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Document Type |
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Thesis |
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Document Title |
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Global dynamics of some viral infection models الديناميكيا الشمولية لبعض نماذج العدوى الفيروسية |
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Subject |
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Faculty of Science |
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Document Language |
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Arabic |
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Abstract |
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analyzed. These models describe the virus dynamics with both cytotoxic T-lymphocytes (CTL) cells and antibodies. These models also take into account both virus-to-cell and cell-to-cell transmissions. Our proposed models are given either by system of ordinary differential equations (ODEs) or by system of delay differential equations (DDEs). This study was carried out by the following: (i) We have considered two forms of virus-cell and cell-cell incidence rates, bilinear and saturation, (ii) we have incorporated two types of discrete or distributed time delays to describe the time between the virus or infected cell contacts an uninfected cell and the emission of new active viruses, (iii) since the immune response plays an important role in controlling the viral infection, therefore, the interactions between the target cells, viruses and the immune system cells in the human body have been taken into account. Two immune responses have been incorporated into the models, CTL immune response and antibody immune response.
In last chapter, we propose and analyze an HCV dynamics model taking into consideration the cure of infected hepatocytes and antibody immune response. We incorporate both virus-to-cell and cell-to-cell transmissions into the model. Moreover, we incorporate a distributed-time delay.
For each of our proposed models, we first have shown that the model is biologically
acceptable in the sense that the solutions of the model are nonnegative and bounded
(or ultimate bounded). Secondly, we have calculated all steady states of the model and
derived the threshold parameters that determine the existence and stability behavior
of the steady states. Thirdly, the global stability of the models has been investigated
by constructing suitable Lyapunov function and using LaSalle's invariance principle.
Finally, we have confirmed the theoretical results by numerical simulations using MATLAB. |
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Supervisor |
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Prof. Dr. Ahmed Mohamed Elaiw |
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Thesis Type |
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Doctorate Thesis |
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Publishing Year |
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1440 AH
2019 AD |
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Added Date |
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Monday, August 26, 2019 |
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Researchers
| شفيق عبده غالب | Ghaleb, Shafeek Abdu | Researcher | Doctorate | |
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