Ordinary and delay differential equation models of viral infection with application to HIV and Hepatitis C virus
| dc.contributor.committeeChair | Allen, Linda J. S. | |
| dc.contributor.committeeMember | Allen, Edward J. | |
| dc.contributor.committeeMember | Hoang, Luan T. | |
| dc.creator | Aavani, Pooya | |
| dc.date.available | 2012-11-07T22:42:28Z | |
| dc.date.issued | 2012-08 | |
| dc.description.abstract | Human adaptive immune response consists of three major types of cells, namely, CD4 T cells, CTL (Cytotoxic T Lymphocytes), and antibodies. CTL attack and kill cells that are infected by viruses. Antibodies are capable of identifying and neutralizing viruses. In the presence of virus infection, CD4 T Cells stimulate the proliferation of CTL. Also the proliferation of antibodies becomes stimulated by viruses. These ideas are used to introduce a new ordinary differential equation model for exploring the dynamics of infection. Production of viruses by infectious CD4 T cells are not instantaneous and they require time to occur. Thus, explaining the dynamics of infections more accurately in the model, it is important to consider a time gap, which is known as delay. The new delay differential equation model, which considers a delay in the production of viruses, is also analyzed in this thesis. Both models are useful to be applied for HIV and hepatitis C infections, because in these models target cells are CD4 T cells, infectious agents are viruses, and the biological implications of the mathematical results are similar to the stages of the infections. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/2346/46950 | |
| dc.language.iso | eng | |
| dc.rights.availability | Unrestricted. | |
| dc.subject | Mathematical immunology | |
| dc.subject | Virus dynamics | |
| dc.subject | Reproduction number | |
| dc.subject | Asymptotic stability | |
| dc.subject | Global stability | |
| dc.title | Ordinary and delay differential equation models of viral infection with application to HIV and Hepatitis C virus | |
| dc.type | Thesis | |
| thesis.degree.department | Mathematics and Statistics | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Texas Tech University | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Science |