Document Details
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Document Type |
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Thesis |
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Document Title |
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Stability of HIV Dynamics Models with Differential Drug Efficacy in Co-circulating Target Cells استقرار نماذج ديناميكا فيروس نقص المناعة المكتسبة مع اختلاف فعالية العلاج في الخلايا المستهدفة المتعاونة |
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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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During the recent years, a tremendous effort has been made in developing mathematical models of
the immunology dynamics under the attack of the human immunodeficiency virus (HIV) and under
the influence of antiretroviral therapies. There are many benefits from mathematical modelling and
analysis of HIV dynamics including: (i) they can be used to test different conditions and provide
new insights into questions that cannot be answered by clinical or experimental studies, (ii) they can
improve diagnosis and treatment strategies in the highest efficiency at the lowest possible cost, and
with minimum of side effects, which raise the hopes of patients infected with HIV, (iii) they can be
used to estimate key parameter values that control the infection process or reduce the viral load in
the body of patient with HIV. The basic and global properties of the HIV infection models, such as
positivity (or non-negativity), boundedness (or ultimate boundedness) of the solutions of the model
and stability analysis of the equilibria which are the most important features of mathematical models
that gives us a detailed information and enhances our understanding about the HIV dynamics. Most
of the HIV dynamics models presented in the literature are based on the assumption that, the HIV
attacks one class of target cells which is CD4+T cells. Other models assume that there are two classes
of target cells, that are CD4+T cells and macrophages. However, most of these two target cells models
assume that the antiviral drugs have the same drug efficacy on both CD4+T cells and macrophages.
Moreover, these models did not differentiate between the short-lived infected cells and long-lived
infected cells. The purpose of this thesis is to propose a class of HIV dynamics models with two classes
of target cells, CD4+T cells and macrophages under the effect of treatment, and study their basic and
global properties. The models take into account both short-lived infected cells and long-lived
chronically infected cells. In the two types of target cells, the drug efficacy is assumed to be different.
Since the immune response plays an important role in controlling the HIV infection, therefore, we
consider the humoral immune response in the HIV dynamics models.
Actually, there exists a latent period between the moment when the virus contacts the uninfected
cells and the moment when the infected cells become active to produce infectious HIV particles.
To incorporate this latent period into the models, we present the HIV infection models as a delay
differential equations (DDEs). The time delay is given by discrete time delay or distributed time
delay. We show that the delay plays the same role of antiviral treatment. Therefore, our results give
us some suggestions on new drugs to prolong the increase the intracellular delay period.
For all models, we define the basic reproduction number, R0 which determines whether or not an
infection can be established. The global asymptotic stability is established using suitable Lyapunov
functions and applying LaSalle's invariance principle. We prove that if R0 1, then the infection-free
equilibrium is globally asymptotically stable (GAS), and if R0 > 1 (or endemic equilibrium exists),
then the endemic equilibrium is GAS. 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. We establish a set of conditions on the general functions which are
sufficient to prove the global stability of the equilibria of the models. We present some examples and
perform numerical simulations in order to illustrate the dynamical behavior. We show that the
numerical results are consistent with the theoretical results. The effect of two types of target cells
and the effect of presence of long-lived chronically infected cells on the dynamic and control of HIV
infection are also studied. Our results show that more accurate treatment can be designed using our
proposed models. |
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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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Monday, February 29, 2016 |
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Researchers
| ندى أحمد المعلم | Almuallem, Nada Ahmed | Researcher | Master | |
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