On complementary levels of description in applied mathematics II. Mathematical models in cancer biology

Abstract

The main stages of mathematical modelling are illustrated by examining some complementary levels of description of tumour growth, and characteristics of cancerous tissue. Four basic types of model are considered, although there can be variations within each category: deterministic diffusion models, probabilistic models, models based on the qualitative theory of differential equations, and topological models. Each category addresses different, but related issues, and exemplifies the contrasting approaches that may be used in establishing coherent mathematical models in the biological and other sciences.