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1、JournalofTheoreticalBiology279(2011)120–131ContentslistsavailableatScienceDirectJournalofTheoreticalBiologyjournalhomepage:www.elsevier.com/locate/yjtbiAdynamicmodelfortuberculosistransmissionandoptimaltreatmentstrategiesinSouthKoreaabb,SungimWhang,Su
2、nhwaChoi,EunokJungaDepartmentofMathematics,AjouUniversity,San5,Woncheon-dong,Yeongtong-gu,Suwon,Kyungki-do443-749,RepublicofKoreabDepartmentofMathematics,KonkukUniversity,1Hwayang-dong,Gwngjin-gu,Seoul143-701,RepublicofKoreaarticleinfoabstractArticlehi
3、story:Wehavedevelopedadynamicmodelfortuberculosis(TB)transmissioninSouthKoreausingaSEIRReceived7June2010modelwiththetime-dependentparameters.SouthKorearankedthehighestTBincidenceamongReceivedinrevisedformmembersoftheOrganizationforEconomicCooperationan
4、dDevelopment(OECD)in2005yr.The15December2010observeddatafromtheKoreaCenterforDiseaseControlandPrevention(KCDC)showsacertainriseofAccepted10March2011active-TBincidenceindividualsafter2001yr.Becauseofthissuddenjump,wehaveconsideredtwoAvailableonline30Mar
5、ch2011differentperiodsforbestfittingthemodel:priorto2001yrandposteriorto2001yr.Theleast-squaresKeywords:fittinghasbeenusedforestimatingmodelparameterstotheobserveddataofactive-TBincidence.OurTuberculosismodelagreeswellwiththeobserveddata.Inthiswork,weals
6、oproposeoptimaltreatmentstrategiesofEpidemicmodelTBmodelinSouthKoreaforthefuture.WehaveconsideredthreecontrolmechanismsrepresentingInfectiousdiseasedistancing,casefindingandcaseholdingefforts.OptimalcontrolprogramshavebeenproposedinOptimalcontroltheoryv
7、ariousscenarios,inordertominimizethenumberofexposedandinfectiousindividualsandthecostMathematicalmodelofimplementingthecontroltreatment.&2011ElsevierLtd.Allrightsreserved.1.IntroductionBothactive-andlatent-TBaretreatableandcurable.Ifnottreated,active-T
8、Bcanbefatal,killingupto60%ofpatients.WhenTuberculosis(TB)isaninfectiousdiseasecausedbyMycobac-treated,acurecanbeachievedin90%ofallcases.Peoplewhoterium(M.)tuberculosisandusuallyattacksthelungs(pulmonaryhavebeentreatedforatleast2weeksare
