Modeling autoimmune disease with differential equations
Anderson, Jennifer Ann
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In this project, I will build a mathematical model of a developed autoimmune process considering cell autoimmunity that plays the main role in any autoimmune disorder using a system of three non-linear differential equations. As model variables, I will use the concentration of target cells not bearing damage, concentration of cytotoxic T- lymphocytes against given cells, and the concentration of the tissue-specific antigen formed because of the destruction of the target cells. All concentrations will be expressed in the moles per liter. We will investigate the model over the time interval [0, T] given either by months or days analytically as well as numerically.