INTERNATIONAL JOURNAL OF ENGINEERING,

In this paper, we have proposed and analyzed a nonlinear mathematical model to study the interaction between tumor and immune cells. The model is extended by the inclusion of an intracellular delay effect. Stability of the steady states of both model systems without and with delay is determined. Conditions for Hopf bifurcation of the system are determined. Moreover, critical value of delay is also found which acts as a bifurcation parameter. Numerical investigations are conducted to confirm the results. It is found that number of tumor cells increase with the decrease in rate of stimulation of hunting cells by resting cells or by the reduction in the concentrations of cytokines. Cytokines are mainly responsible for converting resting cells to hunting cells. So, to reduce the number of tumor cells, attempts should be made to increase the concentration of cytokines artificially. Moreover, effect of tumor antigenicity is also studied. It is observed from our analysis that lower is the antigenicity nastier is the tumor. For certain parameter values limit cycles are obtained