Dynamics of tumor-immune interaction model with time delay

In this paper, we present a theoretical model that describes tumor-immune interactions with a delay time. The system's dynamics are represented by four nonlinear delay differential equations for precursor, tumor, interleukin-2 and cytotoxic lymphocyte cells. We demonstrate that the delay time between the multiplication of interleukin and cytotoxic cells influences the dynamics of the system. For certain parameter values, the system can exhibit various dynamic behaviours, including steady states that manifest stable equilibria, as well as periodic, quasi-periodic and chaotic oscillations.