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 wit h the analysis and simulation of tumor dynamics in competition with the imm une system. The characteristic scales of the phenomena are identified and t he mathematical literature on models and problems developed on each scale i s reviewed and critically analysed. The aim is to provide a general framewo rk towards the development of immune-mathematical theories and to develop r esearch perspectives in this promising new field of applied mathematics. (C ) 2000 Elsevier Science Ltd. All rights reserved.