Global dynamics of the Kirschner–Panetta model for the tumor immunotherapy

In this paper we examine the global dynamics of the Kirschner–Panetta model describing the tumor immunotherapy. We give upper and lower ultimate bounds for densities of cell populations involved in this model. We demonstrate for this dynamics that there is a positively invariant polytope in the positive orthant. We present sufficient conditions on model parameters and treatment parameters under which all trajectories in the positive orthant tend to the tumor-free equilibrium point. We compare our results with Kirschner–Tsygvintsev results and concern biological implications of our assertions.

► Various upper/lower bounds for ultimate dynamics are got. ► Existence of positive invariant domain is proved. ► Sufficient conditions of tumor clearance are described.