Thefigurebelowshowsthemovementofindividualsfromsuscept

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Unformatted text preview: igurebelowshowsthemovementofindividualsfromsusceptibletoinfected andfinallytotherecoveredgroup. S I R 1 IntroductiontoComputationalPhysics Phy265Quiz6(TakeHome) Due12:40p.m.March21,2011 TheDifferentialEquationModel Next,wedevelopthemathematicsofthemodel.Specifically,S(t)isthenumberof susceptibleindividuals,I(t)isthenumberofinfectedindividuals,andR(t)isthe numberofrecoveredindividuals.Inaddition,S(t)+I(t)+R(t)=Nforalltimest.In otherwords,weassumethereisnoimmigrationintothepopulationoremigration outofthepopulationofNpeople.Furthermore,weignoreanybirthsordeaths duringtheperiodofouranalysis. Themodelwillseemmoreintuitiveifweworkwiththefractionofthepopulationin eachgroupasafunctionoftime,ratherthantheabsolutenumberofpeopleineach group.Inotherwords,s(t)=S(t)/N,i(t)=I(t)/N,andr(t)=R(t)/N.Andso,s(t)+i(t) +r(t)=1forallt. Next,wedefinetwomodelparametersthatdescribetheratesthatindividualsmove betweenthegroups.First,supposeeachinfectedindividualhadonaverageb contactsperdaythatweresufficienttospreadtheflu.Forexample,ifaninfected ind...
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