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. We also show that some of those points were overlooked in the analysis done by Burić et al. and Yu et al. However, the existence of such points in the validation of Mayer model is very essential in accordance with the realities in the immunology science. The conditions of the existence of these equilibrium points will be analyzed by a method based on Root Lucas. The stability of system equilibria while having delay has been taken into consideration. It was 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 will be done by the Nyquist stability criterion. Finally some numerical simulations will be presented to depict the results of the computations.