THE GENERAL ON MATHEMATICAL MODEL OF AUTOIMMUNE DISEASES AND ITS TREATMENT

Author: vladimer odisharia
Co-authors: P.Tsereteli
Annotation:

In this paper we propose the general mathematical model of autoimmune diseases obtained by generalization of mathematical model of rheumatoid arthritis [ Odisharia K., Odisharia V., Tsereteli P., Janikashvili N. On the Mathematical Model of Drug Treatment of Rheumatoid Arthritis. Springer International Publishing, Mathematics, Informatics, and their Applications in Natural Sciences and Engineering, Chapter No: 10, pp.161-168, 2019.]. By offered model can be described progress and treatment of various autoimmune diseases. According the model, there are target cells that are recognized as “foreign” cells by immune system and immune system begins to attack them. In this process B-, Treg- and Th- lymphocytes are involved. The model is a system of non-linear ordinary differential equations. Equations determine change of size of target cell population, B- , Th-, Treg- cell populations and amount of drug in the blood. The model assumes that the disease occurs when the number of B lymphocytes exceeds the limit value. The model involves the drug, that promotes target cells proliferation and/or reduction of B-lymphocytes to the limit value by influence on Th- and Treg- cells. Based on the model, it is possible to set a control problem with respect to the dosage and effectiveness of the drug