الفهرس 
INTRODUCTIONOnly 14 pages are availabe for public view
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Abstract
Mathematical modeling is a useful tool in the study of virus dynamics for many types of viruses such as Hepatitis C virus (HCV), Hepatitis B virus (HBV), Human Papillomavirus (HPV), Human immunodeficiency virus (HIV) and COVID-19. These models can be used to comprehend the biological mechanisms and interpret the experimental results. The purpose of this research work is to develop dependable mathematical models for the viral dynamics of the hepatitis C virus. Dynamical analysis is performed for these models. In this dissertation, a novel approximate analytical solution is presented for solving the standard viral dynamic model. Basically, the standard model is used to study viral dynamics in patients for a wide range of viruses like HIV, HPV, HBV, HCV, and COVID-19. Power series solution combined with Laplace-Padé resummation method (PSLP) is used to obtain the approximate analytical solutions for the model. A mathematically identical ordinary differential equations (ODEs) model was derived from a multiscale partial differential equations (PDEs) model of hepatitis C virus infection, which helps to overcome the limitations of the PDE model in clinical data analysis. Another new mathematical model is formulated that describes the interaction between viral dynamics of viruses, intracellular viral RNA, infected cells, and the immune system. Hence, analysis of a new multiscale HCV model incorporating the immune system response is considered in detail. The positivity of the solutions is proven, the basic reproduction number is obtained, and the equilibrium points are specified. The stability at the equilibrium points is analyzed based on the Lyapunov invariance principle. Numerical simulations have been performed for the model. Finally, proposed mathematical model is formulated that describes the multiscale viral dynamics of HCV incorporating hepatocyte proliferation. It is shown that the newly presented model yields a more realistic model for explaining the triphasic profile for some patients and reducing the oscillations that happened in the transformed ODE model after therapy cessation. Numerical simulations have been performed to investigate the effect of the hepatocyte proliferation of both uninfected and infected cells and the direct-acting antivirals agents (DAAs) therapy. The basic reproduction number is obtained, and the equilibrium points are specified. The stability at the equilibrium points is analyzed. A bifurcation analysis is performed to study the effect of varying system parameters, and bifurcation points are specified. Comparison between different mathematical models of HCV RNA kinetics and their use under therapy is presented.