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Periodic solutions and bistability in a model for cytotoxic T-lymphocyte (CTL) response to human T-cell lymphotropic virus type I (HTLV-I)
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- Author / Creator
- Lang, John Cameron
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HTLV-I is the first discovered human retrovirus and a causative agent of both adult T-cell leukemia (ATL) and HTLV-I-associated myelopathy (or tropical spastic paraparesis) (HAM/TSP). Previous models have been successful in providing insight into the progression of HTLV-I infection. The relative simplicity of HTLV as well as its similarities to HIV and other diseases allow HTLV-I research to have diverse applications.
The development of HAM/TSP is precipitated by a CTL immune response. Previous models for CTL response to HTLV-I infection have had relatively simple behaviours. A novel sigmoidal CTL response function results in complex behaviours previously unobserved. We establish the existence of bistability between solutions corresponding to carrier and endemic states. In addition, both super- and sub-critical Hopf bifurcations as well as the resulting stable and unstable periodic solutions are observed. Analytical and numerical results are discussed, as well as the biological consequences of the aforementioned behaviours.
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- Graduation date
- Fall 2009
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- Type of Item
- Thesis
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- Degree
- Master of Science
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- License
- This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.