyhere.Byhowthemodelisconstructed,thefirstequationin

S I Rβ γ

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thesystemreturnsanumberlessthanorequaltozero,thesecondequationreturnsanyrealnumber,andthethirdequationreturnsanumbergreaterthanorequaltozero.

All data analysis was done using R statistical software, version 3.6.2. As described in

Churches[25],weusedtheode() defaultsolverfromthedesolve packagetosolvethesystemofODEsdefiningtheSIRmodel. Next,weusedaquasi-Newtonmethodwithconstraintstofindtheoptimalvaluesforβandγon(0,1)byminimizingthesquarerootofthesumofthesquareddifferencesbetweenI,whichisourprevalence,anditsprediction𝐼, overalltimet[26].Inordertoestablishinitialconditionsformodelfitting,weestimatethepopulationsizeofNCandtheCRItobe10,488,084and2,544,041,respectively,usinginformationtakenfromcensusestimates.Afterobtainingtheestimates𝛽- and𝛾.,tohelpassessmodelgoodness-of-fit,wedefinethefollowingstatistic:

𝑅!"#% = 1 −∑ 1𝐼" − 𝐼, "2

%&"'(

∑ (𝐼" − 𝐼4 ")%&"'(

wheretimeisindexedfrom𝑖 = 1,… , 𝑛,andnisthenumberofprevalencesinthesample.Notethat𝐼4 istheaverageoftheIi’s.

Inordertocomparedifferentscenarios,forbothNCandtheCRI,wedefineaSIRmodel(SIR-Pre) fit to the data from the time of the outbreak until the time of the March 26Mecklenburg County stay-at-home order. Since Mecklenburg County is the state’s secondlargestcounty,thiscouldhaveastrongeffectonthepandemictrajectory,bothintheCRIandthestate;therefore,wehaveusedthisdatetodelineatethedateofthesignificantpublichealthintervention. WefurtherdefineaSIRmodel(SIR-Post) fit tothedatafromthetimeoftheoutbreakuntiltheendofdatacollection.

GiventhemajorpublichealthinterventionimplementedonMarch26,wemodifytheSIR

model for both the CRI and NC to accommodate this (denoted SIR-Int). SIR models withinterventionscanbesimulatedusingtheEpiModel package.WefirstfittheSIRmodelasbeforeto thedataupuntilMarch26, andextracted theestimatesofβandγ.AfterMarch26,weretainedtheremovalrate,butmodifiedtheinfectionrate.First,wesetthepre-interventionprobability of transmission equal to 0.015, which is consistentwith other viral infectiousdiseaseslikeSARSandAIDS[27,28].Wethensettherateofcontactsothattheprobabilityoftransmission multiplied by the rate of contact equaled 𝛽- . To simulate the observedintervention,usingthedefaultRK4ODEsolver,weaffectedtheprobabilityoftransmissionbyiterativelydecreasingthehazardratioofinfectiongivenexposuretotheintervention(stepsizeof0.0001)comparedtonoexposure,untilthefittedinfectioncurveyieldedamaximum𝑅!"#% .

Forexploratorydataanalysis,wegeneratedtimeplotsforprevalence,incidence,andboth

daily and cumulative deaths. The basic reproduction numberR0 is the average number ofsecondarycasesofdiseasecausedbyasingle infected individualoverhisorher infectiousperiodinapopulationwhereallindividualsaresusceptibletoinfection.ToestimateR0,wecompute:

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𝑅-) = 𝛽-/𝛾.

where 𝛽- and 𝛾. are estimates taken from the model fit. Since the SIR model is fullyparameterizedbyβandγ,wealsoobtainpredictions𝑆-and𝑅- overalltimet.Thepercentageofinfectedatpeakprevalencewascomputedbydividing𝐼, bythepopulationsizeN,whilethefinalpercentageofinfectedwascomputedasthelimitof1−𝑆-(∞)/N.Toestimatedoublingtime and compute a 95% confidence interval, we modeled incidence growth by fitting aloglinearmodelasafunctionoftimetusingtheincidence package.

Results

Figure3showstimeplotsofprevalence,cumulativedeaths,incidence,anddailydeathsforNCfromthestartoftheoutbreakonMarch2uptoandincludingApril7.ThefirstdeathwasrecordedinNConMarch24.

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Figure3:TimeplotsforNC.

Figure4showstimeplotsofprevalence,cumulativedeaths,incidence,anddailydeathsfortheCRIfromthestartoftheoutbreakonMarch11uptoandincludingApril7.ThefirstdeathwasrecordedintheCRIonMarch25.

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Figure4:TimeplotsfortheCRI.

Notably, theprevalenceandcumulativedeath curves forboth figures lookexponential.

Whileboth incidencecurvesare increasing, the incidencecurvesbecomevolatileafter thestay-at-homeorderwentintoeffect.PriortoMarch26,doublingtimewasestimatedtobe2.56daysintheCRI(95%CI:(2.11,3.25))and2.94daysinNC(95%CI:(2.33,4.00)).OncedataafterMarch26areincluded,thedoublingtimesincreasedandwereestimatedtobe4.70daysintheCRI(95%CI:(3.77,6.22))and4.01daysinNC(95%CI:(3.43,4.83)).

Tables1and2givesasynopsisof themodel fits foreach locationandmodel type.The

estimatedR0of2.36fortheCRIpriortoMarch26ismoretypicaloftherangeofR0valuesgivenintheliteratureforCOVID-19,whilethevalueof1.79forNCissubstantiallylower[29,30].After the intervention, the estimatedR0values for both locations drop to a similar value,although this result is affected by reduced model fit. A comparison of the efficacy ofintervention,definedas1-thehazardratioofinfection,gives0.25forNCand0.43fortheCRI.

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UsingthesehazardratiostocomputeestimatesofR0fromMarch26onward(𝑅-),+,!-),wederive1.34and1.33forNCandtheCRI,respectively.ThissuggeststheCOVID-19outbreakisrapidlydeceleratinginNCandtheCRIaftertheaggressivepublichealthintervention.

Table1:SummarytableofmodelfitforSIR-PreandSIR-PostmodelsinNCandtheCRI.

Location Model 𝛽- 𝛾. 𝑅-) 𝑅!"#% NC SIR-Pre 0.6415 0.3585 1.79 0.99NC SIR-Post 0.6165 0.3835 1.61 0.84CRI SIR-Pre 0.7020 0.2980 2.36 0.94CRI SIR-Post 0.6381 0.3619 1.76 0.65

Table2:SummarytableofmodelfitforSIR-IntmodelinNCandtheCRI.

Location HazardRatio 𝑅!"#% 𝑅-),+,!-NC 0.75 0.99 1.34CRI 0.57 0.99 1.33

Figures5and6showplotsofthethreefittedmodels’infectioncurvesforNCandtheCRI,

respectively,out toApril7.Thebehavior in the twoplots is thesame.TheSIR-Postmodelclearlydemonstratesalack-of-fittothedata.FortheSIR-Intmodel,wenotethehingepointinducesachangeofbehaviorfromMarch26onward.ThedottedorangelinerepresentsSIR-PreforecastprojectionsfromMarch26onward.Notetheyaremuchlargerthantheactualdata.

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Figure5:InfectionprevalencepredictioncurvesforNCuptoApril7,2020.

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Figure6:InfectionprevalencepredictioncurvesfortheCRIuptoApril7,2020.

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Figures7and8showplotsofthethreefittedmodels’infectioncurvesforNCandtheCRI,respectively,projectedouttothebeginningofAugust.Inbothplots,weseethedramaticeffectofthepublichealthintervention;thatis,theso-called“flatteningofthecurve”.Therearetwoimportantdifferences tonotebetweenNCand theCRI region.First, theCRIvisibly showsrelativelymoreflattening.ThiseffectcanbebestobservedinTable3inthePeak%InfectedandFinal%Infectedcolumns.MovingfromthePretoPosttoIntmodelswithinalocation,thedropinpercentageinfectedismorepronouncedintheCRI.Infact,fortheSIR-Intmodel,thepercentagesarevirtuallythesameforbothlocations;thatis,theCRIhas“sloweddown”tothestateasawhole.Second,thedateofpeakprevalencewasinitially8daysearlierfortheCRIcomparedtoNC.However,usingthecurrentSIR-Intmodel,althoughbothlocationsshowedtheirinfectioncurvesshiftingforwardintime,thedateofpeakprevalenceisnow3dayslaterintheCRI(Table3).Toputthisintocontext,forNC,thetimedurationfromthestartoftheoutbreaktothepeakprevalencehasgonefrom49daysto70days(43%increase).However,fortheCRI,thetimedurationfromthestartoftheoutbreaktothepeakprevalencehasgonefrom32daysto64days(100%increase).

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Figure7:InfectionprevalencepredictioncurvesforNCuptoAugust1,2020.

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Figure8:InfectionprevalencepredictioncurvesfortheCRIuptoAugust1,2020.

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Table3:SummarytabledescribinginfectionunderthreedifferentmodelsinNCandtheCRI.

PeakKinetics

Location Model2020Date 𝑆- 𝐼- 𝑅-

Peak%Infected

Final%Infected

NC SIR-Pre Apr20 5,673,270 1,213,190 3,601,625 12% 73%NC SIR-Post Apr28 6,614,437 866,404 3,007,244 8% 65%NC SIR-Int May11 7,913,011 366,037 2,209,037 3% 46%CRI SIR-Pre Apr12 1,142,320 537,031 864,690 21% 87%CRI SIR-Post Apr24 1,488,530 282,257 773,254 11% 72%CRI SIR-Int May14 1,911,343 89,324 543,374 4% 46%Figures9and10showplotsofthethreefittedmodels’removalcurvesforNCandtheCRI,

respectively, projected out to the beginning of August. These plots supportwhatwe haveobservedsofar.Withthecontinuedintervention,theremovalcurvesarebeginningtocollapse,whichisabehaviorwewouldexpect.FortheSIR-Intmodel,bothlocationsshowaremovalplateaubeingreachedroughlyaroundthebeginningofJuly.

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Figure9:RemovalprevalencepredictioncurvesforNCuptoAugust1,2020.

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Figure10:RemovalprevalencepredictioncurvesfortheCRIuptoAugust1,2020.

Discussion

PrincipalResultsIntermsofmodelfitting,westateseveralobservations.TheSIR-Premodelrepresentsa

“worst case” scenario, as if the disease were allowed to run its course. Hence, early in apandemiclikethis,itservesausefulpurposetohelpleadersunderstandtheconsequencesoftakingnoaction,ordelayedactiononimplementingpublichealthinterventions.Beyondthat,a basic SIRmodel, especially one that is used after being fit only to early pandemic data,impartsnofurthervalueforinformingpandemicresponseplanning,andindeedmayprovideerrant forecasts. This diminished value also holds true when a basic SIR model is fit tocontemporarydata,yetignorestheeffectofapublichealthintervention,asdemonstratedby

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theSIR-Postmodel.Eventually,bothsuchmodelswillprovideapoorfittothedata(Figure5,Figure 6, Table 1). Because the behavior of any epidemic is dynamic, anymodel requiresconstantmonitoring,assessmentoffittolocaldata,andevaluationofefficacyasnewdataarecollected. Our SIR-Int model provides an example where this attention to model fit andincorporation of regional influences allows for appropriate model adaption and carefulcalibration,thusgeneratingthemostaccuratepredictionsavailabletoguideregionaldecisionmakingatthetime.

Summarizing the effect of the intervention, the doubling time for both locations is

substantiallysloweraftertheintervention,withtheCRIdoublingtimeestimate(4.70days)nowbeinggreater than forNC(4.01days).Thestay-at-homeordersstronglyappear tobeworkingasintendedastheinfectioncurvesforbothlocationsarenowbecomingflatter(andshrinking),with peak infectionprevalence nowbeing pushed towardsmid-May (Figure 7,Figure8,Table3),bothlocation’srecoverycurvesstartingtofall(Figure9,Figure10),andmeasurableinterventioneffectsonthehazardratioandR0(Table2).Itisinterestingtonotethat our results match rigorous Monte Carlo simulation studies we conducted weeksbeforehand.

Ifwecomparethetwolocations,theestimatedR0of2.36fortheCRIpriortoMarch26is

moretypicaloftherangeofR0valuesintheliteratureforCOVID-19,whilethevalueof1.79forNCissubstantiallylower(Table1).ThiscouldbeattributedtothefactthattheCRIcontainsthelargestcityinNC,andoneoftheUS’sbusiestairports,settingthestageforthisregiontohavebecomeanotherCOVID-19hotspot. It is interestingtonotethattheNCSIR-IntmodelshowedabetterfitwhenthechangepointwasalsosettoMarch26,ratherthanMarch30whenthestatewidestay-at-homeorderwentintoplace.Onepossibleexplanationforthiscouldbethatasthepandemicbeganinearnest,thegeneralpopulation’sfearofthevirusalsoincreased,perhaps causing most NC citizens to shelter-in-place prior to the order going into effect.Another explanation is that Mecklenburg County accounts for almost 11% of the NCpopulationandsotheeffectofthecountyorderdirectlyimpactedadjoiningcountiesintheCRI, thus influencing the observed effect at the state level. Two additional interestingobservationshighlightthecriticalinfluenceofspatialvariation.First,theCRIinfectioncurveevidencesrelativelymoreflatteningandalaterpeakinfectiondate(Figure7,Figure8,Table3). Second, the intervention effect in the CRI also appears stronger (Table 2). The likelyexplanationsforthesedifferencesaretheMecklenburgCountystay-at-homepolicygoingintoeffectfivedaysbeforethestateorder,thedifferentreactionofthelocalpopulationtotheorderanditsrelatedmessaging,andinnumerableotherunknowncovariatessuchasearlycancelingof religious services, public gatheringpolicies, and canceling of electivemedical visits andprocedures.

Limitations

There are limitations to the SIR model. Some take issue with its deterministic form,

although one could fit a Bayesian SIR model to make it stochastic. Perhaps the biggestlimitation is that β and γ could be time-varying due to different forms of intervention(enhancedpersonalprotectivemeasuresandsocialdistancing).However,aswehaveshown

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here, we can easily leverage pre-existing R functions to incorporate a changepoint thatmodifies the probability of transmission to acknowledge an important public healthintervention.ItisalsopossibletocustomizetheSIRmodelwithinRtodefinemoreadvancedanddifferenttransitionprocesses,andthenparameterizeandsimulatethosemodels.TheSIRmodel is simple to understand and easier to fit, as opposed to other deterministiccompartmentalmodels (e.g., SEIR) or stochastic individual contactmodels [31]. However,these more advanced models will play an increasingly important role in forecasting andunderstandingthedynamicsofthisevolvingpandemic.

The lack of widespread COVID-19 testing, both for symptomatic and asymptomatic

individuals, presents amajor limitation of unknown scale and implications to forecastingmodels[32,33].Datasourcesareknowntoundercountcases,onlyincludingasymptomaticillness by chance, and to define cases inconsistently, based on variable testing criteria,betweenandwithingeographies.Collectively, thesecontributeto imperfectdetection.Asaresult, high-level models may not comprehend the full extent of the outbreak, creatingchallenges inproducingaccurate forecasts. Ourdecisiontobaseourmodelingstrategyonestimated latentprevalenceaddressesthis inconsistencybyadjustingobservedprevalencecounts.ModelingonlytheobservedprevalencehastheeffectofshiftingtheSIRcurvesaheadin timeby several days ormore.While our estimate of the detection probability (0.14) isheuristicallymotivated,athoroughsearchoftheliteraturesupportsouruseofthisestimateasreasonable.Futureworkwillfocusonrefiningthisestimateasnewresearchappearsandtoallowittovaryasafunctionoftime.

ComparisonwithPriorWork

WhilethereisaplethoraofmodelsthatestimatetheimpactofCOVID-19intheUS,thereare far fewer that give localized projections.We note that ourmid-May date for the peakinfectioncurveisroughly3-to-4weekslaterthantheprojectionfromtheoften-citedmodelfrom The Institute for Health Metrics and Evaluation [34]. The later uses a Bayesiangeneralizednonlinearmixedmodeltoexaminecumulativedeathratesandassumesastrictsocialdistancingpolicyisinplace.UsingdataupuntilMarch13,ColumbiaUniversityreportedamid-MaypeaktimeforNCundernocontrolmeasuresandastartofJulypeaktimeundersomecontrolmeasures [35].Theauthors caution that theirmetapopulationSEIRmodel isdesignedtocapturenationaltrends,andlocalprojectionsshouldbeviewedasbroadestimates.Othermodels,suchastheCHIMEmodelfromtheUniversityofPennsylvaniaHealthSystem,reliedondata from threePennsylvaniahospitals to estimatehospital capacity and clinicaldemandandwasnotdesignedtocapturechangingregionalmitigationstrategies[36].PolicyandPracticeImplications

In the context of limited national policy guidelines to reduce COVID-19 transmission,provide resources for healthcare system pandemic preparedness and mitigate healthconsequences, state and local authorities must have reliable and geographically specificmodelstomanagetheunfoldingcrisis.Ourmodelingframeworkprovidesaflexibletoolusingreal-time data to deliver forecasting capabilities that support capacity management and

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evaluationof the epidemiological response to changes inpolicy, treatmentplans and localconditions. Because we frequently refit the model based on a daily update of the data,policymakersandNCpublichealthofficialsareabletouseourresultstoworkwithhospitalsystems toplan forhealthcare capacity and respond to changes in local outbreakprofiles,whileweighingsocialdistancingpolicies.

Usingregionalandstatedata,wedemonstratehowepidemiologicalmodelingbasedon

localcontextiscriticallyimportanttoinformingpandemicpreparednessforhealthsystemsandpolicyleaders.Theresultshighlighttheimportanceforsuchmodelstobecreatedusinglocaldata,asopposedtorunningasimulationwhichmakesmanyassumptionsaboutthetruthof parameter values. Allmodels shouldbe continuously re-calibrated, and adapted to therapid,continuouslychangingsituationsinherenttoapandemic.Aonesizefitsallapproachtotheunderpinningforecastingmodelorrelianceondatathatdoesnotincorporatelocalcontext,setsthestageformisguidedforecasting.Additionally,ourstudyshowsthatwhileaclassicSIRmodelmayperformwellintheearlydaysofthepandemic,itbeginstoloserelevancewiththeemergenceofadditionalinfluenceslikesocialdistancingandenhancedawarenessofpersonalhygiene.

TheSIR-IntmodelhashighpredictiveaccuracybasedondatacollectedfromMarch2to

April7forbothNCandtheCRIandisabletodemonstrateclear,compellingevidenceoftheefficacyofastay-at-homeorder.Bymodelingestimatedlatentprevalenceaswehavedonehere,insteadofobservedprevalence,alagdelayinprojectingpeakinfectioncanbeavoided,reducingtheconsequencestoleaderswhorequireanaccuratetimelineforplanningpurposes(e.g.,surgeplanningofhospitalbeds,supplies,andpersonnel).

Conclusions

All other things being equal, if residents continue to observe the stay-at-home orders,maintainingattentiontosocialdistancingandincreasedpersonalhygiene,thenthiswaveoftheCOVID-19outbreakwouldessentiallybeoverbymid-July.Itispossiblethatwecouldseecontinuedflatteningandshrinkingoftheinfectioncurveinwhichcaseourforecastresultswouldadaptcommensurately.Itisalsopossiblethatinfectionprevalencecouldoscillateatalowlevelovertime,inwhichcasemoreadvancedmodelingandmethodswouldbeneeded.Our resultshighlight the importanceof incorporating local context intopandemic forecastmodeling,aswellastheneedtoremainvigilantandinformedbythedataasweenterintoacriticalperiodoftheoutbreak.WhiletherewillregrettablystillbetragiclossoflifeandmanyNCcitizensinfectedbycoronavirus,thisscenariopalesincomparisontowhatcouldhavebeenafarworseconclusion.AcknowledgementsPT takes full responsibility for the integrity and accuracy of the statistical analysis andassembling the manuscript; SHC generated the map and was involved in discussions onstatistical analysis; YT andMSdrafted the abstract anddiscussion;MKand JPdrafted theintroduction;PTdraftedthemethods,results,andpartofthediscussion;MK,MS,YTandPT

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assembledreferences;YT,SHC,MS,andAWperformedcriticalrevisionofthemanuscriptforimportant intellectualcontent;PPcollectedthedataanddraftedthebibliography;andAWsupervisedthestudy.ConflictsofInterestNonedeclared.References

1.ZhuN,ZhangD,WangW,etal.AnovelcoronavirusfrompatientswithpneumoniainChina,2019.NEnglJMed2020;382:727-33.doi:10.1056/NEJMoa2001017.2.GuanWJ,NiZY,HuY,etal.Clinicalcharacteristicsofcoronavirusdisease2019inChina.NEnglJMed2020.PMID:32109013.3.LaiCC,ShihTP,KoWC,TangHJ,HsuehPR.Severeacuterespiratorysyndromecoronavirus2(SARS-CoV-2)andcoronavirusdisease-2019(COVID-19):Theepidemicandthechallenges.IntJAntimicrobAgents2020;55:105924.PMID:32081636.4.WuZ,McGooganJM.Characteristicsofandimportantlessonsfromthecoronavirusdisease2019(COVID-19)outbreakinChina:summaryofareportof72314casesfromthechinesecenterfordiseasecontrolandprevention.JAMA2020;323(13):1239-1242.doi:10.1001/jama.2020.2648.5.LiQ,GuanX,WuP,etal.Earlytransmissiondynamicsinwuhan,China,ofnovelcoronavirus-infectedpneumonia.NEnglJMed2020;382(13):1199-1207.PMID:31995857.6.RemuzziA,RemuzziG.COVID-19andItaly:whatnext?Lancet2020;395(10231):1225-1228.DOI:https://doi.org/10.1016/S0140-6736(20)30627-9.7.HolshueML,DeBoltC,LindquistS,etal.Firstcaseof2019novelcoronavirusintheUnitedStates.NEnglJMed2020;382(10):929-936.PMID:32004427.8.ArentzM,YimE,KlaffL,etal.Characteristicsandoutcomesof21criticallyillpatientswithCOVID-19inWashingtonState.JAMA2020.PMID:32191259.9.Coronavirusdisease2019(COVID-19):situationreport–63.Geneva:WorldHealthOrganization,March23,2020athttps://www.who.int/docs/default-source/coronaviruse/situation-reports/20200323-sitrep-63-covid-19.pdf?sfvrsn=d97cb6dd_2.)10.OnderG,RezzaG,BrusaferroS.Case-fatalityrateandcharacteristicsofpatientsdyinginrelationtoCOVID-19inItaly.JAMA2020.PMID:32203977.11.SohrabiC,AlsafiZ,O'NeillN,etal.WorldHealthOrganizationdeclaresglobalemergency:Areviewofthe2019novelcoronavirus(COVID-19).IntJSurg2020;76:71-6.PMID:32112977.12.Coronavirusdisease2019(COVID-19)inNorthCarolina.Raleigh:NCdepartmentofhealthandhumanservices,March25,2020.athttps://www.ncdhhs.gov/covid-19-case-count-nc.)

. CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted April 18, 2020. ; https://doi.org/10.1101/2020.04.14.20063420doi: medRxiv preprint

22

13.FergusonNM,LaydonD,Nedjati-GilaniG,etal.Impactofnon-pharmaceuticalinterventions(NPIs)toreduceCOVID19mortalityandhealthcaredemand.ImperialCollegeCOVID-19ResponseTeam2020.DOI:https://doi.org/10.25561/77482.14.WuJT,LeungK,LeungGM.Nowcastingandforecastingthepotentialdomesticandinternationalspreadofthe2019-nCoVoutbreakoriginatinginWuhan,China:amodellingstudy.Lancet2020;395(10225):689-697.PMID:32014114.15.McCloskeyB,HeymannDL.SARStonovelcoronavirus-oldlessonsandnewlessons.EpidemiolInfect2020;148:e22.PMID:32019614.16.DuZ,WangL,CauchemezS,etal.Riskfortransportationof2019novelcoronavirusdiseasefromWuhantoothercitiesinChina.EmergInfectDis2020;26(5).PMID:32053479.17.Wilder-SmithA,FreedmanDO.Isolation,quarantine,socialdistancingandcommunitycontainment:pivotalroleforold-stylepublichealthmeasuresinthenovelcoronavirus(2019-nCoV)outbreak.JTravelMed2020;27(2).PMID:32052841.18.ReadJM,BridgenJR,CummingsD,HoA,andJewellCP.Novelcoronavirus2019-ncov:earlyestimationofepidemiologicalparametersandepidemicpredictions.medRxiv2020.DOI:https://doi.org/10.1101/2020.01,23:20018549.19.VerityR,OkellLC,DorigattiI,WinskillP,WhittakerC,ImaiN,Cuomo-DannenburgG,ThompsonH,WalkerP,FuH,etal.Estimatesoftheseverityofcoronavirusdisease2019:amodel-basedanalysis.TheLancetInfectiousDiseases2020.DOI:https://doi.org/10.1016/S1473-3099(20)30243-7.20.NishiuraH,KobayashiT,YangY,HayashiK,MiyamaT,KinoshitaR,LintonNM,JungS,YuanB,SuzukiA,etal.Therateofunderascertainmentofnovelcoronavirus(2019-ncov)infection:EstimationusingJapanesepassengersdataonevacuationflights.JournalofClinicalMedicine2020;9(2):E419.PMID:32033064.21.WuJT,LeungK,BushmanM,KishoreN,NiehusR,DeSalazarPM,CowlingBJ,LipsitchM,andLeungGM.EstimatingclinicalseverityofCOVID-19fromthetransmissiondynamicsinWuhan,China.NatureMedicine2020:1–5.DOI:https://doi.org/10.1038/s41591-020-0822-7.22.NiehusR,DeSalazarPM,TaylorA,andLipsitchM.QuantifyingbiasofCOVID-19prevalenceandseverityestimatesinwuhan,chinathatdependonreportedcasesininternationaltravelers.medRxiv2020.DOI:https://doi.org/10.1101/2020.02.13.20022707.23.ZhouF,YuT,DuR,FanG,LiuY,LiuZ,XiangJ,WangY,SongB,GuX,etal.ClinicalcourseandriskfactorsformortalityofadultinpatientswithCOVID-19inWuhan,China:aretrospectivecohortstudy.TheLancet2020;395(10229):1054-1062.DOI:https://doi.org/10.1016/S0140-6736(20)30566-3.24.KermackWOandMcKendrickAG.Acontributiontothemathematicaltheoryofepidemics.ProcRSocLondA1927;115:700–721.DOI:https://doi.org/10.1098/rspa.1927.0118.25.ChurchesT.Analysingcovid-19(2019-ncov)outbreakdatawithr-part1,2020.URLhttps://timchurches.github.io.26.ZhuC,ByrdRH,LuP,andNocedalJ.Alimitedmemoryalgorithmforboundconstrainedoptimisation.SIAMJSciStatComput1995;16(5):1190–1208.DOI:https://doi.org/10.1137/0916069.

. CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted April 18, 2020. ; https://doi.org/10.1101/2020.04.14.20063420doi: medRxiv preprint

23

27.PatelP,BorkowfCB,BrooksJT,LasryA,LanskyA,andMerminJ.Estimatingper-actHIVtransmissionrisk:asystematicreview.AIDS2014;28(10):1509–1519.doi:10.1097/QAD.0000000000000298.28.PitzerVE,LeungGM,andLipsitchM.EstimatingvariabilityinthetransmissionofsevereacuterespiratorysyndrometohouseholdcontactsinHongKong,China.Americanjournalofepidemiology2007;166(3):355–363.DOI:10.1093/aje/kwm082.29.LiQ,GuanX,WuP,WangX,ZhouL,TongY,RenR,LeungKSM,LauEHY,WongJY,etal.EarlytransmissiondynamicsinWuhan,China,ofnovelcoronavirus–infectedpneumonia.NEnglMed2020;382(13):1199-1207.DOI:10.1056/NEJMoa2001316.30.ZhangS,DiaoMY,YuW,PeiL,LinZ,andChenD.Estimationofthereproductivenumberofnovelcoronavirus(COVID-19)andtheprobableoutbreaksizeonthediamondprincesscruiseship:Adata-drivenanalysis.InternationalJournalofInfectiousDiseases2020;93:201–204.PMID:32097725.31.ChurchesT,andJormL.COVOID:Aflexible,freelyavailablestochasticindividualcontactmodelforexploringCOVID-19interventionandcontrolstrategies.JMIRPreprints.30/03/2020:18965.DOI:10.2196/preprints.18965.32.VetterP,Eckerle,IandKaiser,L.Covid-19:apuzzlewithmanymissingpieces.BMJ2020;368.DOI:10.1136/bmj.m627.33.SharfsteinJM,BeckerSJ,MelloMM.DiagnosticTestingfortheNovelCoronavirus[publishedonlineaheadofprint,2020Mar9].JAMA2020;10.1001/jama.2020.3864.DOI:10.1001/jama.2020.386434.MurrayC. ForecastingCOVID-19 impact onhospital bed-days, ICU-days, ventilator-days and deaths by US state in the next 4 months. medRxiv 2020. doi:10.1101/2020.03.27.20043752.35.GlanzJ,LeatherbyL,BlochM,etal.CoronaviruscouldoverwhelmUSwithouturgentaction,estimatessay.TheNewYorkTimes2020.36.WeissmanGE,Crane-DroeschA,ChiversC,etal.Locallyinformedsimulationtopredicthospital capacity needs during the COVID-19 pandemic. Ann Intern Med 2020.DOI:10.7326/m20-1260.

. CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted April 18, 2020. ; https://doi.org/10.1101/2020.04.14.20063420doi: medRxiv preprint