Modelling and analysis of delayed tumour–immune system with hunting T-cells

This study proposes a modified prey–predator-like model consisting of tumour cells, hunting T-cells, and resting T-cells to illustrate tumour–immune interaction by incorporating discrete-time-delay with conversion or growth of hunting cells. For analysis, the proposed system has been transformed into a normalized system, and its non-negativity solution has been verified. The linear stability of the system has been analysed at each equilibrium. The discrete-time delay affects the system's stability, and the system undergoes a Hopf bifurcation. Moreover, the length of time delay for which a periodic solution can be preserved has been derived. Finally, numerical computations have been presented that correlate with analytical results and are also relevant from a biological perspective.