Effect of Delay of Immune System Response in Cancer Dynamics: Bifurcation and Chaos Analysis

The mathematical models of cancer dynamics consider interactions between different cells and give a deep understanding the progress of the tumor growth. In most of the cases, the proposed models are formed by assuming that the interactions occur in the exact times, i.e., no delay is incorporated into the models. On the other hand, this assumption may not be valid as the interactions could have possible delays. The purpose of this paper is to determine the effect of delay interactions between tumor cells and immune system cells. By adding delay time to the cancer model, behavior of the new model is analyzed. In this paper, we investigate the stability of equilibria points, Hopf bifurcation and chaotic behavior of the system. The critical value of time delay is computed by an analytical method. Finally, we show that increasing the delay time will lead series of bifurcations to chaos.