Humanimmunodeficiencyvirus(HIV)hashadaninsightfulimpactaboutthestateofhealthinessofhumanimmunesystem.Duetogreatimprovementindrugtherapy,HIVinfectionshavebeenreducedby17%overthepasteightyears.IthasbeenprovedthatmosteffectivetreatmentHAART(HighlyActiveAntiRetroviralTherapy)mainlycontrolsthediseasesprogressionbutitdoesnoteradicatethediseasescompletely.ReverseTranscriptaseInhibitordrugsspeciallyassociatedwithvirusspecificCytotoxicT-Lymphocyte(CTL)thatdeclineswithdiseaseprogression.CTLresponsesagainstAIDSpathogenesiscouldbepotentialinthedynamicsofvirusreplication,recognitionandclearanceofinfectedcells.InthisresearcharticleamathematicalmodelhasbeenproposedonthebasisofCTLresponsesuppressioninthechronicphaseofinfectionduetopresenceofvirus.WealsoconsiderthegrowthoftheviruspopulationfromtheinfectedCD4~+Tcellsbuddingprocessandfromtheotherinfectedcellslikemacrophagesandthymocytes.Ouranalyticalandnumericalstudiesareconsistentwithexistingobservationsfromalliedareas.
