Mathematical Oncology: the interplay between biology, medicine and nonlinear sciences

Due to the vast amount of underlying genetic events and deregulated biochemical networks, the development of tumors and their response to antitumoral treatments are phenomena so complex to be anti-intuitive and to make the outcome of human intervention semi-random.
Currently, the schedulings of therapies are mainly based on empirical basis and on the accumulation of epidemiological inferences.
Nonlinear biophysical models, after being used with great success in ecology, may become a synthetic tool to interpretate the huge amount of experimental results in oncology and also to help medical doctors in planning therapies.
Here some simple models of tumor development and therapies will be illustrated both from a physico-mathematical and biomedical points of view.
In particular, we shall focus on
1) Cell-cell competition
2) Angiogenesis and anti angiogenesis therapies
3) Tumor-Immune system competition and immunotherapies.