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THE IMPACT OF VACCINATION TOWARDS THE
SPREAD OF TUBERCULOSIS USING SEIR MODEL
ALISA QAMARINA BINTI SALLEH SUPERVISOR : MADAM
NORLAILA BINTI MD NOR
K242/27
ABSTRACT
TuberculosisgWTBXgdiseasesghasghadgagsignificantgimpactgongglobalghealthFgpromptinggthegwidespreadgimplementationgofgvaccinationgprograms
togcontrolgitsgspreadKgThisgstudygperformedgthegstabilityganalysisgofgthegSEIRgWSusceptible[Exposed[Infected[RecoveredXgmodelgbygcomputing
andgclassifyinggequilibriumgpointsgWdisease[freegandgendemicXgandgdefininggthegbasicgreproductiongnumbergusinggthegnext[generationgmatrix
methodKgThegimpactgofgvaccinationgongTBgtransmissiongisgalsoganalyzedgthroughgnumericalgsimulationgingMATLABgbygvaryinggthegproportiongof
vaccinationKgThegresultgdiscoveredgthatgTBghasgstoppedgspreadinggingthegabsencegofgdiseasegwhengthegbasicgreproductiongnumbergisglessgthang1
andgdisease[freegequilibriumgpointgisgstableKgThegsimulationgresultsgindicategthatgincreasesgingvaccinationgratesgpromptgrapidgstabilizationgfor
thegpopulationsKgThesegfindingsgimplygthatgoptimizinggthegvaccinationgstrategygisgvitalgingdealinggwithgTBgtransmissiongeffectivelyKg
Methodology &
Problem Statement Implementation STEPg2EgEquilibriumgpoint
Theg Philippinesg hasg oneg ofg theg highestg TB STEPg1gEgSEIRgmodelgdiagramg
incidencegratesgingSoutheastgAsiaFgwithg739F000
newgcasesgrecordedging2023K Disease[freegequilibriumgpointgE
Previousg studyg byg Ramingg etg alKg W2024Xg only
comparedg TBg dynamicsg usingg SEIRg modelg with
andg withoutg vaccinationKg Theg studyg lacksg a
precisegexplanationgonghowgvaryinggvaccination SystemgofgordinarygdifferentialgequationsE
ratesg ing theg populationg resultsg tog faster EndemicgequilibriumgpointgE
eliminationgofgTBgdiseaseK
TogperformgthegstabilityganalysisgofgthegSEIR
modelg byg computingg andg classifying
equilibriumg pointsg Wdisease[freeg and ListgofgparametersgandgvaluesgE
endemicXg andg definingg theg basic
reproductiong numberFg R0g usingg theg next[
generationgmatrixgmethodK
Objectives STEPg3gEgStabilityganalysisgatgdisease[freegequilibriumgpoint
STEPg4gEgBasicgReproductiongNumberFgR0
ToganalyzegthegimpactgofgvaccinationgongTB JacobiangmatrixgE
transmissiong throughg numericalg simulation Next[generationgmatrixgmethodgE
bygvaryinggvaccinationgproportionK
E
Results & Discussion
Withg higherg vaccinationg ratesFg theg ratiog ofg susceptibleF E
exposedgandginfectedgpeoplegdiminishesggraduallygalong
withgthegrisegingthegrecoveredgcountKg
AsgthegvaccinationgbecamegmoregextensiveFgtheginfection
curvegWIXgincreasedgearliergandgtogaglowergvalueFgmeaning
thatgthegdiseasegspreadgslowergandglessgintenselyK
Theg impactg ofg varyingg vaccination
ratesg isg analyzedg throughg simulation
ingMATLABKg
Theg vaccinationg proportionsg are
estimatedgtogbeg0K2Fg0K5gandg0K9K Conclusion
Theg graphsg areg simulatedg byg each
compartmentg ofg SEIRg overg 100g days Theg findingsg indicatedg theg diseaseg willg eventuallyg dieg out
timegspanK whengR0gxg1KgThegstabilityganalysisgrevealsgthatgdisease[free
equilibriumg pointg isg asymptoticallyg stableKg Theg simulation
DatagofgTBgcasesgingthegPhilippinesgon resultsgdiscoveredgthatgvaccinationgisgverygeffectivegagainst
theg yearg 2023g WInitialg valuesg ofg SEIR preventingg transmissiong ofg tuberculosisFg particularlyg when
modelXgE administeredgwithgaghighgenoughgratesKg
Recommendation
Futuregstudiesgmaygextendgthegmodelgtogincludegthegeffects
ofgco[infectionFgparticularlygwithgHIVFgwhichgweakensgthe
immunegsystemgandgcomplicatesgTBgtreatmentgandgcontrol
strategiesK
