Dynamics of HIV-1 Infection Models: Saturation Infection, an Eclipse Stage, CTL Immune Response

Please enable javascript in your browser.

Sabzevari, Mahtab | 2013

5796 Viewed

Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 44765 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Hesaaraki, Mahmoud
Abstract:
In this thesis, three mathematical models are considered for the viral dynamics of HIV-1. The first model is an HIV infection model with saturation infection and intracellular delay, which forms a three-dimensional differential equations system, the second model includes an eclipse stage of infected cells, The viral dynamics of this model is described by four nonlinear ordinary differential equations, and finally, we study a delayed six-dimensional HIV model with CTL immune response, in fact, the main issue is the analysis of the second model (model including an eclipse stage for the infected cells).In this thesis is obtained sufficient conditions for persistence or eradication of the disease; therefore, we investigate global stability and global attractivity of these mod-els equilibria by Lyapunov’s direct method and for the global stability of the infected equilibrium of the model including an eclipse stage of infected cells, in addition to Lyapunov’s direct method, we use a geometric approach to global stability
Keywords:
Global Stability ; Global Attractor ; HIV Infection ; Intracellular Delay ; Eclipse Stage ; Cytotoxic T Lymphocyte (CTL)Immune Response ; Lyapunov Function