## Electronic Theses and Dissertations

#### Keywords

mathematical models, biology

#### Abstract

In this thesis, we examine epidemiological models of two different retroviruses, which infect the human body. The two viruses under study are HIV or the human immunodefiency virus and HTLV-I, which is the human T lymphotropic virus type I. A retrovirus is a virus, which injects its RNA into the host, rather than it's DNA. We will study each of the different mathematical models for each of the viruses separately. Then we use MATLAB-SIMULINK to analyze the models by studying the reproductive numbers in each case and the disease progression by examining the graphs. In Chapter 1, we mention basic ideas associated with HIV and HTLV-I. In Chapter 2 some of the basic mathematical model of epidemiology is presented. Chapter 3 is devoted to a model describing the intra-host dynamics of HIV. Here, we take into account how HIV infects and replicates in the CD4+ T cells. The model studied in this thesis examines the difference between cells, which are susceptible to the virus, and cells, which are not susceptible. Through the graphs associated with this model, we are able to see how this difference affects disease progression. In Chapter 4, we examine the effect of HTLV-I virus on human body. The HTLV-I virus causes a chronic infection in humans and may eventually lead to other diseases. In particular, the development of Adult T-cell Leukemia or ATL is studied in this thesis. The T-cell dynamics and progression to ATL is described using a mathematical model with coupled differential equations. Using mathematical analysis and SIMULINK, we obtain results on stability, asymptotic stability and the manner of progression of the disease. In Chapter 5 and appendices, we mention our inference and the MATLAB-SIMULINK codes used in this thesis, so that a reader can verify the details of the work carried out in this thesis.

2007

#### Semester

Fall

Mohapatra, Ram N.

#### Degree

Master of Science (M.S.)

#### College

College of Sciences

Mathematics

#### Degree Program

Mathematical Science

application/pdf

CFE0001886

#### URL

http://purl.fcla.edu/fcla/etd/CFE0001886

English

December 2007

None

#### Access Status

Masters Thesis (Open Access)

COinS