Computer Science Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/2756
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Item Mathematical Models of Underlying Dynamics in Acute and Chronic Immunology(2019) Wyatt, Asia Alexandria; Levy, Doron; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)During an immune response, it is understood that there are key differences between the cells and cytokines that are present in a primary response versus those present in subsequent responses. Specifically, after a primary response, memory cells are present and drive the clearance of antigen in these later immune responses. When comparing acute infections to chronic infections, there are also differences in the dynamics of the immune system. In this dissertation, we develop three mathematical models to explore these differences in the immune response to acute and chronic infections through the creation, activation, regulation, and long term maintenance of T cells. We mimic this biological behavior through the use of delayed differential equation (DDE) models. The first model explores the dynamics of adaptive immunity in primary and secondary responses to acute infections. It is shown that while we observe similar amounts of antigen stimulation from both immune responses, with the incorporation of memory T cells, we see an increase in both the amount of effector T cells present and the speed of activation of the immune system in the secondary response. We conclude that our model is robust and can be applied to study different types of antigen from viral to bacterial. Extending our work to chronic infections, we develop our second and third models to explore breast cancer dormancy and T cell exhaustion. For our breast cancer dormancy model, we find that our model behaves similar to acute infections, but with constant antigen stimulation. Moreover, we observe the importance of immune protection on the long term survival of breast cancer cells. In our third model we find that while memory T cells play a major role in the effectiveness of the immune system in acute infection, in chronic infections, over long periods of time, T cell exhaustion prevents proper immune function and clearance of antigen. We also observe how the lack of long term maintenance of memory T cells plays an important role in the final outcome of the system. Finally, we propose two potential extensions to the three models developed: creating a simplified acute infection model and creating a combined breast cancer dormancy model with T cell exhaustion.Item Mathematical Models of Immune Regulation and Cancer Vaccines(2012) Wilson, Shelby Nicole; Levy, Doron; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)An array of powerful mathematical tools can be used to identify the key underlying components and interactions that determine the mechanics of biological systems such as the immune system and its interaction with cancer. In this dissertation, we develop mathematical models to study the dynamics of immune regulation in the context of the primary immune response and tumor growth. Regulatory T cells play a key role in the contraction of the immune response, a phase that follows the peak response to bring cell levels back to normal. To understand how the immune response is regulated, it is imperative to study the dynamics of regulatory cells, and in particular, the conditions under which they are functionally stable. There is conflicting biological evidence regarding the ability of regulatory cells to lose their regulatory capabilities and possibly turn into immune promoting cells. We develop dynamical models to investigate the effects of an unstable regulatory T cell population on the immune response. These models display the usual characteristics of an immune response with the added capabilities of being able to correct for initial imbalances in T cell populations. We also observe an increased robustness of the immune response with respect to key parameters. Similar conclusions are demonstrated with regards to the effects of regulatory T cell switching on immunodominance. TGF-beta is an immunoregulatory protein that contributes to inadequate anti-tumor immune responses in cancer patients. Recent experimental data suggests that TGF-beta inhibition alone, provides few clinical benefits, yet it can significantly amplify the anti-tumor immune response when combined with a tumor vaccine. We develop a mathematical model to gain insight into the cooperative interaction between anti-TGF-beta and vaccine treatments. Using numerical simulations and stability analysis we study the following scenarios: a control case of no treatment, anti-TGF-beta treatment, vaccine treatment, and combined anti-TGF-beta vaccine treatments. Consistent with experimental data, we show that monotherapy alone cannot successfully eradicate a tumor. Tumor eradication requires the combination of these therapeutic approaches. We also demonstrate that our model captures the observed experimental results, and hence can be potentially used in designing future experiments involving this approach to immunotherapy.