ORCID Identifier(s)

0000-0003-3052-0886

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

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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