# Forexampleifaninfected

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Unformatted text preview: ividualhadonecontacteverytwodays,thenb=1/2.Notallofthesecontacts werewithsusceptibleindividuals.Infact,bs(t)givesthenumberofcontactsperday perinfectedindividualwithsusceptibleindividuals,andbs(t)I(t)givesthenumber ofnewinfectionsperday.Thesecondmodelparameter,k,isthefractionofinfected individualsthatrecoveredperday.Itisrelatedtotheaveragedurationofthe infection.Forexample,supposetheaverageinfectionlaststhreedays.Theneach day,onethirdoftheinfectedindividualswillrecoverandsok=1/3. Theparametersbandkandthethreefirstorderdifferentialequationsbelow describethechangesinthepopulationsofthethreegroups.Usingfirstprinciples anddimensionalanalysisbesureyoucanexplainthetermsintheequationsbelow. ds = -bs(t)i(t) dt di = bs(t)i(t) - ki(t) dt dr = ki(t) dt ApplicationofModeltoHongKongFluinNewYorkCity Next,let'sapplytheabovemodeltothespreadoftheHongKongfluinNewYork Cityduringthewinterof19681969.First,takeS(0)=N=7,900,000people.In otherwords,theentirepopulationwassusceptibletothefluatt=0.Secondtake I(0)=10,i.e.10individu...
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## This note was uploaded on 02/23/2012 for the course PHYSICS 265 taught by Professor Tegler during the Spring '11 term at N. Arizona.

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