Mathematical Modeling of Autoimmune Diseases

Abstract

The human organism is a very complex system. To be in good health, its components must function properly. One of the most important systems of an organism is the immune system. It protects the body from the harmful effects of various external and internal agents. Sometimes, however, the immune system starts attacking its own healthy cells, tissues and organs. Then autoimmune diseases arise. They are widespread in recent decades. There is evidence that often autoimmune responses occur due to viral infections. In this paper, a new mathematical model of a general autoimmune disease is proposed. It describes the interactions between viral particles and host cells. The model is formulated by using integro-differential equations of Boltzmann type. This approach is typical for the nonequilibrium statistical mechanics. A preliminary qualitative and quantitative analysis of the model is presented.