Metamodeling tumor–immune system interaction, tumor evasion and immunotherapy

The tumor–immune system competitive interaction is very complex, being nonlinear and, to some extent, evolutive. Furthermore, the tumor itself is not a single well defined disease, but, more correctly, a wide family of diseases, characterized by some important common features, but also by many great differences between them. For this reason, we introduced in [A. d’Onofrio, A general framework for modeling tumor–immune system competition and immunotherapy: Mathematical analysis and biomedical inferences, Physica D 208 (2005) 220–235], and in other works, a new mathematical way of studying the interaction of tumors with immune system and immunotherapy. Our approach is not based on new specific models, but on meta-models (i.e. family of models), which are studied with the help of the qualitative theory of differential equations. We review here our work on this field, by illustrating our main results, in view of their possible biomedical applications, and extending them.