Stability Analysis Of Autoimmune Disease Model With Functional Response

In this paper,we propose a mathematical model for autoimmune disease with functional response of immune cells to target Cells,and analyze the dynamic behaviors as well as the biological meanings of these models.When the activation intensity of virus to immune response overtop the limit of tolerance,autoimmune disease may take place. For the first model that is the autoimmune disease model with Holling-Tanner typeâ…¡functional response.The global properties of it are studied using Lyapunov functions and LaSalle's invariance principle.We proved that virus be cleared if the basic reproductive ratio R₀≤1 and virus persists in the host if the basic reproductive ratio of the virus is greater than 1.Then we study the local stability of the autoimmune disease model with Holling-Tanner typeâ…¢functional response using Routh-Hurwitz criteria.We found that virus be cleared if the basic reproductive ratio R₀≤1 and given some conditions that the immune control equilibrium exists and is stable.