Document Details

Document Type : Thesis 
Document Title :
Global dynamics of a class of viral infection models with intracellular delay
الديناميكية الشمولية لفئة من نماذج الإصابة الفيروسية ذات التأخير الخلوي
 
Subject : mathematics department 
Document Language : Arabic 
Abstract : Over the last decade 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. The purpose of this thesis is to propose a class of HIV dynamics models with time delay and study their global properties such as positive invariance properties, boundedness of the solutions and stability analysis of the steady states of the models. Studying such properties is important for understanding the associated characteristics of the HIV dynamics and guide for developing efficient anti-viral drug therapies. By constructing Lyapunov functionals and using LaSalle invariant principle, we establish the global stability of the steady states of the models. Now we present brief description about the thesis: Chapter 1 presents a general background for the research addressed in this thesis. A brief background on immunology and how the virus interacts with the immune system is presented. We give an overview of some HIV mathematical models given in the literature. Model with discrete time delay and model with distributed time delay are also presented. Some basic concepts of ordinary differential equations (ODEs), and delayed differential equations (DDEs) are outlined. In Chapter 2, we investigate the global properties of two HIV dynamics models. The models are 5- dimensional systems of DDEs that describe the interaction process of the HIV with two classes of target cells, CD4+ T cells and macrophages and take into account the time delay between the time the target cells contacted by the virus and the time the emission of infectious (matures) virus particles. In the first model, two types of discrete time delays are incorporated. The second model incorporates two types of distributed time delays. The incidence rate of virus infection is given by the Beddington-DeAngelis functional response. The basic reproduction number R0 is identified which completely determines the global dynamics of the models. By constructing suitable Lyapunov functionals, we have proven that if R0 ≤ 1 then the uninfected steady state is globally asymptotically stable (GAS), and if R0 > 1 then the infected steady state exists and it is GAS. In Chapter 3, we study the global stability of two mathematical models for HIV infection with Crowley- Martin functional response. The models describe the interaction of the HIV with two classes of target cells. Two types of discrete time delays are incorporated in the first model. The second model takes into account two types of distributed delays. The basic properties of these models are studied. Lyapunov functionals are constructed and LaSalle-type theorem is used to establish the global asymptotic stability of the uninfected and infected steady states of these models. We have proven that if the basic reproduction number R0 ≤ 1 then the uninfected steady state is GAS, and if R0 > 1 then the infected steady state exists and it is GAS. Chapter 4 is devoted to study the global stability of HIV infection model with two classes of target cells. We assume that the infection rate is given by a general nonlinear functional response. We have incorporated two types of distributed time delays into the model. We have established a set of conditions which are sufficient for the global stability of the steady states. Using Lyapunov functionals we have proven that if R0 ≤ 1, then the uninfected steady state is GAS, and if the infected steady state exists then it is GAS. 
Supervisor : Dr. Ahmed Mohamed Elaiw 
Thesis Type : Master Thesis 
Publishing Year : 1434 AH
2013 AD 
Added Date : Monday, June 10, 2013 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
عهود شكري الشهريAlshehri, Ahoud ShukriResearcherMaster 

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