  In this work we propose and investigate a family of models, which admits as
particular cases some well known mathematical models of tumor-immune system
interaction, with the additional assumption that the influx of immune system
cells may be a function of the number of cancer cells. Constant, periodic and
impulsive therapies (as well as the non-perturbed system) are investigated both
analytically for the general family and, by using the model by Kuznetsov et al.
(V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor and A. S. Perelson. Nonlinear
dynamics of immunogenic tumors: Parameter estimation and global bifurcation
analysis. Bulletin of Mathematical Biology 56(2): 295-321, (1994)), via
numerical simulations. Simulations seem to show that the shape of the function
modeling the therapy is a crucial factor only for very high values of the
therapy period $T$, whereas for realistic values of $T$, the eradication of the
cancer cells depends on the mean values of the therapy term. Finally, some
medical inferences are proposed.
