Mathematical studies on helper T cells in a tumor immune system

On the basis of the two-dimensional tumor immune dynamics model, two extended models are proposed that aiming at incorporating the influence of helper T cells (HTCs) which change the dynamics of the system substantially. The stability regions of the interior equilibrium are described in the two-dimensional scaled parameter plane. Further, two delays of immune responses are incorporated into the previous model. Stability switch occurs as time delays increase and Hopf bifurcations appear. Numerical simulations are performed to illustrate the theoretical results.