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RESEARCHARTICLE OpenAccessAgent-basedsimulationforweekend-extension strategiestomitigateinfluenzaoutbreaksLiangMaoAbstractBackground: Non-pharmaceuticalstrategiesarevitalincurtailingimpactsofinfluenzaandhavebeenintensively studiedinpublichealth.However,fewstrategieshaveexplicitlyutilizedtheweekendeffect,whichhasbeenwidely reportedtobecapableofreducinginfluenzainfections.Thisstudyaimstoexploresixweekend-extension strategiesagainstseasonalandpandemicfluoutbreaks. Methods: Theweekend-extensionstrategiesweredesignedtoextendregulartwo-dayweekendbyone,twoand threedays,respectively,andincombinationwitheitheracontinuousordiscontinuouspattern.Theireffectivenesswas evaluatedusinganestablishedagent-basedspatiallyexplicitsimulationmodelintheurbanizedareaofBuffalo,NY,US. Results: Iftheextensionslastmorethantwodays,theweekend-extensionstrategiescanremarkablyreducethe overalldiseaseattackrateofseasonalflu.Particularly,athree-daycontinuousextensionissufficienttosuppressthe epidemicandconfinethespreadofdisease.Forthepandemicflu,theweekend-extensionstrategiesonlyproduce afewmitigationeffectsuntiltheextensionsexceedthreedays.Sensitivityanalysisindicatedthatacompliance levelabove75%isnecessaryfortheweekend-extensionstrategiestotakeeffects. Conclusion: Thisresearchisthefirstattempttoincorporatetheweekendeffectintoinfluenzamitigation strategies.Theresultssuggestthatappropriateextensionsoftheregulartwo-dayweekendcanbeapotential measuretofightagainstinfluenzaoutbreaks,whileminimizinginterruptionsonnormalrhythmsofsocio-economy. Theconceptofweekendextensionwouldbeparticularlyusefuliftherewerealackofvaccinestockpiles,e.g.,in countrieswithlimitedhealthresources,orinthecaseofunknownemerginginfectiousdiseases.BackgroundDespiteadvancesinmedicalsciences,influenza(commonlyknownasflu)remainsaremarkablethreattothe publichealthandsocio-economyasawhole.Seasonal flutypicallyinfects10%~20%oftheUSpopulationevery year[1].ThepandemicH1N1influenza(the2009swine flu)wasrecentlyreportedtoberesponsiblefor274,000 hospitalizationsand12,470deathsintheUS[2].Dueto therapidmutationandswiftspreadoffluvirus,preparednessforimminentpandemicsisnowatoppriority ofpublichealth[3].Amongthecoreissuesofpreparednessisthestudyofmitigationstrategiesthatcanminimizeimpactsofinfluenzaonhumansociety. Non-pharmaceuticalmitigationstrategies,suchasthe householdquarantine,workplace/schoolclosure,and travelrestriction,hadbeen embeddedwithinthelatest frameworkofinfluenzapreventionandcontrolrecommendedbytheCDC sAdvisoryCommitteeonImmunizationPractices[4].Thesestrategiesarecriticalbecause theyrepresenttheonlytypeofinterventionmeasure guaranteedtobeavailableagainstanovelstrainofinfluenzaintheearlyphasesofapandemic[5].Theirultimategoalsaretoreduceinfectionsanddelay transmission,therebyallowingtimetoimplementpharmaceuticalstrategies,suchasvaccinationandantiviral prophylaxis.Manystudies,however,havepointedout thatthenon-pharmaceuticalstrategiesareoftendifficult toputintopractice,sincetheireffectivenessishighly dependentonthecomplianceofpopulation[6].Furthermore,thesestrategiesmayinfringeonhumanrightsand involvepsychological,ethicalandlegalissues,e.g.,limitingfreemovementofindivid uals.Arecentevaluation hadconcludedthattherewasagenerallackofscientific evidenceorexpertconsensu sforimplementingthese strategies[7].Duetothesedrawbacks,theexplorationof Correspondence:liangmao@ufl.edu DepartmentofGeography,UniversityofFlorida,Gainesville,Florida,32611, USAMao BMCPublicHealth 2011, 11 :522 http://www.biomedcentral.com/1471-2458/11/522 2011Mao;licenseeBioMedCentralLtd.ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommons AttributionLicense(http://creativecommons.org/licenses/by/2.0),whichpermitsunrestricteduse,distribution,andreproductionin anymedium,providedtheoriginalworkisproperlycited.

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non-pharmaceuticalstrategiesremainsanactivelypursuedtopicinpublichealth. Thispaperproposesanewtypeofnon-pharmaceuticalstrategiesthatextendedtheregulartwo-dayweekend forthepurposesofinterruptinginfluenzatransmission andmitigatingdiseaseimpacts,referredtoas weekendextensionstrategies .Inthecurrentliterature,fewmitigationstrategieshaveconsideredthereductiveeffectof weekendoninfluenzatransmission,althoughthiseffect hasbeenwidelyreported[8-10].Forexample,thestudy byHensetal.ineightEuropeancountriesestimateda 10~20%reductionininfluenzainfectionsduringweekendwhencomparedtoweekdays[10].Researchbyboth Leeetal.andCooleyetal.attributesthevariabilityof influenzaincidencetotheweekday-weekendeffect[8,9]. Aprimaryreasonisthatmo stworkplacesandschools areclosedsimultaneouslyduringweekend,andthus fewerhumancontactstakeplaceasopposedtoweekdays.Forinstance,asurveybyMcCawetal.indicated thatanindividualhas2~4mo repersonalcontactsduringweekendthanweekdays[11].Astudyofuniversity studentsbyEdmundsetal.alsofoundthatindividuals made26contactsperdayduringweekdays,butonly19 perdayduringweekend[12].Thesestudiesimplythat extendingtheweekendperiodmightbeaneffective strategytomitigateinfluenzaoutbreaks. Totesttheeffectivenessofweekend-extensionstrategies,anestablishedagent-basedspatially-explicitmodel wasdevelopedfortheurbanizedareaofBuffalo,New York,US.Themodelsimulatedthesestrategiesandproducedepidemicoutcomesforevaluation.Theremainder ofthisarticleisorganizedintofollowingsections.The secondsectionintroducesthestudyareaandmethods, includingthedesignofweekend-extensionstrategies andtheagent-basedsimulationmodel.Thethirdsection presentssimulationresultsandcomparestheeffectivenessbetweenstrategies.Thefourthsectiondiscusses modeloutcomesandimplications,andthefinalsection concludesthearticle.MethodsDesignofweekend-extensionstrategiesTwodimensionswereinvolvedinthedesignofweekendextensionstrategies.Onedimensionconcernedthelength ofextensions,i.e.,howlongtheregularSaturdayandSundayweekendshouldbeextended.Theotherdimension specifiedthepatternofextensions,i.e.,inwhichmanner theextensionsshouldbeapplied.Acontinuouspattern meansthattheadditionalweekendfollowsrightafterthe regularweekendandlastscontinuously,e.g.,Saturday+ Sunday+(Monday+Tuesday ).Adiscontinuouspattern separatelyarrangestheadditionalweekendwithinaweek, forinstance,Saturday+Sunday+(Tuesday+Thursday). Thecontinuousextensionsproducelongerandless frequentinterruptionsoninfluenzatransmission,while thediscontinuousextensionscauseshorterandmorefrequentinterruptions.Inthisresearch,threelengthsof extensionswereinvestigated,includingone,twoandthree days,incombinationwiththetwopatternsofextensions (continuousanddiscontinuous).Thecombinationofthe twodimensions(3lengths2patterns)resultedinsix strategiestobeevaluated(Table1).Duringtheadditional weekend,allbusinesses(in cludingschools)wereclosed exceptforservice-orientedplaces,suchasutilitycompanies,healthfacilities,restaurants,andgrocerystores.Individualswereassumedtofollowactivitypatternsofeither SaturdayorSunday,e.g.,stayingathome,visitingservice places,ormeetingwithfriendsinneighborhouseholds.StudyareaanddatacollectionThesixproposedstrategieswereinvestigatedinthe urbanizedareaofBuffalo,NewYork,US.Thisstudy areawaschosenbecauseanin fluenzasimulationmodel hadbeenpreviouslyestab lished[13].Theinputdata includedtheinformationabout985,001individualsand 400,870householdsfromUSCensus2000[14],aswell asadatabaseof36,839businesslocationsinyear2009 [15].Individualswereassumedtotravelthroughalocal transportationsystem,taketheirdailyactivitiesat homesandbusinesslocations,havecontactwithone another,andexposethemselvestoinfluenzainfection.Agent-basedinfluenzamodelTheestablishedagent-basedmodelfirstsimulateda contactnetworkinthestudyarea,whichprovideda basisforinfluenzatransmission[13].Thenetworkconsistsof985,001discreteindividualsasnodesandtheir dailycontactsaslinks.Individualcontactswereassumed totakeplaceduringthreetimeperiodsinadayandat fourtypesoflocations.Thethreetimeperiodsincluded: daytime,pastimeandnighttime,whilethefourtypesof locationsreferredtohomes,workplaces(schools,financialoffices,administrativeu nits,industrialfactories, etc.),serviceplaces(utilitycompanies,healthfacilities, grocerystores,etc.),andneighborhouseholds(householdsinthesamecensusblockgroup).Modeledindividualstraveledbetweentimeandlocation,andhad contactwithdifferentgroup sofindividuals,suchas familymembers,co-workers,clerks,andfriends.These spatiotemporallyvaryingcont actslinkedallindividuals intoacity-widenetwork. Toconstructsuchacontactnetwork,threepopulationsofdaytime,nighttimeandpastimeweresynthesizedrespectivelyandthenlinkedtogether[13].The censusdatawasusedtobuildthenighttimepopulation ofindividualsandhouseholdsthatmatchedtherealage andhouseholdstructures.Thenighttimepopulationwas assignedtobusinesslocati onstocreatethedaytimeMao BMCPublicHealth 2011, 11 :522 http://www.biomedcentral.com/1471-2458/11/522 Page2of10

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population,accordingtot hetraveltimetoworkand industrialtypesofbusinesslocations.Next,thepastime populationwasgeneratedbasedontheinformationof previoustwopopulationsandaregionaltravelsurvey [16].Undertheconstraintsoftravelstatistics,individualswerefurtherallocatedtoserviceplacesandneighborhouseholds.Detailedalgorithmstogeneratethese threepopulationscanbereferredtotheworkbyMao andBian[13]. Thisresearchfurtherdistinguishedtheweekdayand weekendactivitiesofindividualsbasedontheregional travelsurvey.Specifically,in dividualswerenotassigned toworkduringweekend(bothregularandadditional) exceptforthosewhoworkatserviceplaces.Thetrips toworkplacesorschools(forchildrenunder18years old)werereplacedbyeitherstayingathomes,orvisiting serviceplaces/neighborhouseholds.Thesimulatedindividualcontactsduringaweekdayandaweekendday (Figure1)haveclearpower-lawdistributions,consistent withtheobserved scale-free propertyofhumansocial networks.Theaveragenumberofcontactsattheweekendis2.4fewerthanthatintheweekday,becausefewer workplacecontactshappenattheweekend.FluinfectivityscenariosToinitializeinfluenzatransmissionthroughthemodeled network,fiveinfectiousindividualswererandomly seededintothestudyareaatthefirstdayofsimulation. Thesimulationtookatri-dailytimestepandlastedfor 200days.Duringeachtimestep,anindividualheldone offourinfectionstatus,i.e.,susceptible,latent,infectious, orrecovered.Theinfectionproceededfor7-10days,with 2dayslatent,1dayasymptomaticandinfectious,followedby4-7daysinfectiousvaryingoveragegroups (Children:<16years;Adults:16-64years;Senior:>64 years)[17].Theprobabilityofdevelopingsymptomsonce infectedwassetto0.5[18],andsymptomaticindividuals werereferredtoas influenzacases insubsequentdiscussion.Further,aproportionofsymptomaticindividuals wasselectedtowithdrawtohomebasedonprevioussurveysoffluself-carebehavior[19,20].Thestochastic simulationrandomizedthefiveinfectiveseeds,thedaily contactsofindividualsandtheinfectionsthroughcontacts,aswellasthedevelopmentofsymptomsandthe withdrawal-to-homeofsymptomaticindividuals. Thetransmissionofinfluenzawassimulatedby repeatedlytracingsusceptiblecontactsofinfectiousindividuals,andidentifyingwhowillreceivetheinfectionin thenexttimestep.Thereceiptofinfectionwasmodeled asastochasticeventdeterminedbytheagegroupsof receiversandtheinfectivit yofviralstrains.Theviral infectivitywasspecifiedby R0(thebasicproductive number),whichisdefinedasthenumberofsecondary casescausedbyasingleinfectedcaseinawhollysusceptiblepopulation[21].Relevanttothisresearch,two scenariosoffluinfectivitywereestablishedtoexamine theeffectivenessofweekend-extensionstrategies:aseasonalfluscenario( R0=1.4)andapandemicfluscenario ( R0=2.0)[22].Comparedtotheseasonalflu,thepandemicfluoccursrarelybuttransmitsmoreeasily betweenhumanbeingsandspreadsquicklyalloverthe world,becausethevirusisoftennoveltohuman immunesystem.Undereachfluscenario,abaselineoutbreakandthesixstrategies(inTable1)weresimulated andcomparedwithoneanother.Thebaselineoutbreak representeda noresponse situationwithnostrategies applied,andservedasareferenceforcomparisonpurposes.Tovalidatethemodel,thebaselineoutcomes werecomparedtoCDCweeklyreportsoflaboratory confirmedspecimensin2004-05fluepidemicinthe studyarea[23].MeasuresofcontroleffectivenessThesixweekend-extensionstrategieswereassumedto beimplementedwhenthecumulativenumberof Table1Designofsixweekend-extensionstrategiesandtheirabbreviationsPatternsLengths(day) Continuous Discontinuous One Monday(Mon) Wednesday(Wed) Two Monday+Tuesday(Mon+Tue) Tuesday+Thursday(Tue+Thur) Three Monday+Tuesday+Wednesday(Mon+Tue+Wed)Monday+Wednesday+Friday(Mon+Wed+Fri) Figure1 Contactpatternsduringaweekdayandaweekend Frequencydistributionsofindividualcontactsduringaregular weekday(blue)andaweekend(red).The X axisrepresentsthe numberofdailycontacts,andthe Y axisdenotesthecorresponding frequencyinthepopulation. Mao BMCPublicHealth 2011, 11 :522 http://www.biomedcentral.com/1471-2458/11/522 Page3of10

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influenzacasesexceeded1,000(about1 ofthepopulation).Thesimulationresultsrecordedthetimeperiod andlocationofeveryinfect ionevent.Theresultswere aggregatedintoadailyepidemiccurve,whichdepicted thenumberofnewinfluenzacasesperdayduringthe courseofanepidemic.Chara cteristicsassociatedwith theepidemiccurvewerealsoextracted,includingan overallattackrate(thetotalpercentofinfluenzacases inthepopulation),anepidemicpeak,andpeaktime.An outbreakwasdeemedtobesuccessfullycontrolledifthe overallattackratecanbereducedbelow10%[5].In addition,theattackrate<5%wasusedasacriterionfor evaluatingifanoutbreakcanbefurtherprevented,since reportedfluepidemicsoftenhaveanattackrateof5% orhigher[1].Tocomparestrategies,arelativeeffectivenesswascalculatedasaratiooftheattackratereduced byastrategytothebaselineattackrate.Thisrelative effectivenessrangesfrom0to1,with0indicatingno effectivenessoninfluenzaoutbreaks.Further,asensitivityanalysisandANOVAtestwereconductedupona rangeofcompliancelevels,including100%,90%,75%, 50%and0%ofbusinesses,accountingforthesituation thatbusinessownerswerereluctanttosuspendtheir businesses. Thisresearchalsodisplayedthespatialeffectivenessof mitigationfromeachstrategy.Thesimulationresults wereconvertedfrompointsofinfectionstogridcellsof infectionsperkm2,asinfectionintensitymaps.Akernel densityfunctionwasutilizedtointerpolatethetotal numberofinfectionsateverycelllocationduringthe 200-daysimulation.Thecellsizewassetto5050m becauseitapproximatedtheaverageextentoflandparcelsinthestudyarea.Aneffectivestrategywasexpected toreducetheinfectioninte nsityateverylocationand confinethespatialextentofaffectedareas.Boththeepidemiccurvesandinfectionintensitymapsshowedthe meanof50modelrunstoaverageoutthevariation causedbythestochasticsimulation.ResultsBaselineoutbreaksofseasonalandpandemicfluThemodeledepidemiccurveunder R0=1.4matched wellwiththeobservedtimecourseofaseasonalfluoutbreakinyear2004-05(Figure2),althoughthemagnitudeofsimulatedcurvewaslargerthanthereported. Thisisbecausealargeproportionofinfectedpeople maynotmanifestsymptomsorseekhealthcare,and thusthenumberofinfluenzacaseswashighlyunderreportedbyCDC.Inthissense,thesimulationmodel performedwellinpredictingthetimetrend,andatleast allowedarepresentationoftheworsecaseresult.The pandemicflu(R0=2.0)causedanearlierandhigher epidemicpeakwithmoreinfluenzacases,becausethis virusstrainisfarmorecontagiousandspreadsfaster.Continuousweekend-extensionstrategiesInthecaseofseasonalflu,theeffectivenessofthree continuousstrategiesdifferstatisticallyfromone another( F =6.89and p -value=0.02fromANOVA). ExtendingtheweekendtoM ondaymildlyreducedthe overallattackratefrom18.61%to16.14%(Table2)and slightlydelayedthepeaktimebyoneweek(Figure3a). Apparentmitigationeffectsoccurredwhentheweekend wasextendedbytwoconsecutivedaysorlonger.Given ahighcompliancelevel(>90%),the Mon+Tue strategy canlessentheoverallattackratecloseto10%andpostponethepeaktimebyalmost7weeks.Extendingthe weekendbythreeconsecutivedays(Mon+Tue+Wed) wascapableofcontrollingtheattackrateunder10%, givenacompliancelevelabove75%.Providedafull compliance,the Mon+Tue+Wed strategycanevenpreventtheepidemicbycurtailingtheattackratefarbelow 5%.Turningtothepandemicfluscenario(Figure3b), thethreecontinuousweekend-extensionstrategiesdid notperformaseffectivelyasintheseasonalfluscenario, buttheireffectivenessremainedstatisticallydifferent( F =14.7and p -value=0.001).Extendingtheweekendby oneortwodaysproducedafeweffectsontheoverall attackrateandpeaktime.Onlythethree-daycontinuousextensioncansignificantlylowertheoverallattack ratefrom26%to20%(Table2).Allthreestrategies werenotcapableofcontrollingthepandemicflu independently. Thecompliancelevelsofb usinesseshadprofound effectsonthecontroleffectiveness(Table2).Thelonger theextensionofweekend,thelowerthecompliance levelwasneededtoachievethesamecontroleffectiveness.Fortheseasonalflu,increasingthecompliance Figure2 Baselinescenariosofse asonalandpandemicflu. Simulatedbaselineoutbreaksofinfluenzaepidemic(Green)and pandemic(Red),comparedtothereportedinfluenzaepidemicby CDCinthesameareaforyear2004-5(Bluebars).Thebarsrepresent thenumberofconfirmedinfluenzaspecimensperweekduringthe epidemic2004-5(Left Y axis).Thecurvesrepresentnewlyinfluenza casesperweekduringthecourseofanepidemicorapandemic (Right Y axis). Mao BMCPublicHealth 2011, 11 :522 http://www.biomedcentral.com/1471-2458/11/522 Page4of10

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levelfrom50%to90%canimprovethecontroleffectivenessby2-3times( F =4.40, p -value=0.008from ANOVA).Withrespecttopandemicflu,thecompliance levelscausedlessvariationincontroleffectivenessbut remainstatisticallydifferent( F =3.36and p -value= 0.02).Eventhe100%compliancecannothelpanyofthe threestrategiestodampentheflupandemics. Thespatialeffectivenessagainstseasonalfluwasof interestaswell.Fortheeaseofdescription,theintensity mapsdividedthestudyareaintothreezones:acentral businessdistrict(CBD),atransitionzone,andasuburb (Figure4).Thezonaldelineationwasbasedondensities ofhouseholdsandbusinesses,aswellasthelayoutof majorroads.The Mon strategy(Figure4a)failedto preventthewidedispersionofinfluenza.Theentire studyareawasdominatedbyhighintensityofinfections (>200infectionsperkm2).The Mon+Tue strategy(Figure4b)apparentlymitigatedinfectionsinallthree zones,butcouldnotdownsizetheaffectedareas.The Mon+Tue+Wed strategyhadanoutstandingeffecton thespatialdispersionofinfluenza(Figure4c).The affectedareaswerelargelyreduced,leavingtheextensive suburbwithonlyasmallnumberofinfectionclusters.Discontinuousweekend-extensionstrategiesComparedtothecontinuousstrategies,thediscontinuousstrategiesresultedinepidemiccurveswithmore oscillations(Figure5).Thisisbecausethedaysonand Table2Sensitivityofcontinuousweekend-extensionstrategiestocompliancelevelsEffectiveness R0=1.4 R0=2.0 ComplianceOverallattackrates%(95%CIa)RelativeeffectivenessbOverallattackrates%(95%CI)Relativeeffectiveness Baseline18.61(18.54,18.71)0.0026.43(26.36,26.53)0.00 Mon100%16.14(16.03,16.26)0.1325.52(25.43,25.62)0.03 90%16.41(16.28,16.54)0.1225.58(25.49,25.67)0.03 75%16.83(16.74,16.96)0.1025.74(25.67,25.82)0.03 50%17.53(17.39,17.65)0.0626.01(25.95,26.09)0.02 Mon+Tue100%11.82(11.58,12.11)0.3623.84(23.73,23.94)0.10 90%12.98(12.80,13.17)0.3024.10(24.00,24.22)0.10 75%14.23(13.93,14.46)0.2324.55(24.41,24.96)0.07 50%15.99(15.81,16.22)0.1425.28(25.16,25.36)0.04 Mon+Tue100%3.26(1.47,4.79)0.8220.30(20.16,20.42)0.23 +Wed90%7.24(4.87,8.21)0.6121.15(21.01,21.34)0.20 75%10.92(10.27,11.37)0.4122.31(22.17,22.43)0.16 50%14.45(14.13,14.80)0.2224.00(23.81,24.15)0.10a95%CIstandsforthe95%confidenceintervalsfrom50modelrealizations.bRelativeeffectiveness=(Baselineattackrate-Strategy-specificattackrate)/Baselineattackrate. Table2comparestheoverallattackratesandrelativeeffectivenessresultedfromthreecontinuousweekend-extensionstrategies(Mon,Mon+Tue,andMon+Tue +Wed).Sensitivityanalysiswasconductedoneachstrategyunderfivecompliancelevelsof0%,50%,75%,90%,and100%. Figure3 Continuousweekend-extensionstrategies(1) .Simulatedepidemiccurvesfromthreecontinuousweekend-extensionstrategies,in comparisonwiththebaselineepidemic. Y axisindicatesthenumberofnewlyinfluenzacasesperdayduringthe200daysimulation.Allcurves areaveragesof50randomlyseededsimulationruns. Mao BMCPublicHealth 2011, 11 :522 http://www.biomedcentral.com/1471-2458/11/522 Page5of10

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offworkswitchedmorefrequentlyandposedmore interruptionsonflutransmission.TheANOVAindicatedsignificantdifferencesbetweentheeffectivenessof threestrategies: F =3.96and p -value=0.05,given R0= 1.4; F =5.62and p -value=0.02,given R0=2.0.The sensitivityanalysisshowedincreasedcontroleffectivenesswithalongerweekendperiodandahighercompliancelevelofbusinesses(Table3).Onlythethree-day discontinuousextension( Mon+Wed+Fri )witha90% compliancelevelcancontroltheseasonalflu(attack rate<10%).Ifthecompliancecouldberaisedto100%, thethree-dayextensionwouldbeadequatetoprevent theseasonalfluepidemic(attackrate<5%).Forthepandemicflu,however,noneofthesethreediscontinuous strategiesproducedsignific antmitigationeffects.Even thethree-dayextensionstrategywitha100%compliance levelfailedtoreducetheattackratebelow20%. Fromaspatialperspective,the Wed strategy(Figure 6a)contributedlittletocontainingtheextensivespread ofseasonalflu.Amajorityofthestudyareaunderwent Figure4 Continuousweekend-extensionstrategies(2) .Spatialpatternsofinfectionsresultedfromthethreecontinuousweekend-extension strategies,given R0=1.4andcompliancelevel=100%:(a)Mon,(b)Mon+Tue,and(c)Mon+Tue+Wed.Each50m50mcellvalueindicates thetotalnumberofinfectionsduringthe200daysatthecelllocation(infections/perkm2).Allcellvaluesareaveragesof50randomlyseeded simulationruns. Figure5 Discontinuousweekend-extensionstrategies(1) .Simulatedepidemiccurvesfromthethreediscontinuousweekend-extension strategies,incomparisonwiththebaselineepidemic. Y axisindicatesthenumberofnewlyinfluenzacasesperdayduringthe200day simulation.Allcurvesareaveragesof50randomlyseededsimulationruns. Mao BMCPublicHealth 2011, 11 :522 http://www.biomedcentral.com/1471-2458/11/522 Page6of10

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ahighintensityabove200infectionsperkm2.The Tue +Thur strategy(Figure6b)slightlychangedthespatial patternsandproducedsmallimprovementasopposed tothe Wed extensionstrategy.The Mon+Wed+Fri strategy(Figure6c)eliminatedinfectionsinmostparts ofthesuburb,buttheCBDandtransitionzone remainedatamoderateintensityofaround100 infectionsperkm2.Geographically,thisstrategyfailedto isolatetheaffectedareaintosmallclustersofinfections.SharesofinfectionsbylocationItisalsonoteworthytocomparehowtheseweekendextensionstrategiesmovethefociofinfectionsbetween thefourtypesoflocation,i.e.,home,workplace,service Table3Sensitivityofdiscontinuousweekend-extensionstrategiestocompliancelevelsEffectiveness R0=1.4 R0=2.0 ComplianceOverallattackrates%(95%CIa)RelativeeffectivenessbOverallattackrates%(95%CI)Relativeeffectiveness Baseline18.61(18.54,18.71)0.0026.43(26.36,26.53)0.00 Wed100%16.53(16.42,16.64)0.1125.67(25.58,25.75)0.03 90%16.76(16.60,16.90)0.1025.73(25.67,25.79)0.03 75%17.10(16.98,17.21)0.0825.86(25.77,25.95)0.02 50%17.70(17.54,17.87)0.0526.08(26.01,26.14)0.01 Tue+Thur100%14.43(14.30,14.58)0.2224.77(24.68,24.84)0.06 90%15.00(14.87,15.16)0.1924.93(24.83,25.00)0.06 75%15.73(15.63,15.83)0.1525.23(25.17,25.29)0.05 50%16.90(16.79,17.02)0.0925.70(25.62,25.77)0.03 Mon+Wed+100%5.49(1.59,6.88)0.6921.41(21.27,21.52)0.19 Fri90%9.23(8.11,9.80)0.5022.07(21.95,22.23)0.16 75%11.92(11.64,12.27)0.3623.00(22.81,23.11)0.13 50%14.95(14.72,15.28)0.2024.42(24.32,24.56)0.08a95%CIstandsforthe95%confidenceintervalsfrom50modelrealizations.bRelativeeffectiveness=(Baselineattackrate-Strategy-specificattackrate)/Baselineattackrate. Table3comparestheoverallattackratesandrelativeeffectivenessresultedfromthreediscontinuousweekend-extensionstrategies(Wed,Tue+Thur,andMon +Wed+Fri).Sensitivityanalysiswasconductedoneachstrategyunderfivecompliancelevelsof0%,50%,75%,90%,and100%. Figure6 Discontinuousweekend-extensionstrategies(2) .Spatialpatternsofinfectionsresultedfromthethreediscontinuousweekendextensionstrategiesgiven R0=1.4andcompliancelevel=100%:(a)Wed,(b)Tue+Thur,and(c)Mon+Wed+Fri.Each50m50mcellvalue indicatesthetotalnumberofinfectionsduringthe200daysatthecelllocation(infections/perkm2).Allcellvaluesareaveragesof50randomly seededsimulationruns. Mao BMCPublicHealth 2011, 11 :522 http://www.biomedcentral.com/1471-2458/11/522 Page7of10

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place,andneighborhousehold(Figure7).Foreach strategy,theresultantsharesofinfections(%)werecalculatedbycountingthenumberofinfectionsoccurring ateachtypeoflocation,anddividingitbythetotal numberofinfectionsduringtheepidemic.Forthebaselinescenario( R0=1.4),theworkplacesandhomeshad thesameshareofinfections(38%).Astheextension daysincreaseupto3days,theweekend-extensionstrategiesheavilyreducedtheshareofinfectionsatworkplacesfrom38%to20%,whilegreatlyelevatedtheshare athomesfrom38%to50%.Thesharesofinfectionsat neighborhouseholdsandserviceplaceswerealso slightlyenlargedby3%.DiscussionAnalysesaboveimplythattheeffectivenessofweekendextensionstrategiesissensitivetothelengthofextensions,thecompliancelevelofbusinesses,andtheinfectivityofinfluenzavirus .Thethree-dayextension strategyiscapableofcontrollingseasonalfluepidemics, andevenpreventstheepid emicsifahighcompliance levelcanbeachieved.Thereasonisthatindividuals wouldhavefarfewercontactsduetoalargelyreduced weekdayschedule.Mostinfectionsarelimitedwithin households,butcannotspreadouttoworkplacesuntil individualsgobacktowork,makingthetransmission inefficient.However,theweekend-extensionstrategies alonearenotabletocontrolpandemicflu,becausethis virusstrainissocontagiousthatonlyafewhumancontactscouldsustainthechainoftransmission.Tobe effectiveinflupandemics,thesestrategiesneedtobe complementedbyotherpharma ceuticalstrategiesthat offerdirectprotectiontoindividuals,suchasthemass vaccinationandantiviralprophylaxis. Comparisonshowedthatthethreediscontinuous extensionstrategies(Table3)arelesseffectivethan theircontinuouscounterpa rts(Table2),becausethe resultantattackratesare1~3%higher.Thissuggests thatlongerandlessfrequentinterruptionsoninfluenza transmissionwouldbemoreeffectiveindiseasecontrol thanshorterandmorefrequentinterruptions.Aprobableexplanationisthatthetransmissionofinfluenza wouldbedoublyeffectiveifinfectiousindividualsconstantlymeetwithsusceptibleindividualsatbothhomes andworkplaces.Acontinuousweekendextensionallows diseasetransmissionbetweenhouseholdmembers,but eliminatesthetransmissionamongco-workersfora relativelongperiod(e.g.,3~5days).Hence,thepossible routesfortransmissionarequicklyexhaustedathomes, andepidemicscannotfurtherdevelopuntilindividuals gobacktowork.Incontrast,adiscontinuousweekend extensionallowsinfluenzanotonlyspreadingwithin households,butalsotransmittingintermittentlywithin workplacecontexts(e.g.,everyotherday).Thepoolof susceptibleindividualscanbereplenishedatashort timeinterval,resultinginmoreinfections. Figure7 ShareofInfectionsbylocation .Shareofinfections(inpercentage)atthefourtypesoflocationsrespectively,asaresultofthesix weekend-extensionstrategiesunder R0=1.4.Allpercentagesareaveragesof50randomizedmodelruns. Mao BMCPublicHealth 2011, 11 :522 http://www.biomedcentral.com/1471-2458/11/522 Page8of10

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Aspeoplespendmoretimeathomeduringthe extendedweekend,itisnotsurprisingthatthefociof infectiongraduallymovefromworkplacestohomes (Figure7).Thisalsoexplainswhythehighestintensity ofinfectionsoftenoccurswithintheCBD(Figure4and 6).Withahouseholddensityof1,189.30/km2,theCBD hasamuchhigherconcentrat ionofresidentsthanthe transitionzone(879.30/km2)andsuburb(21.30/km2). ThedensecontactnetworkwovenbyconcentratedresidentsretainedtheCBDrelativelyinsensitivetothe weekend-extensionstrategies.Inthiscase,theCBD couldbefurthertargetedbyhouseholdprophylaxisor householdquarantinestrategies,ascomplementary interventions.AvaccinationprogramprioritizingCBD residentswouldalsobeawisepreparationforweekendextensionstrategies. Inadditiontothelandusepatterns,thetravelbehaviorofindividualsisanotherkeyfactorfordiseasedispersion[13].Thisexpl ainswhythethree-day continuousextensionstrategyisthemosteffectiveto confinethespatialspreadofseasonalflu.Thelong weekendperiodgreatlyreducesthetravelbetween homesandworkplaces,whichisamajorcomponentof individualdailyactivities.Manyinfectiousindividuals stayhomefor5consecutivedays, usingup theinfectiousperiodofinfluenzavirus.Whentheseindividuals gobacktowork,theyarenolongerinfectiousandcannotinfecttheirco-workers,therebylimitingthelongdistancedispersionofinfluenza. Fromperspectivesofpsychology,ethicsandlaw,the weekend-extensionstrategymayinvolvemilderissues thanothernon-pharmaceuticalstrategies,suchasthe caseisolationorhouseholdquarantine.Ithasbeen widelyreportedthatmanynon-pharmaceuticalstrategies,particularlyforlongduration,cancauseloneliness, emotionaldetachmentandinfringementofindividual rights,suchasthefreedomofmovement[24].Differently,theweekend-extensionstrategyonlycausesshorttermsocialseparation,andallowspeopletomovefreely toanywheretheywantduringtheextendedweekend. Manyethicalandlegalissuesthereforecouldbepossibly mitigatedoravoided. Thesocio-economiclossfromwork/schoolabsenteeismisapotentialproblemforimplementingweekend extensionstrategies.Onesolutionistoencouragepeopletoworkathomeduringtheextendedweekend, completebusinesstransactionsthroughtelecommunication,andtakecoursesonline.Insuchamanner,the face-to-facecontactsforinfectionarereduced,while long-terminterruptionsonsocio-economycouldbe minimized.Ifthelong-distanceworkingandlearning arenotfeasibleforcertainoccupations,analternativeis tograntthesegroupsofpeopleahigherpriorityfor receivingpharmaceuticalinterventions.ConclusionsThisresearchisthefirstattempttoconsidertheweekendeffectoninfluenzacontrolandprevention,and startsanewdirectionfordesigningmitigationstrategies. Theeffectivenessofweekend-extensionstrategies dependsonthelengthandpatternofextensions,aswell asthecomplianceofbusinesses.Thesimulationresults suggestthattheextensionofregularweekendbymore thantwodayscansignificantlymitigateseasonalfluepidemics.Forpandemicflu,theweekend-extensionstrategiesarenoteffectivealone,butwouldbeuseful complementstopharmaceuticalstrategies. Likeothernon-pharmaceuticalstrategies,theweekend-extensionstrategycouldbeafeasiblemeasurefor countrieswithlimitedhealthresources,becauseno stockpilesofvaccinesandantiviraldrugsareneeded. Althoughinfluenzaistakenasanexampleinthis research,itisbelievedthattheconceptofweekend extensionscanalsohelpfightotheremerginginfectiousdiseasesthatarepoorlyunderstoodandunpreparedfor,suchasnewstrainsofinfluenza,SARS (Severeacuterespiratorysyndrome),andEbola.With theadvanceintelecommunicationtechnologiesand theshiftofworkingstylesfromworkplacetohome, theweekend-extensionstrategymayhavelong-term containmentbenefitsforthisclassofdiseases,and wouldbeawiseoptionforpublichealthplannersin thenearfuture.Acknowledgements Theauthoristhankfulforthevaluablecommentsfromtheeditorandtwo reviewers.PublicationofthisarticlewasfundedbytheUniversityofFlorida Open-AccessPublishingFund. Authors contributions LMconceivedanddesignedthework,performedallcodingandsimulation, carriedoutallanalyses,andistheauthorofthemanuscript. Competinginterests Theauthordeclaresnocompetinginterests. Received:9March2011Accepted:30June2011 Published:30June2011 References1. KeyFactsAboutSeasonalInfluenza(Flu). 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