Preventing an Avian Flu Pandemic论文.docx
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Preventing an Avian Flu Pandemic论文.docx
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PreventinganAvianFluPandemic
GangLiuYuxuGengHaoranZhaoAbstract
AsweknowtheAvianFluPandemicragedforseveraltimesintheworldinthoseyears.Ourgovernmentandsocialorganizationshadmadealotofmeasurestopreventpeoplefrominfected.Wearenowmakingasimplemodeltomakeyouknowhowdidthefluinfectpeople,andwhatcanwedotokeepthefluawayorcureourselves.
Ourmodeltakestwopartstosolvethisquestion.First,wemadeafunctionofI(t)withtheSIRmodel,thelikelynumberofpeopleinfectedasafunctionoftime,andoptimizethismodel;andthenwegiveaplanofthestockpilesbestoredwithinChina,forthisquestion,weneedtoknowthepopulationdistributionofChina,andtheinfectionrateofAvianFlu.AllthisquestionwillbegiveinIntroduction.
KeyWords:
AvianFlu AntiviralDrugs StockpilesPopulation
Introduction
H5N1,thefullnameisavianinfluenza,isacontagiousdiseaseofanimalscausedbyvirus,whichusuallyinfectbirds.Theavianinfluenzavirususuallyinfectbirdsonly,butinararecase,itwouldinfecthumanbeing.TheWHOpayagreatattentiontotheavianinfluenzasincethefirstcasethathumanwasinfectedwithH5N1comeupinHK,in1997.Fromthenon,theavianinfluenzapandemicstartsjumpingtoourhumanbeing.
Usually,humanswhoareinfectedwithH5N1havesymptomslikefever,cough,sorethroatetc..
H5N1causesaterriblethreatentohuman’slife,about60%ofpeoplewhowereinfectedhavediedformit.Tilltonow,nohighlyeffectivedrugswasdeveloped,butwecoulduseantiviraldrugs(likeTamiflu)tosuppressthesymptomsandreducetheprobabilityofthediseasebeingpassedbythosealreadyinfectedtothosestillsusceptible.Avaccination,whichcomes6mouthslaterthantheoutbreak.
Topreventavianinfluenzapandemic,severalH5N1vaccineshavebeendevelopedforseveralkindsofavianH5N1varieties,buttheH5N1keepchanging.Nowherecomesahypotheticalnewstrain(H5N1++)ofthenewmutationof
H5N1,whichparticularlydeadlyandcontagious,capableofbeingpassedfromhumantohuman.
TheDescriptionofProblem
Considerahypotheticalnewstrainofthebirdflu(H5N1++)amutatedvirus,particularlydeadlyandcontagious,capableofbeingpassedfromhumantohuman.Antiviraldrugs(e.g.,Tamiflu)suppressthesymptomsandthusreducetheprobabilityofthediseasebeingpassedbythosealreadyinfectedtothosestillsusceptible.Avaccination,ontheotherhand,reducesthesusceptibilityofthosenotyetinfected.Boththevaccineandantiviraldrugsreducetheprobabilityofadeathoutcomeforthoseinfected.
Weareaskedtosolvethosequstionsbellow:
1.Providerecommendationsontheamountofantiviraldrugs&vaccinethatshouldbestockpiledtopreventanepidemicinChina.
2.Asofrightnow,atotalof2.5milliondosesofTamifluarecurrentlyonhandintheChina.Itisestimatedthatlimitedamountsofareliablevaccinewillbecomeavailableonly6monthsafterthefirstoutbreak.ProvideanestimateforI(t),thelikelynumberofpeopleinfectedasafunctionoftime.
InvestigatetheimpactonI(t)ofdifferentquarantinepolicies.
3.Thedraftreportofthecentralgovernment'semergencyplanpredictsthatasmanyas200,0000personswilldiewithinafewmonthsasaresultofanavianfluoutbreak.Howconservativeisthisestimate?
4.Whereshouldthestockpilesbestoredwithinthecountry?
AssumethateachStorageCentercanefficientlydistributevaccineanddrugstothepeoplewithin150milesfromit,andthatthosenotcoveredbyanyCenterincuranadditionaldelayof
5daysinreceivingallmedicine.GiventhegeographicdistributionoftheChinapopulation,whatistheminimalnumberofCentersneededtoavoidtheepidemic?
Now,currenteffortsfocusondevelopingamodelaboutthenumberofinfectedasafunctionoftime.Accordingtothemodel,wewillpredicthowmanyantiviraldrugsandvaccinesareneeded.Furthermore,basedonthemodel,wecanpredictthenumberofinfectedhumansatacertaintime.Finally,weshouldascertainthelocationandnumberofstockpileswhichdistributedrugsandvaccinestoavoidpandemic.thispaperaimstosolvetheseproblems.
DefinitionsandNotation
SThepopulationofsusceptiblepeople
I ThepopulationofinfectedpeopleRThepopulationofimmunepeopleNThetotalpopulationinacity
l Contactrate
m Excludingrate
b BirthandDeathrate
q Curerate
L Numberofcovereddots
L′ Totalnumberofdotsf Coveragerate
Assumptions
Wemustmakesomeassumptionstosimplifythevirustransmissionproblematfirst.
1、Theimmunepeoplewhohavebeencuredbeforewill
neverbeinfectedby thevirusforever.Thatmeansweignoretherepeatinginfectionphenomenon.
2、Thelatentperiodisneglectedforitsshortness,namely
theinfectedpersonbeco
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