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dc.contributor.advisorVaidya, Naveen K.
dc.contributor.authorUhl, Peter Maurice
dc.date.issued2017
dc.date.submitted2017 Fall
dc.descriptionTitle from PDF of title page viewed January 31, 2018
dc.descriptionThesis advisor: Naveen K. Vaidya,
dc.descriptionVita
dc.descriptionIncludes bibliographical references (pages 33-37)
dc.descriptionThesis (M.S.)--Department of Mathematics and Statistics. University of Missouri--Kansas City, 2017
dc.description.abstractInjection drug use is one of the greatest risk factors associated with contracting human immunodeficiency virus (HIV), and drug abusers infected with HIV suffer from a higher viral load and rapid pathogenesis. Replication of HIV may result in a large number of mutant viruses that can escape recognition of the hosts immune response. Experimental results have shown that the presence of morphine can decrease the viral mutation rate and cellular immune responses. This thesis presents a mathematical model to determine if the decrease in mutation and cellular immune response in the presence of morphine can account for the increased viral load. Two viral species are considered: a wild-type and a mutant. The morphine-altered mutation rate and cellular immune response is shown to allow the wild-type virus to out compete the mutant, resulting in a higher set point viral load. Calculation of the basic reproduction number for each species shows that the dominant species is determined by a threshold morphine concentration, with the mutant dominating below the threshold and the wild-type dominating above. Stability analysis is performed on the infection free and mutant only equilibria of the system and numerical simulations reflect the increased viral load associated with morphine use.eng
dc.description.tableofcontentsIntroduction -- Background and literature review -- Mathematical models -- Model analysis -- Simulations -- Discussion and future work
dc.format.extentix, 38 pages
dc.identifier.urihttps://hdl.handle.net/10355/62672
dc.publisherUniversity of Missouri--Kansas Cityeng
dc.subject.lcshHIV infections -- Research -- Mathematical models
dc.subject.lcshMorphine
dc.subject.otherThesis -- University of Missouri--Kansas City -- Mathematics
dc.titleModeling the Effects of Drugs of Abuse on HIV Infections with Two Viral Specieseng
dc.typeThesiseng
thesis.degree.disciplineMathematics (UMKC)
thesis.degree.disciplineStatistics (UMKC)
thesis.degree.grantorUniversity of Missouri--Kansas City
thesis.degree.levelMasters
thesis.degree.nameM.S.


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