Hopf bifurcation analysis and numerical simulations in an ODE model of the immune system with positive immune response

In this paper, we consider an ordinary differential equations (ODE) for tumor–immune system with positive immune response and a unique nontrivial positive equilibrium. Its dynamics are studied in terms of the local stability and of the description of the Hopf bifurcation which is proven to exist as the parameter of the normal rate of the flow of adult ECs into the tumor site crosses some critical values. We illustrate these results numerically.