Agent-based simulation for weekend-extension strategies to mitigate influenza outbreaks
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Title: Agent-based simulation for weekend-extension strategies to mitigate influenza outbreaks
Physical Description: Journal Article
Creator: Mao, Liang
Publisher: BMC Public Health
Publication Date: June 30 2011
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Abstract: Background Non-pharmaceutical strategies are vital in curtailing impacts of influenza and have been intensively studied in public health. However, few strategies have explicitly utilized the weekend effect, which has been widely reported to be capable of reducing influenza infections. This study aims to explore six weekend-extension strategies against seasonal and pandemic flu outbreaks. Methods The weekend-extension strategies were designed to extend regular two-day weekend by one, two and three days, respectively, and in combination with either a continuous or discontinuous pattern. Their effectiveness was evaluated using an established agent-based spatially explicit simulation model in the urbanized area of Buffalo, NY, US. Results If the extensions last more than two days, the weekend-extension strategies can remarkably reduce the overall disease attack rate of seasonal flu. Particularly, a three-day continuous extension is sufficient to suppress the epidemic and confine the spread of disease. For the pandemic flu, the weekend-extension strategies only produce a few mitigation effects until the extensions exceed three days. Sensitivity analysis indicated that a compliance level above 75% is necessary for the weekend-extension strategies to take effects. Conclusion This research is the first attempt to incorporate the weekend effect into influenza mitigation strategies. The results suggest that appropriate extensions of the regular two-day weekend can be a potential measure to fight against influenza outbreaks, while minimizing interruptions on normal rhythms of socio-economy. The concept of weekend extension would be particularly useful if there were a lack of vaccine stockpiles, e.g., in countries with limited health resources, or in the case of unknown emerging infectious diseases.
Acquisition: Collected for University of Florida's Institutional Repository by the UFIR Self-Submittal tool. Submitted by Liang Mao.
Publication Status: Published
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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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