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Document Type |
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Thesis |
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Document Title |
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Global Dynamics of a Class of Viral Infection Models with Long Lived Infected Cells الديناميكا الشمولية لفئة من نماذج الاصابة الفيروسية ذات الخلايا المصابة المزمنة |
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Subject |
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Faculty of Sciences > mathematics department |
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Document Language |
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Arabic |
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Abstract |
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Over the last decade, a tremendous effort has been made in developing mathematical models which describe the viral infection as well as the effect of antiviral treatment. The humoral immune response plays an important role in controlling the virus progression. The purpose of this thesis is to propose a class of virus dynamics models with humoral immunity and study their basic and global properties. The models contain five compartments; uninfected target cells, short-lived infected cells, long-lived chronically infected cells, free virus particles and B cells. We present the virus dynamics models as delay differential equations (DDEs) which incorporate the latent period between the moment when the virus contacts the uninfected cells and the moment when the infected cells become active to produce infectious virus particles. The time delay is given by discrete time delay or distributed time delay. We consider several forms of the incidence rate of infection, such as bilinear incidence, saturated incidence, Beddington-DeAngelis incidence, Crowley-Martin incidence and general incidence. The existence and stability of all equilibria are completely established by two bifurcation parameters: the basic infection reproduction number R0 and the humoral immune response activation number R1. The global asymptotic stability of the steady states are proven using Lyapunov method and Lasalle's invariance principle. We prove that, if R0<1, then the uninfected steady state is globally asymptotically stable (GAS), if R1<1 < R0, then the infected steady state without humoral immune response is GAS, and if R1>1, then the infected steady state with humoral immune response is GAS. In case of the general incidence rate, we present a set of sufficient conditions which guarantee the global stability of model. We perform numerical simulations to confirm our theoretical results. |
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Supervisor |
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Dr. Ahmed Mohamed Elaiw |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1437 AH
2016 AD |
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Added Date |
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Sunday, April 17, 2016 |
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Researchers
| نوف عبد الله الغامدي | Alghamdi, Nouf Abdullah | Researcher | Master | |
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