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Nowadays autoimmune diseases are widely distributed. More than 80 illnesses are included into this group of conditions. Their causes are not clear exactly, but it is believed that among them are genetic factors, viral infections, socio-economic conditions, etc. We propose a new mathematical model describing a general autoimmune disease in order to analyze some mechanisms of autoimmune disorders. The model is a system of ordinary differential equations. We perform preliminary qualitative analysis of the model as well as propose an algorithm for numerical simulations. Some results of our numerical experiments are presented and commented from a biological point of view.

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A mathematical model of adaptive immune response after transplantation is formulated by five nonlinear ordinary differential equations. Theorems of existence, uniqueness and nonnegativity of solution are proven. Numerical simulations of immune response after transplantation without suppression of acquired cellular immunity and after suppression were performed.