Modelling and mathematical problems related to tumor evolution and its interaction with the immune system

This paper provides a survey of mathematical models and methods dealing with the analysis and simulation of tumor dynamics in competition with the immune system. The characteristic scales of the phenomena are identified and the mathematical literature on models and problems developed on each scale is reviewed and critically analysed. The aim is to provide a general framework towards the development of immuno-mathematical theories and to develop research perspectives in this promising new field of applied mathematics.