Modeling Interventions and Logistics

7/31/2019 Modeling Interventions and Logistics

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S C H O O L O F P U B L I C H E A LT H

LI KA SHING FACULTY OF MEDICINE

THE UNIVERSITY OF HONG KONG

Modelinginterventionsandlogistics

JosephTWu

September8,2010

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Twocasestudies

Firstcase:

Secondcase:

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Case1:Asmallpoxmodelingstudy

Thegoalofthistutorialistobuildthemodelonestepatatime.

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Naturalcourseofinfectionandtransmissibility

Transmissionroutesofsmallpox: Primaryrouteoftransmissionisthroughdirectface-to-facecontactwith

aninfectedindividual

Historicallymostcaseswereinchildren-longdurationofimmunityfollowingexposure(estimatesupto20yearsormore)althoughopinions

divided

Naturalhistoryofsmallpox:Incubation period

Fever (2-3 days)

Recovery

Death (20-30%)

Scab lesionsPustules (7 days)

Rash (7 days)

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SEIRmodel

=forceofinfection=I(t) =rateatwhichinfectiouscontactsoccur =probabilitythattheinfectiouscontactsresultininfection =rateoflatent(E)becominginfectious=1/(meanlatent

period)

=rateofinfectious(I)becomingrecoveredordead(U)=1/(meaninfectiousperiod)

S E I U

SusceptibleExposedInfectiousRemoved

State:theboxesRate:thearrows

RateofoutBlowfromastate=1/Averagedurationspentinthatstate

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Flowdiagramvsequations

Themodelcanbespeciiedusinglowdiagramsorequations.

EachequationrepresentsastateintheBlowdiagram EachtermontherighthandsideofanequationrepresentsanarrowintheBlowdiagram

Eachtermis(rate)(numberofindividualsinthestate)

S E I U

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Parameterizethemodel

ParametervaluesinGanietal: Meanlatentperiod=14.5days(12to14daysofincubationplus2

to3daysoffever),so=1/14.5=0.07days-1.

Meaninfectiousperiod=8.5days(rashismostinfectiousforjustoveraweek),so=1/8.5=0.12days-1.

andobtainedfromtheirrelationshipwiththereproductivenumberR0:

AssumeR0=5.

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(1)

Modelingquarantine

Quarantineindividualsastheybecomeinfectious How?MovesomeproportionofexposedindividualsintoanewstateQ

astheybecomeinfectious

=proportionofnewlyinfectiousindividualswhoarequarantined Q(t)=thenumberofinfectiousindividualsquarantined(attimet) 2=rateofquarantinerelease=1/(meanquarantineperiod) Quarantinedindividualsrecoveratratewhichdependsbothonrecoveryfromdiseaseanddurationofquarantine Hereweassume25daysinquarantine(i.e.aroundthreetimesthe

meaninfectiousperiodof1/=8.5days),so2=0.04days-1

S E I U

S E I U

Q2

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Modelingquarantine

(1)S E I U

S E I U

Q2

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Eficacyofquarantine

Usingthemodeltoassesshowincreasingquarantineratesreducesthenumberofdeaths

Modelcouldbeusedtolookatresourceconstraints,cost-effectiveness(numberquarantinedpercaseaverted)etc.


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CostandbeneitofquarantinePerson-dayquarantined:IfXtpeoplearequarantinedondayt,then

theperson-dayquarantinedondaytisXt

.Thetotalperson-day

quarantinedfromday1anddaynisthenX1+X2+Xn-1+Xn.

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=proportionofcontactsthataretraced 1=rateofreleasefromquarantineforuninfectedcontacts=1/(mean

durationofquarantineforcontacts)

En=numberofcontactswhoareuntracedbutlatent Ei=numberofcontactswhoaretracedandlatent Ci=numberofcontactswhotracedbutuninfected

(1)

(1)I

Quarantinecontactsofinfectiouspersons

(1)

S E I U

S En I U

Q2

Ci

1

Ei

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(1)

(1)I

Quarantinecontactsofinfectiouspersons

(1)

S E I U

S En I U

Q2

Ci

1

Ei

dS

dt=

1C

i

release of those tracedbut uninfected

(1 )IS

infected but not traced

IS

infected and traced

(1)IS

uninfected but traced

, dI

dt= (1)E

n

1 of those becominginfectious are not quarantined

I

dEn

dt= (1 )IS


(1)E

n


En

of those becominginfectious are quarantined

,dU

dt= I+

2Q

quarantine release

,

dEidt

= IS

infected and traced

Ei

traced contacts becominginfectious and quarantined

, dQdt

= Eitraced contacts becominginfectious and quarantined

+ En of those becominginfectious are quarantined

2Q

quarantine release

.

dCi

dt= (1)IS


1C

i

release of those tracedbut uninfected

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Impactofcontacttracingandquarantine

=0.4(=0.95inthearticle)


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1(11) (12)

(1)

(1)I

Vaccinatecontactsofinfectiouspersons

(1)

S E I U

S En I U

Q2

Ci Ei 12

11

15

1=vaccineeficacyinuninfected(probabilityofcompleteprotection)

2=vaccineeficacyininfected(probabilityofcompleteprotection)


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1(11)

dS

dt=

1(1

1)C

i

release of those uninfectedbut traced withunsuccessful vacccination

(1 )IS


IS

infected and traced

(1)IS


,

dEn

dt= (1 )IS


(1)En


En


,

dEi

dt= IS

infected and traced

(1

2)E

i

infected and traced withunsuccessful vaccination

becoming infectious andquarantined

1

2E

i

release of those infectedand traced withsuccessful vaccination

,

dI

dt= (1)En


I,

dU

dt = I+ 2Qquarantine release

,

dQ

dt = (1 2 )Ei

infected and traced withunsuccessful vaccination

becoming infectious andquarantined

+ En


2Qquarantine release

,

dCi

dt= (1)IS


1(1

1)C

i

release of those uninfectedbut traced withunsuccessful vacccination

1

1C

i

release of thoseuninfected but traced withsuccessful vaccination

,dV

dt=

1

2E

i

release of those infectedand traced withsuccessful vaccination

+ 1

1C

i

release of thoseuninfected but traced withsuccessful vaccination

(12)

(1)

(1)I

Vaccinatecontactsofinfectiouspersons

(1)

S E I U

S En I U

Q2

Ci Ei 12

11

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Case2:Modelinglogisticsofepidemicresponse

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Passiveimmunotherapyforpandemiclu

Treatingseverecaseswithserumantibodiesextractedfromrecoveredindividuals:(i)Directplasmatransfusionor(ii)hyperimmuneIVIG

Treatmentstrategiesforseverecasesofpandemicinluenzahavefocusedonantiviralsandanti-inlammatoryagents.Incontrast,passiveimmunotherapyhasreceivedlimitedattention.

Arecentmeta-analysisstudysuggestedthatduringthe1918inluenzapandemic,transfusionofconvalescentbloodproductsreducedthemortalityrateofseverecasesbymorethan50%.

TheproofofprincipleforthistherapeuticapproachwasrecentlydemonstratedwhenapatientinShenzhencriticallyillwithavianinluenzaA/H5N1virusinfectionin2006wasadministeredconvalescentplasmafromawomanwhohadsurvivedinfection.Thepatient,whoseconditionwasworsening

despitetreatmentwithoseltamivir,recoveredafterreceivingseveralinfusionsofconvalescentplasma(CP).

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Motivations

Intheory,thepolyclonalnatureofneutralizingantibodiesinCPwouldlowertheprobabilityofanescapemutantemergingintreatedpatients.

Besidesprovidingneutralizingantibodiesagainstthepandemicvirus,CPalsomightcarryantibodiestootherbacterialpathogens,

whichmightdecreasetheseverityofcoexistingbacterialinfections.

CPmightnotonlyreducethecasefatalityratebutalsoincreasetherecoveryrateandthereforeshortenthehospitalizationdurationofseverecases.

Theproposedpassiveimmunotherapyprogramcanthussigniicantlyreducetheburdenonthehealthcaresystem,especially

theintensivecareunit,whichwilllikelybestressed,ifnot

overloaded,atthepeakofaninluenzapandemicwave,hence

beneitingthegeneralpublicandnotonlythosereceivingpassive

immunotherapy.

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Studyobjectives

Outcome Treatmentcoverage,deinedasthepercentageofseverecasesthat

canbeofferedpassiveimmunotherapybytheproposedprogram

(i.e.%demandmet)

Researchquestions: Whatistheminimaldonorpercentageneededtomaximizethe

plasmaproductioncapacityoftheprogram?

WhatisthelikelytreatmentcoveragewiththecurrentproductioncapacityinHongKong?

Howsensitiveistheoutcometo(i)theparametersofsupplyanddemand,and(ii)thenaturalhistoryandtransmissiondynamicsof

thedisease?

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TheproposedprogramCollectconvalescentplasmafrom20-55yoadultsfortreatingseverecases

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Themathematicalmodel

Deterministicage-structuredSIRmodelfordiseasetransmission DeterministicqueueingmodelforCPharvesting Thepopulationisstratiiedintoagegroupsof5years(0-4,5-9,10-14,

15-19,20-24,25-29,30-34,35-39,40-44,etc).

TheWAIFWmatrixisconstructedusingsocialcontactdata.

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CPproductionconstraints

Screening

FiveBSL3-trainedtechniciansto

runtheserologicaltests,each

running150testsevery3days.

i.e.5x150serverswithmean

servicetimeof3days

Plasmapheresis

9machines.12-hrdailyoperation.

Eachplasmadonationtakesabout40min.

i.e.9serverswithmeanservicetimeof1/16day.

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Patternsofdemandandsupply

Basic reproductive numberR0 = 1.4Mean latent duration = 1.2 days

Mean symptomatic/asymptomatic duration = 4.1 days

Proportion of infections symptomatic = 2/3

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Donorpercentageneeded

rTpHis the lumped demand parameter:

rTis the number donors needed for treating one patient on average (range: 2 to 10)pHis the proportion of symptomatic cases that become severe cases (range: 0.1% to 1%)

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DonorpercentageneededTreatment coverage increases rapidly as donor percentage increases fro 0%.

The average blood donation percentage is around 5%.15% to 20% donor percentage is sufficient to treat over 80% of cases

for a moderately severe pandemicIncreasing donor percentage beyond this level has small marginal benefit

Treatment coverage

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Conclusions

WithplasmapheresiscapacitysimilartothatinHongKong,theproposedpassiveimmunotherapyprogramcansupplyCPtransfusiontotreatmorethan82%ofseverecasesinamoderatepandemic(R0


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THEEND

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Modeling Interventions and Logistics

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