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In this paper, a non-linear mathematical model for tumor-immune system is formulated and analyzed by considering saturated incidence for the interaction between tumor cells and cytotoxic-T lymphocytes (CTLs). It is assumed that both the tumor cells as well as T-helper cells follow logistic growth. In Addition, a time lag exists in the activation of CTLs because of T-helper cells. Existence and stability of different equilibria of the model are discussed in detail. The model is analyzed using the theory of delay differential equations. It was observed that delay played an important role in defining the dynamics of the system. The system exhibited Hopf-bifurcation when the value of time delay crossed a certain threshold. Existence of Hopf-bifurcation and condition for stability switch are discussed in detail. Numerical simulation is performed to support the analytical findings.

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