Graduation Semester and Year
2017
Language
English
Document Type
Thesis
Degree Name
Master of Science in Mathematics
Department
Mathematics
First Advisor
Hristo Kojouharov
Abstract
This thesis introduces a mathematical model of differential equations for the chronic hepatitis C virus (HCV) infection, which is a contagious disease that infects the liver cells. Firstly, we present the early mathematical models for the basic dynamics of virus infection that developed and analyzed to understand the dynamics of human immunodeficiency virus (HIV), hepatitis B virus (HBV), and some other viruses. Next, we present the extended model of the basic HCV virus dynamics that incorporate the effectiveness of a treatment. After that, the mathematical model that includes proliferation terms for both infected and uninfected hepatocytes is discussed. Lastly, the mathematical model that is considering the interaction between HCV virus and immune responses in a host is introduced. In this thesis, we formulate an ordinary differential equations (ODE) model to describe the interactions between the hepatitis C (HCV) virus and the immune system in a human body under treatment, taking into consideration the proliferation for both infected and uninfected hepatocytes. Analysis of the model reveals the existence of multiple equilibrium states: the disease-free steady state in which no virus is present, an infected state with no immune responses, an infected steady state with immune responses in which virus and infected cells are present, an infected steady state with dominant CTLs responses in which no antibody (B-cell) is present, an infected steady state with dominant antibody responses in which no CTLs is present, and an infected steady state with coexistence responses in which all are present. Finally, we run simulations and compare our model to other models in the literature. In addition, several different scenarios were numerically simulated to demonstrate the practical applications of the mathematical model.
Keywords
HCV, Mathematical models
Disciplines
Mathematics | Physical Sciences and Mathematics
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Hadi, Huda Amer, "A Mathematical Model of Hepatitis C Virus Infection Incorporating Immune Responses and Cell Proliferation" (2017). Mathematics Theses. 20.
https://mavmatrix.uta.edu/math_theses/20
Comments
Degree granted by The University of Texas at Arlington