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Mathematical analysis of some virus models
Useni, Paul F.
Useni, Paul F.
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2014-09
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dissertation
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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.
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University of Chester
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Thesis or dissertation
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en