On some dynamical properties of a seven-dimensional cancer model with immunotherapy

In this paper we study some features of global behavior of a seven-dimensional tumor growth model under immunotherapy described by Joshi et al. [2009]. We find the upper bounds for ultimate dynamics of all types of cell populations involved in this model. A few lower bounds are found as well. Further, we prove the existence of the bounded positively invariant polytope. Finally, we show that if the parameter modeling the flow of antigen presenting cells is very large then the tumor-free equilibrium point attracts all points in the positive orthant.