A simple mathematical model for Guillain–Barré syndrome

Abstract

In this paper, four different forms of a model to describe the dynamics of autoimmune diseases (with emphasis on Guillain–Barré syndrome) are proposed. In the first two cases, the immune response is supposed to be linear, while in the other two cases it is supposed to be in the Holling type III form. In case of linear immune response, the model has a basic reproduction number and shows forward bifurcation. However, in the nonlinear Holling type III immune response cases, the model does not have a basic reproduction number and two positive equilibria do exist for a range of the parameters. The stability analysis of the model’s steady states has been established. Our analytical results have been illustrated by numerical simulations.