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Document Type |
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Thesis |
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Document Title |
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MODELING AND ANALYSIS OF MOSQUITO-BORNE VIRAL INFECTIONS نمذجة وتحليل الإصابة بالفيروسات التي تنتقل عن طريق البعوض |
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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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In this thesis, a class of mosquito-born viral infection models with humoral immune response has been proposed and analyzed. Most of these models take into account two modes of infection, attaching a virus to a host cell, and contacting an infected cell with an uninfected cell. All models are given by either system of ordinary differential equations (ODEs) or system of delay differential equations (DDEs). This study is concerned with stability in some models related to various aspects: (i) Different forms of cellular and viral incidence rates of infection such as bilinear, saturation, holling type-II and general incidence are considered. (ii) Actually, there exists a latent period between the moment when the virus contacts an uninfected cell and the moment when the infected cell become active to produce infectious viruses. Based on this fact, we consider two classes of infected cells, latently infected cells and actively infected cells. (iii) Regarding to some biological facts discrete or distributed time delays have been incorporated into some of those models. We have shown that the delay plays the same significant role of antiviral treatments. (iv) Models with virus DNA-containing capsids are investigated. (v) Due to the importance of the immune response in controlling the viral infection we consider the humoral immune response, which is more effective in case of mosquito borne viral infections.
For each of our proposed models, we show that it is biologically feasible in the sense that no population goes negative or grows without bound. We study the nonnegativity and boundedness of the solutions of those models. Further, we derive the threshold parameter, that is the basic reproduction number R0, which determines the existence and stability behavior of all equilibria of the model. In case of the general viral infec- tion model, we establish a set of conditions on the general functions which are sufficient to prove the existence and global stability of all equilibria of the model. The global stability of the model is established by constructing suitable Lyapunov functionals and applying LaSalle’s invariance principle. We present some examples and perform numer- ical simulations in order to illustrate the dynamical behavior of the system. We show that the numerical results are consistent with the theoretical results. The outcomes of this thesis are published in several ISI International Journals. |
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Supervisor |
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Prof. 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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1441 AH
2020 AD |
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Co-Supervisor |
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Dr. Aatef Hobiny |
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Added Date |
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Tuesday, February 11, 2020 |
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Researchers
| سامي عيضه المالكي | Almalki, Sami Eydhah | Researcher | Doctorate | |
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