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In this work we propose and investigate a family of models, which admits asparticular cases some well known mathematical models of tumor-immune systeminteraction, with the additional assumption that the influx of immune systemcells may be a function of the number of cancer cells. Constant, periodic andimpulsive therapies (as well as the non-perturbed system) are investigated bothanalytically 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. Nonlineardynamics of immunogenic tumors: Parameter estimation and global bifurcationanalysis. Bulletin of Mathematical Biology 56(2): 295-321, (1994)), vianumerical simulations. Simulations seem to show that the shape of the functionmodeling the therapy is a crucial factor only for very high values of thetherapy period $T$, whereas for realistic values of $T$, the eradication of thecancer cells depends on the mean values of the therapy term. Finally, somemedical inferences are proposed.

A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences