A mathematical model for immune and autoimmune response mediated by T-cells

How do we recast the effects of molecular mimicry and genetic alterations affecting the T-cell response against self and non-self antigens into a mathematical model for the development of autoimmune disorders? Bearing this question in mind, we propose a model describing the evolution of a sample composed of immune cells and cells expressing self and non-self antigens. The model is stated in terms of integro-differential equations for structured populations and ordinary differential equations for unstructured populations. A global existence result is established and computational analyses are performed to verify the consistency with experimental data, making particular reference to the autoimmune lymphoproliferative syndrome (ALPS) as the model disease. Using our model as a virtual laboratory, we test different hypothetical scenarios and come to the conclusion that, besides molecular mimicry, genetic alterations leading to an over-proliferation of the T-cells and a less effective action against non-self antigens can be driving forces of autoimmunity.