Hdl Handle:
http://hdl.handle.net/10034/345680
Title:
Mathematical analysis of some virus models
Authors:
Useni, Paul F.
Abstract:
The Mathematical Analysis of some virus models such as SIR epidemic model, HIV infection model and Ebola virus model are hereby presented. The stability of both the SIR and HIV infection models were investigated using linearization method. The SIR model has an endemic infection when the equilibrium is unstable i.e R0 > 1, and attain a disease-free equilibrium with regards to the existing population when the equilibrium is asymptotically stable i.e R0 = ra+ < 1. The analysis shows that the threshold behavior is directly related to the relative removal rate and that an epidemic will reach its maximum when S = with a condition that I(t) = 0. Also, there is an oscillatory behavior of susceptible and that of infective at the zero point and highest point respectively. Then the homosexual population and T-cell infection models consisting of supply rate solution and that of clonal production solution were discussed. In particular the stability of T-cell infection model was also investigated for HIV virus and it was proven that the unique critical point is globally asymptotically stable.In the last chapter of this thesis, the formulation of EVD model and its numerical solution using Euler's method is also presented. Finally, the conclusion and future work suggestions are stated.
Advisors:
Kavallaris, Nikos I.; Yan, Yubin; Gildea, Joe; Roberts, Jason A.
Publisher:
University of Chester
Publication Date:
Sep-2014
URI:
http://hdl.handle.net/10034/345680
Type:
Thesis or dissertation
Language:
en
Appears in Collections:
Masters Dissertations

Full metadata record

DC FieldValue Language
dc.contributor.advisorKavallaris, Nikos I.en
dc.contributor.advisorYan, Yubinen
dc.contributor.advisorGildea, Joeen
dc.contributor.advisorRoberts, Jason A.en
dc.contributor.authorUseni, Paul F.en
dc.date.accessioned2015-02-27T14:51:14Zen
dc.date.available2015-02-27T14:51:14Zen
dc.date.issued2014-09en
dc.identifier.urihttp://hdl.handle.net/10034/345680en
dc.description.abstractThe Mathematical Analysis of some virus models such as SIR epidemic model, HIV infection model and Ebola virus model are hereby presented. The stability of both the SIR and HIV infection models were investigated using linearization method. The SIR model has an endemic infection when the equilibrium is unstable i.e R0 > 1, and attain a disease-free equilibrium with regards to the existing population when the equilibrium is asymptotically stable i.e R0 = ra+ < 1. The analysis shows that the threshold behavior is directly related to the relative removal rate and that an epidemic will reach its maximum when S = with a condition that I(t) = 0. Also, there is an oscillatory behavior of susceptible and that of infective at the zero point and highest point respectively. Then the homosexual population and T-cell infection models consisting of supply rate solution and that of clonal production solution were discussed. In particular the stability of T-cell infection model was also investigated for HIV virus and it was proven that the unique critical point is globally asymptotically stable.In the last chapter of this thesis, the formulation of EVD model and its numerical solution using Euler's method is also presented. Finally, the conclusion and future work suggestions are stated.en
dc.language.isoenen
dc.publisherUniversity of Chesteren
dc.subjectmathematical analysisen
dc.subjectvirus modelsen
dc.titleMathematical analysis of some virus modelsen
dc.typeThesis or dissertationen
dc.type.qualificationnameMScen
dc.type.qualificationlevelMasters Degreeen
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