Stability and Bifurcation of Tumor Immune Model with Time Delay

In this paper, we investigate the effect of time delay on stability tumor immune system using theoretical calculations and numerical simulations. Since it takes a certain for cells to recognize make an appropriate response, model tumor-immune interaction with is established by considering in process. The four equilibrium points are solved simplifying Taylor expansion small delay. Then each point under determined calculating characteristic roots simulation software. results show that has bistability phenomenon. saddle stable node not affected delay, while only foci changes Hopf bifurcation. This study can help determine optimal treatment provide reference analyzing status treatment.