Nonlinear dynamics in tumor-immune system interaction models with delays

In this paper, we review some recent results on the nonlinear dynamics of delayed differential equation models describing interaction between tumor cells and effector immune system, in which delays represent times necessary for molecule production, proliferation, differentiation cells, transport, etc. First consider a tumor-immune system model with single delay present existence local stability equilibria as well Hopf bifurcation when varies. Second investigate two show that undergoes various possible bifurcations including Hopf, Bautin, Fold-Hopf (zero-Hopf), Hopf-Hopf bifurcations. Finally discuss three demonstrate exhibits more complex behaviors chaos. Numerical simulations are provided to illustrate models. More interesting issues questions modeling analyzing given discussion section.