Analysis of a basic model of immune response with delay: Existence and stability of equilibria

In this paper, we analyze stability of the equilibrium points in the Mayer model in case of having delay. It is shown that some of those points were overlooked in the analysis done by Buric et al. and Yu et al. However, the existence of such points in the validation of Mayer model is so essential in accordance with the realities in the immunology science. The conditions of the existence of these equilibrium points are analyzed by a method based on Root Lucas. The stability of the system equilibria while having delay is taken into consideration. It is demonstrated that while the delay on system having no effects on the stability in some of these points, they can also has effects on one of these points. The analysis of the stability in this equilibrium point is done by the Nyquist stability criterion. Finally some numerical simulations are presented to depict the results of the computations.