Chapter 2: Models of cancer evolution

To develop an understanding of cancer evolution and its implications, e.g. for therapy, we examine some simple models of mutation and population growth. This is based on branching processes, Markov processes (either discrete or continuous time) that describe probabilistic growth processes. A key assumption is that cells are independent, i.e. birth and death rates are independent of population size, composition and neighbouring cells. Although a strong assumption, it is likely to be true until resource competition occurs which will only occur once tumours are of sufficient size. The branching process material is predominantly taken from [1] where the reader can find additional results.