| We develop models of immune dynamics based on systems of delay differential equations, systems of difference equations, and systems of partial differential equations. Our models focus on the dynamics of the immune response to chronic myelogenous leukemia (CML) and immune regulation during a primary immune response.;The first part of the thesis analyzes immune dynamics after a CML patient receives a stem cell transplant. This model studies the interactions between the immune cell populations from the patient and the donor stem cells. We observe that a successful transplant results from a blood-restricted graft versus host response, in which donor immune cells attack and destroy all the patient's blood cells. We hypothesize that a high population of general, non-leukemic host blood cells prior to transplantation favors a successful outcome.;The second part of the thesis considers a combining the biological drug Gleevec with cancer vaccinations as a treatment for CML. The model is based on experimental data showing that most CML patients exhibit brief anti-leukemia immune responses during the course of Gleevec treatment. We hypothesize that these brief immune responses can be magnified via cancer vaccines to lead to a robust anti-leukemia immune response.;The third part of the thesis develops a model that involves several aspects of the adaptive immune response, including antigen presenting cells, helper and killer T cells, and regulatory T cells. The model studies the dynamics of self/non-self discrimination and immune regulation. We hypothesize that the immune system contains a population of naturally-occurring regulatory T cells that are primarily reactive to foreign antigen. These regulatory cells modulate the strength of the primary immune response during an infection. |
